firstprimes.c

/*
(*************************************************************)
(*      This file is distributed under the terms of the      *)
(*      GNU Lesser General Public License Version 2.1        *)
(*************************************************************)
(*    Benjamin.Gregoire@inria.fr Laurent.Thery@inria.fr      *)
(*************************************************************)
*/

#include <stdlib.h>
#include <stdio.h>
#include <string.h>
#include "gmp.h"
#include "certif.h"
#include "factorize.h"

static unsigned int tprimes[] =
  {
       2,      3,      5,      7,     11,     13,     17,     19,     23,
      29,     31,     37,     41,     43,     47,     53,     59,     61,
      67,     71,     73,     79,     83,     89,     97,    101,    103,
     107,    109,    113,    127,    131,    137,    139,    149,    151,
     157,    163,    167,    173,    179,    181,    191,    193,    197,
     199,    211,    223,    227,    229,    233,    239,    241,    251,
     257,    263,    269,    271,    277,    281,    283,    293,    307,
     311,    313,    317,    331,    337,    347,    349,    353,    359,
     367,    373,    379,    383,    389,    397,    401,    409,    419,
     421,    431,    433,    439,    443,    449,    457,    461,    463,
     467,    479,    487,    491,    499,    503,    509,    521,    523,
     541,    547,    557,    563,    569,    571,    577,    587,    593,
     599,    601,    607,    613,    617,    619,    631,    641,    643,
     647,    653,    659,    661,    673,    677,    683,    691,    701,
     709,    719,    727,    733,    739,    743,    751,    757,    761,
     769,    773,    787,    797,    809,    811,    821,    823,    827,
     829,    839,    853,    857,    859,    863,    877,    881,    883,
     887,    907,    911,    919,    929,    937,    941,    947,    953,
     967,    971,    977,    983,    991,    997,   1009,   1013,   1019,
    1021,   1031,   1033,   1039,   1049,   1051,   1061,   1063,   1069,
    1087,   1091,   1093,   1097,   1103,   1109,   1117,   1123,   1129,
    1151,   1153,   1163,   1171,   1181,   1187,   1193,   1201,   1213,
    1217,   1223,   1229,   1231,   1237,   1249,   1259,   1277,   1279,
    1283,   1289,   1291,   1297,   1301,   1303,   1307,   1319,   1321,
    1327,   1361,   1367,   1373,   1381,   1399,   1409,   1423,   1427,
    1429,   1433,   1439,   1447,   1451,   1453,   1459,   1471,   1481,
    1483,   1487,   1489,   1493,   1499,   1511,   1523,   1531,   1543,
    1549,   1553,   1559,   1567,   1571,   1579,   1583,   1597,   1601,
    1607,   1609,   1613,   1619,   1621,   1627,   1637,   1657,   1663,
    1667,   1669,   1693,   1697,   1699,   1709,   1721,   1723,   1733,
    1741,   1747,   1753,   1759,   1777,   1783,   1787,   1789,   1801,
    1811,   1823,   1831,   1847,   1861,   1867,   1871,   1873,   1877,
    1879,   1889,   1901,   1907,   1913,   1931,   1933,   1949,   1951,
    1973,   1979,   1987,   1993,   1997,   1999,   2003,   2011,   2017,
    2027,   2029,   2039,   2053,   2063,   2069,   2081,   2083,   2087,
    2089,   2099,   2111,   2113,   2129,   2131,   2137,   2141,   2143,
    2153,   2161,   2179,   2203,   2207,   2213,   2221,   2237,   2239,
    2243,   2251,   2267,   2269,   2273,   2281,   2287,   2293,   2297,
    2309,   2311,   2333,   2339,   2341,   2347,   2351,   2357,   2371,
    2377,   2381,   2383,   2389,   2393,   2399,   2411,   2417,   2423,
    2437,   2441,   2447,   2459,   2467,   2473,   2477,   2503,   2521,
    2531,   2539,   2543,   2549,   2551,   2557,   2579,   2591,   2593,
    2609,   2617,   2621,   2633,   2647,   2657,   2659,   2663,   2671,
    2677,   2683,   2687,   2689,   2693,   2699,   2707,   2711,   2713,
    2719,   2729,   2731,   2741,   2749,   2753,   2767,   2777,   2789,
    2791,   2797,   2801,   2803,   2819,   2833,   2837,   2843,   2851,
    2857,   2861,   2879,   2887,   2897,   2903,   2909,   2917,   2927,
    2939,   2953,   2957,   2963,   2969,   2971,   2999,   3001,   3011,
    3019,   3023,   3037,   3041,   3049,   3061,   3067,   3079,   3083,
    3089,   3109,   3119,   3121,   3137,   3163,   3167,   3169,   3181,
    3187,   3191,   3203,   3209,   3217,   3221,   3229,   3251,   3253,
    3257,   3259,   3271,   3299,   3301,   3307,   3313,   3319,   3323,
    3329,   3331,   3343,   3347,   3359,   3361,   3371,   3373,   3389,
    3391,   3407,   3413,   3433,   3449,   3457,   3461,   3463,   3467,
    3469,   3491,   3499,   3511,   3517,   3527,   3529,   3533,   3539,
    3541,   3547,   3557,   3559,   3571,   3581,   3583,   3593,   3607,
    3613,   3617,   3623,   3631,   3637,   3643,   3659,   3671,   3673,
    3677,   3691,   3697,   3701,   3709,   3719,   3727,   3733,   3739,
    3761,   3767,   3769,   3779,   3793,   3797,   3803,   3821,   3823,
    3833,   3847,   3851,   3853,   3863,   3877,   3881,   3889,   3907,
    3911,   3917,   3919,   3923,   3929,   3931,   3943,   3947,   3967,
    3989,   4001,   4003,   4007,   4013,   4019,   4021,   4027,   4049,
    4051,   4057,   4073,   4079,   4091,   4093,   4099,   4111,   4127,
    4129,   4133,   4139,   4153,   4157,   4159,   4177,   4201,   4211,
    4217,   4219,   4229,   4231,   4241,   4243,   4253,   4259,   4261,
    4271,   4273,   4283,   4289,   4297,   4327,   4337,   4339,   4349,
    4357,   4363,   4373,   4391,   4397,   4409,   4421,   4423,   4441,
    4447,   4451,   4457,   4463,   4481,   4483,   4493,   4507,   4513,
    4517,   4519,   4523,   4547,   4549,   4561,   4567,   4583,   4591,
    4597,   4603,   4621,   4637,   4639,   4643,   4649,   4651,   4657,
    4663,   4673,   4679,   4691,   4703,   4721,   4723,   4729,   4733,
    4751,   4759,   4783,   4787,   4789,   4793,   4799,   4801,   4813,
    4817,   4831,   4861,   4871,   4877,   4889,   4903,   4909,   4919,
    4931,   4933,   4937,   4943,   4951,   4957,   4967,   4969,   4973,
    4987,   4993,   4999,   5003,   5009,   5011,   5021,   5023,   5039,
    5051,   5059,   5077,   5081,   5087,   5099,   5101,   5107,   5113,
    5119,   5147,   5153,   5167,   5171,   5179,   5189,   5197,   5209,
    5227,   5231,   5233,   5237,   5261,   5273,   5279,   5281,   5297,
    5303,   5309,   5323,   5333,   5347,   5351,   5381,   5387,   5393,
    5399,   5407,   5413,   5417,   5419,   5431,   5437,   5441,   5443,
    5449,   5471,   5477,   5479,   5483,   5501,   5503,   5507,   5519,
    5521,   5527,   5531,   5557,   5563,   5569,   5573,   5581,   5591,
    5623,   5639,   5641,   5647,   5651,   5653,   5657,   5659,   5669,
    5683,   5689,   5693,   5701,   5711,   5717,   5737,   5741,   5743,
    5749,   5779,   5783,   5791,   5801,   5807,   5813,   5821,   5827,
    5839,   5843,   5849,   5851,   5857,   5861,   5867,   5869,   5879,
    5881,   5897,   5903,   5923,   5927,   5939,   5953,   5981,   5987,
    6007,   6011,   6029,   6037,   6043,   6047,   6053,   6067,   6073,
    6079,   6089,   6091,   6101,   6113,   6121,   6131,   6133,   6143,
    6151,   6163,   6173,   6197,   6199,   6203,   6211,   6217,   6221,
    6229,   6247,   6257,   6263,   6269,   6271,   6277,   6287,   6299,
    6301,   6311,   6317,   6323,   6329,   6337,   6343,   6353,   6359,
    6361,   6367,   6373,   6379,   6389,   6397,   6421,   6427,   6449,
    6451,   6469,   6473,   6481,   6491,   6521,   6529,   6547,   6551,
    6553,   6563,   6569,   6571,   6577,   6581,   6599,   6607,   6619,
    6637,   6653,   6659,   6661,   6673,   6679,   6689,   6691,   6701,
    6703,   6709,   6719,   6733,   6737,   6761,   6763,   6779,   6781,
    6791,   6793,   6803,   6823,   6827,   6829,   6833,   6841,   6857,
    6863,   6869,   6871,   6883,   6899,   6907,   6911,   6917,   6947,
    6949,   6959,   6961,   6967,   6971,   6977,   6983,   6991,   6997,
    7001,   7013,   7019,   7027,   7039,   7043,   7057,   7069,   7079,
    7103,   7109,   7121,   7127,   7129,   7151,   7159,   7177,   7187,
    7193,   7207,   7211,   7213,   7219,   7229,   7237,   7243,   7247,
    7253,   7283,   7297,   7307,   7309,   7321,   7331,   7333,   7349,
    7351,   7369,   7393,   7411,   7417,   7433,   7451,   7457,   7459,
    7477,   7481,   7487,   7489,   7499,   7507,   7517,   7523,   7529,
    7537,   7541,   7547,   7549,   7559,   7561,   7573,   7577,   7583,
    7589,   7591,   7603,   7607,   7621,   7639,   7643,   7649,   7669,
    7673,   7681,   7687,   7691,   7699,   7703,   7717,   7723,   7727,
    7741,   7753,   7757,   7759,   7789,   7793,   7817,   7823,   7829,
    7841,   7853,   7867,   7873,   7877,   7879,   7883,   7901,   7907,
    7919,   7927,   7933,   7937,   7949,   7951,   7963,   7993,   8009,
    8011,   8017,   8039,   8053,   8059,   8069,   8081,   8087,   8089,
    8093,   8101,   8111,   8117,   8123,   8147,   8161,   8167,   8171,
    8179,   8191,   8209,   8219,   8221,   8231,   8233,   8237,   8243,
    8263,   8269,   8273,   8287,   8291,   8293,   8297,   8311,   8317,
    8329,   8353,   8363,   8369,   8377,   8387,   8389,   8419,   8423,
    8429,   8431,   8443,   8447,   8461,   8467,   8501,   8513,   8521,
    8527,   8537,   8539,   8543,   8563,   8573,   8581,   8597,   8599,
    8609,   8623,   8627,   8629,   8641,   8647,   8663,   8669,   8677,
    8681,   8689,   8693,   8699,   8707,   8713,   8719,   8731,   8737,
    8741,   8747,   8753,   8761,   8779,   8783,   8803,   8807,   8819,
    8821,   8831,   8837,   8839,   8849,   8861,   8863,   8867,   8887,
    8893,   8923,   8929,   8933,   8941,   8951,   8963,   8969,   8971,
    8999,   9001,   9007,   9011,   9013,   9029,   9041,   9043,   9049,
    9059,   9067,   9091,   9103,   9109,   9127,   9133,   9137,   9151,
    9157,   9161,   9173,   9181,   9187,   9199,   9203,   9209,   9221,
    9227,   9239,   9241,   9257,   9277,   9281,   9283,   9293,   9311,
    9319,   9323,   9337,   9341,   9343,   9349,   9371,   9377,   9391,
    9397,   9403,   9413,   9419,   9421,   9431,   9433,   9437,   9439,
    9461,   9463,   9467,   9473,   9479,   9491,   9497,   9511,   9521,
    9533,   9539,   9547,   9551,   9587,   9601,   9613,   9619,   9623,
    9629,   9631,   9643,   9649,   9661,   9677,   9679,   9689,   9697,
    9719,   9721,   9733,   9739,   9743,   9749,   9767,   9769,   9781,
    9787,   9791,   9803,   9811,   9817,   9829,   9833,   9839,   9851,
    9857,   9859,   9871,   9883,   9887,   9901,   9907,   9923,   9929,
    9931,   9941,   9949,   9967,   9973,  10007,  10009,  10037,  10039,
   10061,  10067,  10069,  10079,  10091,  10093,  10099,  10103,  10111,
   10133,  10139,  10141,  10151,  10159,  10163,  10169,  10177,  10181,
   10193,  10211,  10223,  10243,  10247,  10253,  10259,  10267,  10271,
   10273,  10289,  10301,  10303,  10313,  10321,  10331,  10333,  10337,
   10343,  10357,  10369,  10391,  10399,  10427,  10429,  10433,  10453,
   10457,  10459,  10463,  10477,  10487,  10499,  10501,  10513,  10529,
   10531,  10559,  10567,  10589,  10597,  10601,  10607,  10613,  10627,
   10631,  10639,  10651,  10657,  10663,  10667,  10687,  10691,  10709,
   10711,  10723,  10729,  10733,  10739,  10753,  10771,  10781,  10789,
   10799,  10831,  10837,  10847,  10853,  10859,  10861,  10867,  10883,
   10889,  10891,  10903,  10909,  10937,  10939,  10949,  10957,  10973,
   10979,  10987,  10993,  11003,  11027,  11047,  11057,  11059,  11069,
   11071,  11083,  11087,  11093,  11113,  11117,  11119,  11131,  11149,
   11159,  11161,  11171,  11173,  11177,  11197,  11213,  11239,  11243,
   11251,  11257,  11261,  11273,  11279,  11287,  11299,  11311,  11317,
   11321,  11329,  11351,  11353,  11369,  11383,  11393,  11399,  11411,
   11423,  11437,  11443,  11447,  11467,  11471,  11483,  11489,  11491,
   11497,  11503,  11519,  11527,  11549,  11551,  11579,  11587,  11593,
   11597,  11617,  11621,  11633,  11657,  11677,  11681,  11689,  11699,
   11701,  11717,  11719,  11731,  11743,  11777,  11779,  11783,  11789,
   11801,  11807,  11813,  11821,  11827,  11831,  11833,  11839,  11863,
   11867,  11887,  11897,  11903,  11909,  11923,  11927,  11933,  11939,
   11941,  11953,  11959,  11969,  11971,  11981,  11987,  12007,  12011,
   12037,  12041,  12043,  12049,  12071,  12073,  12097,  12101,  12107,
   12109,  12113,  12119,  12143,  12149,  12157,  12161,  12163,  12197,
   12203,  12211,  12227,  12239,  12241,  12251,  12253,  12263,  12269,
   12277,  12281,  12289,  12301,  12323,  12329,  12343,  12347,  12373,
   12377,  12379,  12391,  12401,  12409,  12413,  12421,  12433,  12437,
   12451,  12457,  12473,  12479,  12487,  12491,  12497,  12503,  12511,
   12517,  12527,  12539,  12541,  12547,  12553,  12569,  12577,  12583,
   12589,  12601,  12611,  12613,  12619,  12637,  12641,  12647,  12653,
   12659,  12671,  12689,  12697,  12703,  12713,  12721,  12739,  12743,
   12757,  12763,  12781,  12791,  12799,  12809,  12821,  12823,  12829,
   12841,  12853,  12889,  12893,  12899,  12907,  12911,  12917,  12919,
   12923,  12941,  12953,  12959,  12967,  12973,  12979,  12983,  13001,
   13003,  13007,  13009,  13033,  13037,  13043,  13049,  13063,  13093,
   13099,  13103,  13109,  13121,  13127,  13147,  13151,  13159,  13163,
   13171,  13177,  13183,  13187,  13217,  13219,  13229,  13241,  13249,
   13259,  13267,  13291,  13297,  13309,  13313,  13327,  13331,  13337,
   13339,  13367,  13381,  13397,  13399,  13411,  13417,  13421,  13441,
   13451,  13457,  13463,  13469,  13477,  13487,  13499,  13513,  13523,
   13537,  13553,  13567,  13577,  13591,  13597,  13613,  13619,  13627,
   13633,  13649,  13669,  13679,  13681,  13687,  13691,  13693,  13697,
   13709,  13711,  13721,  13723,  13729,  13751,  13757,  13759,  13763,
   13781,  13789,  13799,  13807,  13829,  13831,  13841,  13859,  13873,
   13877,  13879,  13883,  13901,  13903,  13907,  13913,  13921,  13931,
   13933,  13963,  13967,  13997,  13999,  14009,  14011,  14029,  14033,
   14051,  14057,  14071,  14081,  14083,  14087,  14107,  14143,  14149,
   14153,  14159,  14173,  14177,  14197,  14207,  14221,  14243,  14249,
   14251,  14281,  14293,  14303,  14321,  14323,  14327,  14341,  14347,
   14369,  14387,  14389,  14401,  14407,  14411,  14419,  14423,  14431,
   14437,  14447,  14449,  14461,  14479,  14489,  14503,  14519,  14533,
   14537,  14543,  14549,  14551,  14557,  14561,  14563,  14591,  14593,
   14621,  14627,  14629,  14633,  14639,  14653,  14657,  14669,  14683,
   14699,  14713,  14717,  14723,  14731,  14737,  14741,  14747,  14753,
   14759,  14767,  14771,  14779,  14783,  14797,  14813,  14821,  14827,
   14831,  14843,  14851,  14867,  14869,  14879,  14887,  14891,  14897,
   14923,  14929,  14939,  14947,  14951,  14957,  14969,  14983,  15013,
   15017,  15031,  15053,  15061,  15073,  15077,  15083,  15091,  15101,
   15107,  15121,  15131,  15137,  15139,  15149,  15161,  15173,  15187,
   15193,  15199,  15217,  15227,  15233,  15241,  15259,  15263,  15269,
   15271,  15277,  15287,  15289,  15299,  15307,  15313,  15319,  15329,
   15331,  15349,  15359,  15361,  15373,  15377,  15383,  15391,  15401,
   15413,  15427,  15439,  15443,  15451,  15461,  15467,  15473,  15493,
   15497,  15511,  15527,  15541,  15551,  15559,  15569,  15581,  15583,
   15601,  15607,  15619,  15629,  15641,  15643,  15647,  15649,  15661,
   15667,  15671,  15679,  15683,  15727,  15731,  15733,  15737,  15739,
   15749,  15761,  15767,  15773,  15787,  15791,  15797,  15803,  15809,
   15817,  15823,  15859,  15877,  15881,  15887,  15889,  15901,  15907,
   15913,  15919,  15923,  15937,  15959,  15971,  15973,  15991,  16001,
   16007,  16033,  16057,  16061,  16063,  16067,  16069,  16073,  16087,
   16091,  16097,  16103,  16111,  16127,  16139,  16141,  16183,  16187,
   16189,  16193,  16217,  16223,  16229,  16231,  16249,  16253,  16267,
   16273,  16301,  16319,  16333,  16339,  16349,  16361,  16363,  16369,
   16381,  16411,  16417,  16421,  16427,  16433,  16447,  16451,  16453,
   16477,  16481,  16487,  16493,  16519,  16529,  16547,  16553,  16561,
   16567,  16573,  16603,  16607,  16619,  16631,  16633,  16649,  16651,
   16657,  16661,  16673,  16691,  16693,  16699,  16703,  16729,  16741,
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   21059,  21061,  21067,  21089,  21101,  21107,  21121,  21139,  21143,
   21149,  21157,  21163,  21169,  21179,  21187,  21191,  21193,  21211,
   21221,  21227,  21247,  21269,  21277,  21283,  21313,  21317,  21319,
   21323,  21341,  21347,  21377,  21379,  21383,  21391,  21397,  21401,
   21407,  21419,  21433,  21467,  21481,  21487,  21491,  21493,  21499,
   21503,  21517,  21521,  21523,  21529,  21557,  21559,  21563,  21569,
   21577,  21587,  21589,  21599,  21601,  21611,  21613,  21617,  21647,
   21649,  21661,  21673,  21683,  21701,  21713,  21727,  21737,  21739,
   21751,  21757,  21767,  21773,  21787,  21799,  21803,  21817,  21821,
   21839,  21841,  21851,  21859,  21863,  21871,  21881,  21893,  21911,
   21929,  21937,  21943,  21961,  21977,  21991,  21997,  22003,  22013,
   22027,  22031,  22037,  22039,  22051,  22063,  22067,  22073,  22079,
   22091,  22093,  22109,  22111,  22123,  22129,  22133,  22147,  22153,
   22157,  22159,  22171,  22189,  22193,  22229,  22247,  22259,  22271,
   22273,  22277,  22279,  22283,  22291,  22303,  22307,  22343,  22349,
   22367,  22369,  22381,  22391,  22397,  22409,  22433,  22441,  22447,
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   22549,  22567,  22571,  22573,  22613,  22619,  22621,  22637,  22639,
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   22721,  22727,  22739,  22741,  22751,  22769,  22777,  22783,  22787,
   22807,  22811,  22817,  22853,  22859,  22861,  22871,  22877,  22901,
   22907,  22921,  22937,  22943,  22961,  22963,  22973,  22993,  23003,
   23011,  23017,  23021,  23027,  23029,  23039,  23041,  23053,  23057,
   23059,  23063,  23071,  23081,  23087,  23099,  23117,  23131,  23143,
   23159,  23167,  23173,  23189,  23197,  23201,  23203,  23209,  23227,
   23251,  23269,  23279,  23291,  23293,  23297,  23311,  23321,  23327,
   23333,  23339,  23357,  23369,  23371,  23399,  23417,  23431,  23447,
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   23801,  23813,  23819,  23827,  23831,  23833,  23857,  23869,  23873,
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   23971,  23977,  23981,  23993,  24001,  24007,  24019,  24023,  24029,
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   24107,  24109,  24113,  24121,  24133,  24137,  24151,  24169,  24179,
   24181,  24197,  24203,  24223,  24229,  24239,  24247,  24251,  24281,
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   24623,  24631,  24659,  24671,  24677,  24683,  24691,  24697,  24709,
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   24841,  24847,  24851,  24859,  24877,  24889,  24907,  24917,  24919,
   24923,  24943,  24953,  24967,  24971,  24977,  24979,  24989,  25013,
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   25121,  25127,  25147,  25153,  25163,  25169,  25171,  25183,  25189,
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   25589,  25601,  25603,  25609,  25621,  25633,  25639,  25643,  25657,
   25667,  25673,  25679,  25693,  25703,  25717,  25733,  25741,  25747,
   25759,  25763,  25771,  25793,  25799,  25801,  25819,  25841,  25847,
   25849,  25867,  25873,  25889,  25903,  25913,  25919,  25931,  25933,
   25939,  25943,  25951,  25969,  25981,  25997,  25999,  26003,  26017,
   26021,  26029,  26041,  26053,  26083,  26099,  26107,  26111,  26113,
   26119,  26141,  26153,  26161,  26171,  26177,  26183,  26189,  26203,
   26209,  26227,  26237,  26249,  26251,  26261,  26263,  26267,  26293,
   26297,  26309,  26317,  26321,  26339,  26347,  26357,  26371,  26387,
   26393,  26399,  26407,  26417,  26423,  26431,  26437,  26449,  26459,
   26479,  26489,  26497,  26501,  26513,  26539,  26557,  26561,  26573,
   26591,  26597,  26627,  26633,  26641,  26647,  26669,  26681,  26683,
   26687,  26693,  26699,  26701,  26711,  26713,  26717,  26723,  26729,
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   26839,  26849,  26861,  26863,  26879,  26881,  26891,  26893,  26903,
   26921,  26927,  26947,  26951,  26953,  26959,  26981,  26987,  26993,
   27011,  27017,  27031,  27043,  27059,  27061,  27067,  27073,  27077,
   27091,  27103,  27107,  27109,  27127,  27143,  27179,  27191,  27197,
   27211,  27239,  27241,  27253,  27259,  27271,  27277,  27281,  27283,
   27299,  27329,  27337,  27361,  27367,  27397,  27407,  27409,  27427,
   27431,  27437,  27449,  27457,  27479,  27481,  27487,  27509,  27527,
   27529,  27539,  27541,  27551,  27581,  27583,  27611,  27617,  27631,
   27647,  27653,  27673,  27689,  27691,  27697,  27701,  27733,  27737,
   27739,  27743,  27749,  27751,  27763,  27767,  27773,  27779,  27791,
   27793,  27799,  27803,  27809,  27817,  27823,  27827,  27847,  27851,
   27883,  27893,  27901,  27917,  27919,  27941,  27943,  27947,  27953,
   27961,  27967,  27983,  27997,  28001,  28019,  28027,  28031,  28051,
   28057,  28069,  28081,  28087,  28097,  28099,  28109,  28111,  28123,
   28151,  28163,  28181,  28183,  28201,  28211,  28219,  28229,  28277,
   28279,  28283,  28289,  28297,  28307,  28309,  28319,  28349,  28351,
   28387,  28393,  28403,  28409,  28411,  28429,  28433,  28439,  28447,
   28463,  28477,  28493,  28499,  28513,  28517,  28537,  28541,  28547,
   28549,  28559,  28571,  28573,  28579,  28591,  28597,  28603,  28607,
   28619,  28621,  28627,  28631,  28643,  28649,  28657,  28661,  28663,
   28669,  28687,  28697,  28703,  28711,  28723,  28729,  28751,  28753,
   28759,  28771,  28789,  28793,  28807,  28813,  28817,  28837,  28843,
   28859,  28867,  28871,  28879,  28901,  28909,  28921,  28927,  28933,
   28949,  28961,  28979,  29009,  29017,  29021,  29023,  29027,  29033,
   29059,  29063,  29077,  29101,  29123,  29129,  29131,  29137,  29147,
   29153,  29167,  29173,  29179,  29191,  29201,  29207,  29209,  29221,
   29231,  29243,  29251,  29269,  29287,  29297,  29303,  29311,  29327,
   29333,  29339,  29347,  29363,  29383,  29387,  29389,  29399,  29401,
   29411,  29423,  29429,  29437,  29443,  29453,  29473,  29483,  29501,
   29527,  29531,  29537,  29567,  29569,  29573,  29581,  29587,  29599,
   29611,  29629,  29633,  29641,  29663,  29669,  29671,  29683,  29717,
   29723,  29741,  29753,  29759,  29761,  29789,  29803,  29819,  29833,
   29837,  29851,  29863,  29867,  29873,  29879,  29881,  29917,  29921,
   29927,  29947,  29959,  29983,  29989,  30011,  30013,  30029,  30047,
   30059,  30071,  30089,  30091,  30097,  30103,  30109,  30113,  30119,
   30133,  30137,  30139,  30161,  30169,  30181,  30187,  30197,  30203,
   30211,  30223,  30241,  30253,  30259,  30269,  30271,  30293,  30307,
   30313,  30319,  30323,  30341,  30347,  30367,  30389,  30391,  30403,
   30427,  30431,  30449,  30467,  30469,  30491,  30493,  30497,  30509,
   30517,  30529,  30539,  30553,  30557,  30559,  30577,  30593,  30631,
   30637,  30643,  30649,  30661,  30671,  30677,  30689,  30697,  30703,
   30707,  30713,  30727,  30757,  30763,  30773,  30781,  30803,  30809,
   30817,  30829,  30839,  30841,  30851,  30853,  30859,  30869,  30871,
   30881,  30893,  30911,  30931,  30937,  30941,  30949,  30971,  30977,
   30983,  31013,  31019,  31033,  31039,  31051,  31063,  31069,  31079,
   31081,  31091,  31121,  31123,  31139,  31147,  31151,  31153,  31159,
   31177,  31181,  31183,  31189,  31193,  31219,  31223,  31231,  31237,
   31247,  31249,  31253,  31259,  31267,  31271,  31277,  31307,  31319,
   31321,  31327,  31333,  31337,  31357,  31379,  31387,  31391,  31393,
   31397,  31469,  31477,  31481,  31489,  31511,  31513,  31517,  31531,
   31541,  31543,  31547,  31567,  31573,  31583,  31601,  31607,  31627,
   31643,  31649,  31657,  31663,  31667,  31687,  31699,  31721,  31723,
   31727,  31729,  31741,  31751,  31769,  31771,  31793,  31799,  31817,
   31847,  31849,  31859,  31873,  31883,  31891,  31907,  31957,  31963,
   31973,  31981,  31991,  32003,  32009,  32027,  32029,  32051,  32057,
   32059,  32063,  32069,  32077,  32083,  32089,  32099,  32117,  32119,
   32141,  32143,  32159,  32173,  32183,  32189,  32191,  32203,  32213,
   32233,  32237,  32251,  32257,  32261,  32297,  32299,  32303,  32309,
   32321,  32323,  32327,  32341,  32353,  32359,  32363,  32369,  32371,
   32377,  32381,  32401,  32411,  32413,  32423,  32429,  32441,  32443,
   32467,  32479,  32491,  32497,  32503,  32507,  32531,  32533,  32537,
   32561,  32563,  32569,  32573,  32579,  32587,  32603,  32609,  32611,
   32621,  32633,  32647,  32653,  32687,  32693,  32707,  32713,  32717,
   32719,  32749,  32771,  32779,  32783,  32789,  32797,  32801,  32803,
   32831,  32833,  32839,  32843,  32869,  32887,  32909,  32911,  32917,
   32933,  32939,  32941,  32957,  32969,  32971,  32983,  32987,  32993,
   32999,  33013,  33023,  33029,  33037,  33049,  33053,  33071,  33073,
   33083,  33091,  33107,  33113,  33119,  33149,  33151,  33161,  33179,
   33181,  33191,  33199,  33203,  33211,  33223,  33247,  33287,  33289,
   33301,  33311,  33317,  33329,  33331,  33343,  33347,  33349,  33353,
   33359,  33377,  33391,  33403,  33409,  33413,  33427,  33457,  33461,
   33469,  33479,  33487,  33493,  33503,  33521,  33529,  33533,  33547,
   33563,  33569,  33577,  33581,  33587,  33589,  33599,  33601,  33613,
   33617,  33619,  33623,  33629,  33637,  33641,  33647,  33679,  33703,
   33713,  33721,  33739,  33749,  33751,  33757,  33767,  33769,  33773,
   33791,  33797,  33809,  33811,  33827,  33829,  33851,  33857,  33863,
   33871,  33889,  33893,  33911,  33923,  33931,  33937,  33941,  33961,
   33967,  33997,  34019,  34031,  34033,  34039,  34057,  34061,  34123,
   34127,  34129,  34141,  34147,  34157,  34159,  34171,  34183,  34211,
   34213,  34217,  34231,  34253,  34259,  34261,  34267,  34273,  34283,
   34297,  34301,  34303,  34313,  34319,  34327,  34337,  34351,  34361,
   34367,  34369,  34381,  34403,  34421,  34429,  34439,  34457,  34469,
   34471,  34483,  34487,  34499,  34501,  34511,  34513,  34519,  34537,
   34543,  34549,  34583,  34589,  34591,  34603,  34607,  34613,  34631,
   34649,  34651,  34667,  34673,  34679,  34687,  34693,  34703,  34721,
   34729,  34739,  34747,  34757,  34759,  34763,  34781,  34807,  34819,
   34841,  34843,  34847,  34849,  34871,  34877,  34883,  34897,  34913,
   34919,  34939,  34949,  34961,  34963,  34981,  35023,  35027,  35051,
   35053,  35059,  35069,  35081,  35083,  35089,  35099,  35107,  35111,
   35117,  35129,  35141,  35149,  35153,  35159,  35171,  35201,  35221,
   35227,  35251,  35257,  35267,  35279,  35281,  35291,  35311,  35317,
   35323,  35327,  35339,  35353,  35363,  35381,  35393,  35401,  35407,
   35419,  35423,  35437,  35447,  35449,  35461,  35491,  35507,  35509,
   35521,  35527,  35531,  35533,  35537,  35543,  35569,  35573,  35591,
   35593,  35597,  35603,  35617,  35671,  35677,  35729,  35731,  35747,
   35753,  35759,  35771,  35797,  35801,  35803,  35809,  35831,  35837,
   35839,  35851,  35863,  35869,  35879,  35897,  35899,  35911,  35923,
   35933,  35951,  35963,  35969,  35977,  35983,  35993,  35999,  36007,
   36011,  36013,  36017,  36037,  36061,  36067,  36073,  36083,  36097,
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  199967, 199999, 200003, 200009, 200017, 200023, 200029, 200033, 200041,
  200063, 200087, 200117, 200131, 200153, 200159, 200171, 200177, 200183,
  200191, 200201, 200227, 200231, 200237, 200257, 200273, 200293, 200297,
  200323, 200329, 200341, 200351, 200357, 200363, 200371, 200381, 200383,
  200401, 200407, 200437, 200443, 200461, 200467, 200483, 200513, 200569,
  200573, 200579, 200587, 200591, 200597, 200609, 200639, 200657, 200671,
  200689, 200699, 200713, 200723, 200731, 200771, 200779, 200789, 200797,
  200807, 200843, 200861, 200867, 200869, 200881, 200891, 200899, 200903,
  200909, 200927, 200929, 200971, 200983, 200987, 200989, 201007, 201011,
  201031, 201037, 201049, 201073, 201101, 201107, 201119, 201121, 201139,
  201151, 201163, 201167, 201193, 201203, 201209, 201211, 201233, 201247,
  201251, 201281, 201287, 201307, 201329, 201337, 201359, 201389, 201401,
  201403, 201413, 201437, 201449, 201451, 201473, 201491, 201493, 201497,
  201499, 201511, 201517, 201547, 201557, 201577, 201581, 201589, 201599,
  201611, 201623, 201629, 201653, 201661, 201667, 201673, 201683, 201701,
  201709, 201731, 201743, 201757, 201767, 201769, 201781, 201787, 201791,
  201797, 201809, 201821, 201823, 201827, 201829, 201833, 201847, 201881,
  201889, 201893, 201907, 201911, 201919, 201923, 201937, 201947, 201953,
  201961, 201973, 201979, 201997, 202001, 202021, 202031, 202049, 202061,
  202063, 202067, 202087, 202099, 202109, 202121, 202127, 202129, 202183,
  202187, 202201, 202219, 202231, 202243, 202277, 202289, 202291, 202309,
  202327, 202339, 202343, 202357, 202361, 202381, 202387, 202393, 202403,
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  202679, 202693, 202717, 202729, 202733, 202747, 202751, 202753, 202757,
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  202907, 202921, 202931, 202933, 202949, 202967, 202973, 202981, 202987,
  202999, 203011, 203017, 203023, 203039, 203051, 203057, 203117, 203141,
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  203821, 203843, 203857, 203869, 203873, 203897, 203909, 203911, 203921,
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  204019, 204023, 204047, 204059, 204067, 204101, 204107, 204133, 204137,
  204143, 204151, 204161, 204163, 204173, 204233, 204251, 204299, 204301,
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  205483, 205487, 205493, 205507, 205519, 205529, 205537, 205549, 205553,
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  205661, 205663, 205703, 205721, 205759, 205763, 205783, 205817, 205823,
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  207343, 207367, 207371, 207377, 207401, 207409, 207433, 207443, 207457,
  207463, 207469, 207479, 207481, 207491, 207497, 207509, 207511, 207517,
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  207619, 207629, 207643, 207653, 207661, 207671, 207673, 207679, 207709,
  207719, 207721, 207743, 207763, 207769, 207797, 207799, 207811, 207821,
  207833, 207847, 207869, 207877, 207923, 207931, 207941, 207947, 207953,
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  208379, 208387, 208391, 208393, 208409, 208433, 208441, 208457, 208459,
  208463, 208469, 208489, 208493, 208499, 208501, 208511, 208513, 208519,
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  208927, 208931, 208933, 208961, 208963, 208991, 208993, 208997, 209021,
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  209179, 209189, 209201, 209203, 209213, 209221, 209227, 209233, 209249,
  209257, 209263, 209267, 209269, 209299, 209311, 209317, 209327, 209333,
  209347, 209353, 209357, 209359, 209371, 209381, 209393, 209401, 209431,
  209441, 209449, 209459, 209471, 209477, 209497, 209519, 209533, 209543,
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  209639, 209647, 209659, 209669, 209687, 209701, 209707, 209717, 209719,
  209743, 209767, 209771, 209789, 209801, 209809, 209813, 209819, 209821,
  209837, 209851, 209857, 209861, 209887, 209917, 209927, 209929, 209939,
  209953, 209959, 209971, 209977, 209983, 209987, 210011, 210019, 210031,
  210037, 210053, 210071, 210097, 210101, 210109, 210113, 210127, 210131,
  210139, 210143, 210157, 210169, 210173, 210187, 210191, 210193, 210209,
  210229, 210233, 210241, 210247, 210257, 210263, 210277, 210283, 210299,
  210317, 210319, 210323, 210347, 210359, 210361, 210391, 210401, 210403,
  210407, 210421, 210437, 210461, 210467, 210481, 210487, 210491, 210499,
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  210659, 210671, 210709, 210713, 210719, 210731, 210739, 210761, 210773,
  210803, 210809, 210811, 210823, 210827, 210839, 210853, 210857, 210869,
  210901, 210907, 210911, 210913, 210923, 210929, 210943, 210961, 210967,
  211007, 211039, 211049, 211051, 211061, 211063, 211067, 211073, 211093,
  211097, 211129, 211151, 211153, 211177, 211187, 211193, 211199, 211213,
  211217, 211219, 211229, 211231, 211241, 211247, 211271, 211283, 211291,
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  211867, 211873, 211877, 211879, 211889, 211891, 211927, 211931, 211933,
  211943, 211949, 211969, 211979, 211997, 212029, 212039, 212057, 212081,
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  212369, 212383, 212411, 212419, 212423, 212437, 212447, 212453, 212461,
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  232411, 232417, 232433, 232439, 232451, 232457, 232459, 232487, 232499,
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  232633, 232643, 232663, 232669, 232681, 232699, 232709, 232711, 232741,
  232751, 232753, 232777, 232801, 232811, 232819, 232823, 232847, 232853,
  232861, 232871, 232877, 232891, 232901, 232907, 232919, 232937, 232961,
  232963, 232987, 233021, 233069, 233071, 233083, 233113, 233117, 233141,
  233143, 233159, 233161, 233173, 233183, 233201, 233221, 233231, 233239,
  233251, 233267, 233279, 233293, 233297, 233323, 233327, 233329, 233341,
  233347, 233353, 233357, 233371, 233407, 233417, 233419, 233423, 233437,
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  233617, 233621, 233641, 233663, 233669, 233683, 233687, 233689, 233693,
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  233881, 233911, 233917, 233921, 233923, 233939, 233941, 233969, 233983,
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  234131, 234139, 234149, 234161, 234167, 234181, 234187, 234191, 234193,
  234197, 234203, 234211, 234217, 234239, 234259, 234271, 234281, 234287,
  234293, 234317, 234319, 234323, 234331, 234341, 234343, 234361, 234383,
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  235117, 235159, 235171, 235177, 235181, 235199, 235211, 235231, 235241,
  235243, 235273, 235289, 235307, 235309, 235337, 235349, 235369, 235397,
  235439, 235441, 235447, 235483, 235489, 235493, 235513, 235519, 235523,
  235537, 235541, 235553, 235559, 235577, 235591, 235601, 235607, 235621,
  235661, 235663, 235673, 235679, 235699, 235723, 235747, 235751, 235783,
  235787, 235789, 235793, 235811, 235813, 235849, 235871, 235877, 235889,
  235891, 235901, 235919, 235927, 235951, 235967, 235979, 235997, 236017,
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  236143, 236153, 236167, 236207, 236209, 236219, 236231, 236261, 236287,
  236293, 236297, 236323, 236329, 236333, 236339, 236377, 236381, 236387,
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  236653, 236659, 236681, 236699, 236701, 236707, 236713, 236723, 236729,
  236737, 236749, 236771, 236773, 236779, 236783, 236807, 236813, 236867,
  236869, 236879, 236881, 236891, 236893, 236897, 236909, 236917, 236947,
  236981, 236983, 236993, 237011, 237019, 237043, 237053, 237067, 237071,
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  237173, 237179, 237203, 237217, 237233, 237257, 237271, 237277, 237283,
  237287, 237301, 237313, 237319, 237331, 237343, 237361, 237373, 237379,
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  237857, 237859, 237877, 237883, 237901, 237911, 237929, 237959, 237967,
  237971, 237973, 237977, 237997, 238001, 238009, 238019, 238031, 238037,
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  238157, 238159, 238163, 238171, 238181, 238201, 238207, 238213, 238223,
  238229, 238237, 238247, 238261, 238267, 238291, 238307, 238313, 238321,
  238331, 238339, 238361, 238363, 238369, 238373, 238397, 238417, 238423,
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  238681, 238691, 238703, 238709, 238723, 238727, 238729, 238747, 238759,
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  238991, 239017, 239023, 239027, 239053, 239069, 239081, 239087, 239119,
  239137, 239147, 239167, 239171, 239179, 239201, 239231, 239233, 239237,
  239243, 239251, 239263, 239273, 239287, 239297, 239329, 239333, 239347,
  239357, 239383, 239387, 239389, 239417, 239423, 239429, 239431, 239441,
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  240341, 240347, 240349, 240353, 240371, 240379, 240421, 240433, 240437,
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  248137, 248141, 248161, 248167, 248177, 248179, 248189, 248201, 248203,
  248231, 248243, 248257, 248267, 248291, 248293, 248299, 248309, 248317,
  248323, 248351, 248357, 248371, 248389, 248401, 248407, 248431, 248441,
  248447, 248461, 248473, 248477, 248483, 248509, 248533, 248537, 248543,
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  248641, 248657, 248683, 248701, 248707, 248719, 248723, 248737, 248749,
  248753, 248779, 248783, 248789, 248797, 248813, 248821, 248827, 248839,
  248851, 248861, 248867, 248869, 248879, 248887, 248891, 248893, 248903,
  248909, 248971, 248981, 248987, 249017, 249037, 249059, 249079, 249089,
  249097, 249103, 249107, 249127, 249131, 249133, 249143, 249181, 249187,
  249199, 249211, 249217, 249229, 249233, 249253, 249257, 249287, 249311,
  249317, 249329, 249341, 249367, 249377, 249383, 249397, 249419, 249421,
  249427, 249433, 249437, 249439, 249449, 249463, 249497, 249499, 249503,
  249517, 249521, 249533, 249539, 249541, 249563, 249583, 249589, 249593,
  249607, 249647, 249659, 249671, 249677, 249703, 249721, 249727, 249737,
  249749, 249763, 249779, 249797, 249811, 249827, 249833, 249853, 249857,
  249859, 249863, 249871, 249881, 249911, 249923, 249943, 249947, 249967,
  249971, 249973, 249989, 250007, 250013, 250027, 250031, 250037, 250043,
  250049, 250051, 250057, 250073, 250091, 250109, 250123, 250147, 250153,
  250169, 250199, 250253, 250259, 250267, 250279, 250301, 250307, 250343,
  250361, 250403, 250409, 250423, 250433, 250441, 250451, 250489, 250499,
  250501, 250543, 250583, 250619, 250643, 250673, 250681, 250687, 250693,
  250703, 250709, 250721, 250727, 250739, 250741, 250751, 250753, 250777,
  250787, 250793, 250799, 250807, 250813, 250829, 250837, 250841, 250853,
  250867, 250871, 250889, 250919, 250949, 250951, 250963, 250967, 250969,
  250979, 250993, 251003, 251033, 251051, 251057, 251059, 251063, 251071,
  251081, 251087, 251099, 251117, 251143, 251149, 251159, 251171, 251177,
  251179, 251191, 251197, 251201, 251203, 251219, 251221, 251231, 251233,
  251257, 251261, 251263, 251287, 251291, 251297, 251323, 251347, 251353,
  251359, 251387, 251393, 251417, 251429, 251431, 251437, 251443, 251467,
  251473, 251477, 251483, 251491, 251501, 251513, 251519, 251527, 251533,
  251539, 251543, 251561, 251567, 251609, 251611, 251621, 251623, 251639,
  251653, 251663, 251677, 251701, 251707, 251737, 251761, 251789, 251791,
  251809, 251831, 251833, 251843, 251857, 251861, 251879, 251887, 251893,
  251897, 251903, 251917, 251939, 251941, 251947, 251969, 251971, 251983,
  252001, 252013, 252017, 252029, 252037, 252079, 252101, 252139, 252143,
  252151, 252157, 252163, 252169, 252173, 252181, 252193, 252209, 252223,
  252233, 252253, 252277, 252283, 252289, 252293, 252313, 252319, 252323,
  252341, 252359, 252383, 252391, 252401, 252409, 252419, 252431, 252443,
  252449, 252457, 252463, 252481, 252509, 252533, 252541, 252559, 252583,
  252589, 252607, 252611, 252617, 252641, 252667, 252691, 252709, 252713,
  252727, 252731, 252737, 252761, 252767, 252779, 252817, 252823, 252827,
  252829, 252869, 252877, 252881, 252887, 252893, 252899, 252911, 252913,
  252919, 252937, 252949, 252971, 252979, 252983, 253003, 253013, 253049,
  253063, 253081, 253103, 253109, 253133, 253153, 253157, 253159, 253229,
  253243, 253247, 253273, 253307, 253321, 253343, 253349, 253361, 253367,
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  253651, 253661, 253679, 253681, 253703, 253717, 253733, 253741, 253751,
  253763, 253769, 253777, 253787, 253789, 253801, 253811, 253819, 253823,
  253853, 253867, 253871, 253879, 253901, 253907, 253909, 253919, 253937,
  253949, 253951, 253969, 253987, 253993, 253999, 254003, 254021, 254027,
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  254161, 254179, 254197, 254207, 254209, 254213, 254249, 254257, 254279,
  254281, 254291, 254299, 254329, 254369, 254377, 254383, 254389, 254407,
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  254731, 254741, 254747, 254753, 254773, 254777, 254783, 254791, 254803,
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  254993, 255007, 255019, 255023, 255043, 255049, 255053, 255071, 255077,
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  256133, 256147, 256163, 256169, 256181, 256187, 256189, 256199, 256211,
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  257863, 257867, 257869, 257879, 257893, 257903, 257921, 257947, 257953,
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  259001, 259009, 259019, 259033, 259099, 259121, 259123, 259151, 259157,
  259159, 259163, 259169, 259177, 259183, 259201, 259211, 259213, 259219,
  259229, 259271, 259277, 259309, 259321, 259339, 259379, 259381, 259387,
  259397, 259411, 259421, 259429, 259451, 259453, 259459, 259499, 259507,
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  259627, 259631, 259639, 259643, 259657, 259667, 259681, 259691, 259697,
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  260201, 260207, 260209, 260213, 260231, 260263, 260269, 260317, 260329,
  260339, 260363, 260387, 260399, 260411, 260413, 260417, 260419, 260441,
  260453, 260461, 260467, 260483, 260489, 260527, 260539, 260543, 260549,
  260551, 260569, 260573, 260581, 260587, 260609, 260629, 260647, 260651,
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  260791, 260807, 260809, 260849, 260857, 260861, 260863, 260873, 260879,
  260893, 260921, 260941, 260951, 260959, 260969, 260983, 260987, 260999,
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  277483, 277493, 277499, 277513, 277531, 277547, 277549, 277567, 277577,
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  277687, 277691, 277703, 277741, 277747, 277751, 277757, 277787, 277789,
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  277903, 277919, 277961, 277993, 277999, 278017, 278029, 278041, 278051,
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 1129253,1129283,1129307,1129313,1129333,1129343,1129367,1129391,1129399,
 1129409,1129433,1129439,1129441,1129459,1129477,1129487,1129489,1129501,
 1129511,1129519,1129523,1129559,1129561,1129571,1129577,1129603,1129619,
 1129643,1129663,1129679,1129693,1129699,1129717,1129729,1129741,1129747,
 1129757,1129763,1129787,1129789,1129819,1129831,1129841,1129847,1129853,
 1129859,1129861,1129889,1129897,1129951,1129957,1129963,1129991,1130011,
 1130023,1130039,1130047,1130053,1130057,1130081,1130099,1130117,1130123,
 1130131,1130191,1130237,1130251,1130257,1130267,1130273,1130281,1130287,
 1130293,1130299,1130317,1130321,1130351,1130359,1130369,1130407,1130413,
 1130417,1130429,1130431,1130447,1130471,1130497,1130501,1130527,1130561,
 1130579,1130581,1130587,1130621,1130627,1130629,1130639,1130641,1130651,
 1130677,1130693,1130699,1130711,1130719,1130737,1130741,1130777,1130783,
 1130803,1130807,1130809,1130813,1130819,1130827,1130863,1130929,1130939,
 1130947,1130951,1130953,1130957,1130963,1130981,1131023,1131047,1131049,
 1131077,1131079,1131083,1131103,1131113,1131121,1131131,1131133,1131139,
 1131157,1131181,1131191,1131217,1131223,1131239,1131253,1131259,1131269,
 1131271,1131307,1131323,1131329,1131331,1131341,1131343,1131353,1131379,
 1131397,1131413,1131419,1131421,1131437,1131451,1131463,1131467,1131479,
 1131491,1131509,1131523,1131547,1131553,1131569,1131617,1131629,1131643,
 1131653,1131671,1131677,1131701,1131721,1131727,1131737,1131749,1131751,
 1131763,1131769,1131787,1131799,1131821,1131827,1131829,1131839,1131857,
 1131863,1131869,1131881,1131883,1131913,1131917,1131919,1131937,1131943,
 1131959,1131961,1131973,1131997,1132003,1132009,1132063,1132067,1132091,
 1132123,1132139,1132141,1132177,1132199,1132223,1132249,1132259,1132291,
 1132301,1132309,1132321,1132333,1132393,1132403,1132409,1132423,1132429,
 1132447,1132463,1132471,1132477,1132487,1132499,1132507,1132511,1132519,
 1132529,1132541,1132561,1132567,1132583,1132597,1132601,1132603,1132627,
 1132633,1132639,1132643,1132661,1132667,1132673,1132679,1132697,1132721,
 1132739,1132753,1132783,1132787,1132793,1132811,1132823,1132861,1132877,
 1132883,1132909,1132919,1132927,1132933,1132949,1132969,1132979,1132987,
 1132991,1132993,1132997,1133009,1133017,1133039,1133047,1133053,1133071,
 1133131,1133147,1133149,1133159,1133173,1133177,1133183,1133189,1133191,
 1133219,1133227,1133239,1133257,1133261,1133263,1133287,1133303,1133317,
 1133333,1133357,1133359,1133381,1133387,1133459,1133467,1133477,1133479,
 1133501,1133507,1133513,1133519,1133533,1133537,1133551,1133579,1133591,
 1133621,1133623,1133633,1133641,1133651,1133653,1133659,1133677,1133681,
 1133683,1133689,1133731,1133777,1133789,1133809,1133819,1133827,1133837,
 1133843,1133851,1133857,1133861,1133893,1133897,1133903,1133911,1133933,
 1133947,1133959,1133963,1133971,1133989,1134031,1134037,1134043,1134047,
 1134059,1134071,1134079,1134113,1134137,1134143,1134149,1134151,1134163,
 1134169,1134179,1134187,1134193,1134239,1134241,1134247,1134271,1134283,
 1134299,1134311,1134313,1134389,1134391,1134403,1134421,1134437,1134443,
 1134449,1134467,1134479,1134481,1134487,1134503,1134517,1134541,1134557,
 1134559,1134583,1134587,1134607,1134611,1134619,1134649,1134667,1134673,
 1134691,1134697,1134703,1134709,1134719,1134769,1134781,1134787,1134811,
 1134821,1134841,1134863,1134871,1134877,1134883,1134907,1134923,1134929,
 1134961,1134967,1134977,1134989,1135007,1135009,1135019,1135021,1135061,
 1135063,1135081,1135087,1135091,1135093,1135103,1135111,1135129,1135133,
 1135159,1135171,1135187,1135201,1135217,1135229,1135237,1135241,1135247,
 1135261,1135279,1135283,1135291,1135327,1135333,1135339,1135363,1135367,
 1135403,1135411,1135427,1135429,1135439,1135451,1135469,1135483,1135513,
 1135531,1135597,1135613,1135619,1135633,1135643,1135657,1135663,1135699,
 1135703,1135711,1135721,1135733,1135751,1135777,1135819,1135831,1135837,
 1135847,1135853,1135859,1135861,1135873,1135879,1135891,1135903,1135913,
 1135919,1135921,1135951,1135963,1135969,1135997,1135999,1136041,1136053,
 1136063,1136077,1136081,1136087,1136089,1136111,1136117,1136123,1136129,
 1136147,1136153,1136183,1136203,1136221,1136227,1136231,1136237,1136287,
 1136299,1136309,1136327,1136329,1136339,1136357,1136363,1136383,1136389,
 1136393,1136411,1136417,1136449,1136459,1136461,1136477,1136483,1136557,
 1136567,1136579,1136587,1136593,1136609,1136617,1136623,1136627,1136633,
 1136647,1136651,1136659,1136669,1136699,1136717,1136719,1136741,1136749,
 1136767,1136809,1136813,1136819,1136831,1136833,1136843,1136869,1136897,
 1136917,1136921,1136939,1136951,1136969,1136981,1136983,1136999,1137001,
 1137007,1137029,1137067,1137091,1137109,1137137,1137139,1137161,1137163,
 1137167,1137179,1137203,1137209,1137229,1137233,1137247,1137263,1137271,
 1137289,1137313,1137329,1137337,1137341,1137403,1137407,1137427,1137439,
 1137457,1137481,1137503,1137527,1137529,1137547,1137551,1137553,1137569,
 1137611,1137613,1137629,1137659,1137667,1137673,1137677,1137707,1137733,
 1137743,1137749,1137767,1137781,1137803,1137809,1137811,1137817,1137859,
 1137863,1137869,1137881,1137883,1137887,1137889,1137911,1137919,1137937,
 1137953,1137959,1137973,1137977,1137991,1138019,1138057,1138061,1138091,
 1138097,1138117,1138127,1138141,1138147,1138171,1138183,1138213,1138237,
 1138273,1138363,1138367,1138369,1138391,1138393,1138409,1138411,1138427,
 1138429,1138433,1138441,1138451,1138457,1138483,1138519,1138547,1138559,
 1138567,1138589,1138591,1138637,1138639,1138649,1138667,1138673,1138679,
 1138681,1138703,1138717,1138729,1138733,1138741,1138751,1138757,1138771,
 1138777,1138793,1138829,1138831,1138849,1138853,1138867,1138883,1138901,
 1138919,1138957,1138961,1138967,1138979,1138987,1138997,1138999,1139003,
 1139011,1139041,1139059,1139081,1139087,1139123,1139141,1139143,1139147,
 1139191,1139197,1139227,1139239,1139249,1139263,1139269,1139273,1139287,
 1139291,1139293,1139309,1139321,1139329,1139353,1139387,1139393,1139407,
 1139423,1139461,1139471,1139473,1139483,1139491,1139503,1139519,1139521,
 1139531,1139539,1139549,1139557,1139573,1139587,1139623,1139669,1139681,
 1139683,1139687,1139713,1139717,1139741,1139771,1139773,1139779,1139807,
 1139819,1139843,1139849,1139851,1139861,1139863,1139869,1139909,1139911,
 1139917,1139921,1139951,1139959,1139989,1139993,1140091,1140101,1140103,
 1140121,1140127,1140131,1140137,1140143,1140157,1140163,1140197,1140203,
 1140233,1140239,1140253,1140257,1140281,1140289,1140311,1140319,1140341,
 1140353,1140371,1140379,1140383,1140389,1140413,1140421,1140431,1140439,
 1140449,1140463,1140487,1140493,1140533,1140539,1140563,1140569,1140571,
 1140577,1140611,1140619,1140637,1140677,1140679,1140691,1140697,1140709,
 1140721,1140749,1140787,1140803,1140847,1140851,1140859,1140863,1140871,
 1140901,1140911,1140913,1140929,1140949,1140959,1140967,1140973,1140983,
 1140991,1141009,1141013,1141027,1141031,1141033,1141039,1141061,1141067,
 1141081,1141087,1141093,1141097,1141103,1141109,1141123,1141139,1141171,
 1141219,1141223,1141229,1141241,1141243,1141253,1141267,1141271,1141277,
 1141279,1141289,1141291,1141303,1141319,1141321,1141351,1141373,1141379,
 1141381,1141391,1141417,1141423,1141447,1141453,1141477,1141507,1141523,
 1141529,1141531,1141541,1141571,1141573,1141597,1141631,1141633,1141649,
 1141661,1141667,1141717,1141739,1141757,1141769,1141801,1141813,1141837,
 1141849,1141853,1141867,1141871,1141901,1141909,1141949,1141963,1141967,
 1141969,1141999,1142003,1142017,1142021,1142039,1142041,1142059,1142069,
 1142083,1142129,1142131,1142159,1142161,1142171,1142191,1142201,1142233,
 1142237,1142243,1142263,1142269,1142279,1142287,1142311,1142321,1142333,
 1142353,1142357,1142359,1142363,1142389,1142423,1142431,1142473,1142483,
 1142503,1142507,1142509,1142539,1142549,1142569,1142573,1142593,1142599,
 1142633,1142651,1142677,1142693,1142707,1142737,1142759,1142773,1142777,
 1142783,1142789,1142809,1142821,1142833,1142837,1142851,1142863,1142881,
 1142891,1142909,1142917,1142923,1142929,1142941,1142959,1142969,1142971,
 1143013,1143019,1143047,1143049,1143053,1143061,1143067,1143071,1143073,
 1143089,1143091,1143101,1143113,1143143,1143161,1143167,1143193,1143217,
 1143223,1143227,1143239,1143257,1143269,1143281,1143283,1143299,1143341,
 1143347,1143371,1143391,1143407,1143433,1143469,1143473,1143481,1143487,
 1143529,1143551,1143563,1143577,1143587,1143589,1143601,1143619,1143643,
 1143647,1143661,1143679,1143697,1143719,1143749,1143763,1143799,1143803,
 1143809,1143817,1143829,1143851,1143887,1143893,1143943,1143949,1143953,
 1143959,1143977,1144001,1144007,1144019,1144037,1144061,1144081,1144103,
 1144139,1144141,1144147,1144153,1144163,1144183,1144193,1144211,1144223,
 1144243,1144249,1144261,1144271,1144277,1144279,1144291,1144301,1144327,
 1144333,1144343,1144349,1144357,1144379,1144393,1144399,1144417,1144439,
 1144441,1144453,1144477,1144483,1144499,1144511,1144519,1144523,1144529,
 1144537,1144573,1144589,1144603,1144607,1144621,1144643,1144657,1144667,
 1144681,1144691,1144721,1144723,1144727,1144739,1144757,1144783,1144823,
 1144837,1144867,1144877,1144879,1144889,1144901,1144903,1144907,1144919,
 1144931,1144939,1144951,1144973,1144981,1144993,1145003,1145021,1145057,
 1145059,1145077,1145093,1145099,1145107,1145129,1145141,1145143,1145173,
 1145189,1145191,1145203,1145213,1145227,1145269,1145281,1145293,1145299,
 1145303,1145311,1145323,1145327,1145329,1145359,1145369,1145371,1145381,
 1145387,1145393,1145411,1145429,1145461,1145479,1145497,1145509,1145533,
 1145537,1145539,1145593,1145611,1145621,1145623,1145659,1145689,1145693,
 1145713,1145723,1145741,1145743,1145747,1145773,1145789,1145797,1145801,
 1145803,1145831,1145843,1145849,1145873,1145897,1145899,1145971,1145983,
 1145999,1146037,1146043,1146049,1146071,1146083,1146091,1146097,1146133,
 1146143,1146179,1146217,1146221,1146263,1146281,1146307,1146323,1146329,
 1146331,1146347,1146367,1146391,1146407,1146413,1146419,1146421,1146461,
 1146487,1146491,1146511,1146521,1146529,1146533,1146539,1146559,1146569,
 1146581,1146661,1146671,1146679,1146697,1146703,1146709,1146713,1146727,
 1146731,1146763,1146773,1146779,1146781,1146787,1146791,1146793,1146797,
 1146799,1146809,1146823,1146829,1146833,1146841,1146857,1146869,1146877,
 1146881,1146911,1146917,1146931,1146947,1146953,1146967,1146989,1147009,
 1147021,1147039,1147043,1147051,1147067,1147073,1147099,1147103,1147117,
 1147127,1147141,1147169,1147183,1147187,1147189,1147193,1147213,1147229,
 1147231,1147243,1147247,1147249,1147253,1147271,1147273,1147297,1147301,
 1147331,1147339,1147351,1147379,1147387,1147409,1147417,1147423,1147427,
 1147441,1147451,1147453,1147459,1147463,1147499,1147507,1147511,1147561,
 1147567,1147571,1147579,1147583,1147591,1147613,1147621,1147637,1147639,
 1147669,1147697,1147709,1147711,1147717,1147739,1147759,1147793,1147819,
 1147841,1147843,1147889,1147897,1147903,1147921,1147931,1147969,1147981,
 1147987,1147997,1148029,1148039,1148047,1148087,1148089,1148099,1148111,
 1148167,1148171,1148177,1148219,1148249,1148261,1148263,1148291,1148293,
 1148297,1148311,1148327,1148339,1148359,1148377,1148387,1148437,1148453,
 1148489,1148501,1148507,1148513,1148527,1148549,1148561,1148593,1148599,
 1148621,1148629,1148647,1148663,1148677,1148681,1148687,1148701,1148713,
 1148729,1148731,1148737,1148747,1148753,1148761,1148773,1148837,1148839,
 1148857,1148867,1148879,1148921,1148933,1148941,1148957,1148963,1148971,
 1148977,1148981,1148989,1148999,1149007,1149017,1149037,1149053,1149059,
 1149061,1149131,1149151,1149157,1149163,1149167,1149191,1149193,1149209,
 1149221,1149227,1149229,1149233,1149259,1149283,1149307,1149341,1149349,
 1149361,1149373,1149403,1149409,1149413,1149427,1149457,1149469,1149487,
 1149493,1149503,1149509,1149521,1149527,1149539,1149559,1149569,1149581,
 1149587,1149593,1149601,1149607,1149619,1149637,1149641,1149661,1149679,
 1149689,1149737,1149749,1149769,1149773,1149779,1149803,1149817,1149857,
 1149859,1149881,1149887,1149901,1149913,1149917,1149919,1149943,1149971,
 1149979,1149983,1149989,1149991,1150027,1150031,1150057,1150063,1150073,
 1150081,1150103,1150117,1150139,1150141,1150151,1150159,1150183,1150187,
 1150199,1150211,1150213,1150217,1150229,1150243,1150249,1150301,1150309,
 1150349,1150351,1150363,1150397,1150403,1150411,1150417,1150421,1150423,
 1150447,1150489,1150511,1150519,1150531,1150537,1150547,1150561,1150579,
 1150603,1150609,1150631,1150649,1150651,1150657,1150661,1150673,1150687,
 1150703,1150717,1150729,1150733,1150739,1150741,1150757,1150763,1150769,
 1150777,1150783,1150823,1150837,1150847,1150861,1150867,1150871,1150873,
 1150879,1150909,1150921,1150927,1150939,1150949,1150957,1150973,1150987,
 1151021,1151041,1151047,1151057,1151063,1151069,1151083,1151089,1151113,
 1151141,1151147,1151159,1151167,1151177,1151179,1151203,1151209,1151221,
 1151233,1151237,1151243,1151251,1151287,1151303,1151317,1151327,1151333,
 1151363,1151369,1151383,1151389,1151399,1151401,1151413,1151417,1151431,
 1151441,1151443,1151471,1151473,1151483,1151519,1151537,1151569,1151581,
 1151593,1151599,1151603,1151611,1151629,1151639,1151651,1151653,1151659,
 1151671,1151687,1151701,1151713,1151729,1151737,1151747,1151753,1151779,
 1151807,1151861,1151873,1151879,1151881,1151911,1151933,1151963,1151981,
 1151987,1151993,1151999,1152023,1152029,1152037,1152071,1152077,1152079,
 1152091,1152113,1152119,1152121,1152149,1152157,1152161,1152163,1152181,
 1152187,1152227,1152233,1152287,1152313,1152317,1152337,1152343,1152367,
 1152383,1152391,1152397,1152419,1152421,1152493,1152509,1152517,1152523,
 1152527,1152589,1152623,1152629,1152631,1152637,1152643,1152649,1152653,
 1152667,1152677,1152707,1152733,1152751,1152757,1152761,1152763,1152773,
 1152791,1152793,1152799,1152841,1152857,1152881,1152887,1152913,1152917,
 1152937,1152941,1152979,1152989,1152997,1153001,1153007,1153021,1153027,
 1153049,1153057,1153063,1153073,1153099,1153109,1153123,1153147,1153153,
 1153157,1153171,1153177,1153183,1153199,1153211,1153219,1153223,1153237,
 1153241,1153247,1153249,1153261,1153267,1153277,1153309,1153337,1153343,
 1153349,1153367,1153393,1153421,1153429,1153441,1153457,1153459,1153463,
 1153483,1153487,1153511,1153517,1153531,1153553,1153573,1153577,1153589,
 1153597,1153609,1153613,1153639,1153643,1153681,1153687,1153721,1153729,
 1153751,1153753,1153759,1153769,1153777,1153799,1153811,1153849,1153853,
 1153871,1153891,1153921,1153967,1153973,1154017,1154029,1154033,1154039,
 1154047,1154051,1154119,1154123,1154129,1154159,1154173,1154177,1154183,
 1154207,1154221,1154227,1154233,1154239,1154243,1154267,1154291,1154297,
 1154299,1154311,1154323,1154327,1154339,1154353,1154359,1154369,1154401,
 1154411,1154431,1154449,1154467,1154473,1154509,1154513,1154537,1154539,
 1154551,1154561,1154563,1154567,1154579,1154581,1154603,1154633,1154639,
 1154651,1154653,1154707,1154723,1154737,1154753,1154771,1154789,1154819,
 1154821,1154849,1154863,1154887,1154893,1154897,1154911,1154927,1154947,
 1154969,1154971,1154987,1155001,1155017,1155019,1155053,1155061,1155071,
 1155097,1155101,1155107,1155127,1155149,1155151,1155169,1155179,1155211,
 1155223,1155233,1155239,1155247,1155263,1155293,1155311,1155317,1155373,
 1155377,1155379,1155403,1155419,1155431,1155437,1155449,1155457,1155461,
 1155499,1155527,1155529,1155569,1155577,1155601,1155607,1155611,1155613,
 1155617,1155619,1155629,1155631,1155653,1155659,1155689,1155697,1155701,
 1155703,1155709,1155733,1155821,1155823,1155829,1155841,1155851,1155859,
 1155863,1155899,1155901,1155907,1155919,1155923,1155929,1155937,1155943,
 1155953,1155961,1155967,1155971,1155977,1155997,1156009,1156013,1156019,
 1156031,1156033,1156037,1156039,1156073,1156079,1156087,1156097,1156109,
 1156121,1156151,1156157,1156171,1156217,1156229,1156231,1156249,1156261,
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 1231577,1231579,1231589,1231597,1231613,1231631,1231663,1231669,1231687,
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 1231877,1231883,1231889,1231943,1231961,1231981,1231987,1231999,1232003,
 1232069,1232071,1232083,1232089,1232171,1232183,1232201,1232213,1232221,
 1232227,1232243,1232269,1232291,1232299,1232327,1232339,1232351,1232353,
 1232377,1232389,1232393,1232401,1232411,1232417,1232431,1232437,1232453,
 1232461,1232477,1232527,1232531,1232537,1232563,1232573,1232603,1232611,
 1232617,1232657,1232659,1232683,1232689,1232713,1232719,1232771,1232797,
 1232801,1232809,1232831,1232843,1232849,1232851,1232879,1232893,1232909,
 1232941,1232947,1232977,1232981,1232983,1232999,1233019,1233047,1233073,
 1233079,1233097,1233101,1233107,1233121,1233143,1233179,1233181,1233187,
 1233209,1233241,1233251,1233259,1233263,1233301,1233313,1233319,1233361,
 1233371,1233373,1233377,1233409,1233431,1233433,1233437,1233439,1233473,
 1233493,1233497,1233509,1233523,1233527,1233539,1233563,1233569,1233577,
 1233587,1233593,1233599,1233607,1233611,1233619,1233641,1233647,1233653,
 1233709,1233721,1233751,1233761,1233763,1233779,1233781,1233851,1233887,
 1233899,1233907,1233923,1233929,1233949,1233983,1234001,1234003,1234039,
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 1234231,1234237,1234241,1234243,1234253,1234271,1234309,1234333,1234349,
 1234351,1234367,1234379,1234391,1234393,1234417,1234439,1234463,1234511,
 1234517,1234531,1234537,1234543,1234547,1234577,1234603,1234613,1234627,
 1234657,1234687,1234703,1234721,1234747,1234757,1234759,1234769,1234777,
 1234787,1234789,1234799,1234813,1234819,1234837,1234841,1234843,1234853,
 1234873,1234889,1234901,1234951,1234967,1234969,1234991,1235021,1235027,
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 1235159,1235167,1235177,1235183,1235191,1235239,1235243,1235249,1235251,
 1235263,1235281,1235287,1235303,1235309,1235321,1235327,1235363,1235369,
 1235383,1235389,1235417,1235419,1235431,1235447,1235449,1235459,1235473,
 1235477,1235497,1235501,1235503,1235539,1235569,1235573,1235593,1235651,
 1235653,1235659,1235669,1235701,1235711,1235761,1235789,1235791,1235803,
 1235807,1235821,1235831,1235833,1235867,1235879,1235887,1235891,1235909,
 1235929,1235933,1235947,1235977,1235981,1235987,1235999,1236017,1236073,
 1236077,1236161,1236163,1236173,1236203,1236211,1236229,1236233,1236239,
 1236259,1236307,1236317,1236329,1236337,1236383,1236397,1236419,1236439,
 1236449,1236467,1236479,1236481,1236491,1236517,1236527,1236533,1236541,
 1236553,1236583,1236611,1236623,1236629,1236643,1236659,1236661,1236667,
 1236701,1236709,1236713,1236727,1236737,1236743,1236751,1236757,1236761,
 1236769,1236787,1236791,1236797,1236803,1236811,1236827,1236857,1236883,
 1236901,1236953,1236959,1236979,1237001,1237013,1237031,1237037,1237043,
 1237051,1237057,1237063,1237079,1237091,1237121,1237129,1237139,1237151,
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 1291139,1291153,1291159,1291163,1291177,1291193,1291211,1291217,1291219,
 1291223,1291229,1291249,1291271,1291313,1291321,1291327,1291343,1291349,
 1291357,1291369,1291379,1291387,1291391,1291421,1291447,1291453,1291471,
 1291481,1291483,1291489,1291501,1291523,1291547,1291567,1291579,1291603,
 1291637,1291669,1291673,1291691,1291783,1291793,1291799,1291817,1291819,
 1291831,1291861,1291877,1291883,1291907,1291909,1291931,1291957,1291963,
 1291967,1291991,1291999,1292009,1292023,1292029,1292063,1292069,1292089,
 1292099,1292113,1292131,1292141,1292143,1292149,1292167,1292177,1292219,
 1292237,1292243,1292251,1292257,1292261,1292281,1292293,1292309,1292329,
 1292339,1292353,1292371,1292383,1292387,1292419,1292429,1292441,1292477,
 1292491,1292503,1292509,1292539,1292549,1292563,1292567,1292579,1292587,
 1292591,1292593,1292597,1292609,1292633,1292639,1292653,1292657,1292659,
 1292693,1292701,1292713,1292717,1292729,1292737,1292783,1292789,1292801,
 1292813,1292831,1292843,1292857,1292887,1292927,1292947,1292953,1292957,
 1292971,1292983,1292989,1292999,1293001,1293011,1293031,1293077,1293119,
 1293133,1293137,1293157,1293169,1293179,1293199,1293203,1293233,1293239,
 1293247,1293251,1293277,1293283,1293287,1293307,1293317,1293319,1293323,
 1293329,1293361,1293367,1293373,1293401,1293419,1293421,1293433,1293473,
 1293491,1293493,1293499,1293529,1293533,1293541,1293553,1293559,1293583,
 1293587,1293613,1293619,1293647,1293659,1293701,1293739,1293757,1293763,
 1293791,1293797,1293821,1293829,1293839,1293841,1293857,1293869,1293899,
 1293917,1293923,1293931,1293947,1293949,1293961,1293967,1293977,1293979,
 1293983,1294019,1294021,1294031,1294037,1294039,1294061,1294081,1294087,
 1294103,1294121,1294123,1294129,1294169,1294177,1294199,1294201,1294231,
 1294253,1294273,1294277,1294301,1294303,1294309,1294339,1294351,1294361,
 1294367,1294369,1294393,1294399,1294453,1294459,1294471,1294477,1294483,
 1294561,1294571,1294583,1294597,1294609,1294621,1294627,1294633,1294639,
 1294649,1294651,1294691,1294721,1294723,1294729,1294753,1294757,1294759,
 1294817,1294823,1294841,1294849,1294939,1294957,1294967,1294973,1294987,
 1294999,1295003,1295027,1295033,1295051,1295057,1295069,1295071,1295081,
 1295089,1295113,1295131,1295137,1295159,1295183,1295191,1295201,1295207,
 1295219,1295221,1295243,1295263,1295279,1295293,1295297,1295299,1295309,
 1295317,1295321,1295323,1295339,1295347,1295369,1295377,1295387,1295389,
 1295447,1295473,1295491,1295501,1295513,1295533,1295543,1295549,1295551,
 1295561,1295563,1295603,1295611,1295617,1295639,1295647,1295653,1295681,
 1295711,1295717,1295737,1295741,1295747,1295761,1295783,1295803,1295809,
 1295813,1295839,1295849,1295867,1295869,1295873,1295881,1295947,1295953,
 1295989,1295993,1296007,1296011,1296019,1296023,1296037,1296041,1296059,
 1296077,1296089,1296101,1296109,1296137,1296143,1296167,1296181,1296187,
 1296209,1296227,1296277,1296283,1296287,1296293,1296319,1296331,1296341,
 1296343,1296371,1296391,1296409,1296413,1296419,1296467,1296473,1296481,
 1296499,1296511,1296521,1296523,1296551,1296557,1296563,1296571,1296583,
 1296587,1296593,1296601,1296613,1296623,1296629,1296649,1296679,1296689,
 1296703,1296721,1296727,1296749,1296781,1296787,1296803,1296817,1296829,
 1296833,1296839,1296877,1296899,1296907,1296929,1296949,1296973,1296983,
 1297001,1297003,1297013,1297019,1297027,1297057,1297061,1297063,1297091,
 1297103,1297123,1297129,1297139,1297147,1297157,1297169,1297171,1297193,
 1297201,1297211,1297217,1297229,1297243,1297249,1297271,1297273,1297279,
 1297297,1297313,1297333,1297337,1297349,1297357,1297367,1297369,1297393,
 1297397,1297399,1297403,1297411,1297421,1297447,1297451,1297459,1297477,
 1297487,1297501,1297507,1297519,1297523,1297537,1297561,1297573,1297601,
 1297607,1297619,1297631,1297633,1297649,1297651,1297657,1297669,1297687,
 1297693,1297727,1297739,1297771,1297781,1297799,1297841,1297847,1297853,
 1297873,1297927,1297963,1297973,1297979,1297993,1298027,1298039,1298047,
 1298053,1298057,1298111,1298113,1298117,1298119,1298131,1298149,1298161,
 1298173,1298191,1298197,1298221,1298261,1298279,1298291,1298309,1298317,
 1298329,1298333,1298351,1298357,1298371,1298387,1298467,1298489,1298491,
 1298537,1298551,1298573,1298581,1298611,1298617,1298641,1298651,1298653,
 1298699,1298719,1298723,1298747,1298771,1298779,1298789,1298797,1298809,
 1298819,1298831,1298849,1298863,1298887,1298909,1298911,1298923,1298951,
 1298963,1298981,1298989,1299007,1299013,1299019,1299029,1299041,1299059,
 1299061,1299079,1299097,1299101,1299143,1299169,1299173,1299187,1299203,
 1299209,1299211,1299223,1299227,1299257,1299269,1299283,1299289,1299299,
 1299317,1299323,1299341,1299343,1299349,1299359,1299367,1299377,1299379,
 1299437,1299439,1299449,1299451,1299457,1299491,1299499,1299533,1299541,
 1299553,1299583,1299601,1299631,1299637,1299647,1299653,1299673,1299689,
 1299709,1299721,1299743,1299763,1299791,1299811,1299817,1299821,1299827
};


#define MAXSIZE 108000

int time;

void print_trivial_lemma(FILE* out, pock_certif_t c)
{
  int i, size;
  mpz_ptr *p;
  
  p = c->_dec;
  size = c->_used;

  fprintf(out, "Lemma prime"); 
  mpz_out_str (out, 10, c->_N);
  fprintf(out, " : prime ");mpz_out_str (out, 10, c->_N);
  fprintf(out, ".\n");
  fprintf(out, "Proof.\n");
  fprintf(out, " apply (Pocklington_refl "); 
  print_pock_certif(out, c);
  fprintf(out, "\n        (");
  for(i=0; i < size; i++) {
    fprintf(out, "(Proof_certif ");
    mpz_out_str (out, 10, p[i]);
    fprintf(out, " prime");
    mpz_out_str (out, 10, p[i]);
    fprintf(out, ") :: ");
  }
  fprintf(out, "(Proof_certif 2 prime2) :: nil)).\n");
  fprintf(out,"  native_cast_no_check (refl_equal true).\n");
  if (time) fprintf(out,"Time ");
  fprintf(out,"Qed.\n\n");
}

int 
main (int argc, char *argv[])
{
  FILE * out;
  int i,min,max;
  mpz_t t;
  pock_certif_t c;
  pre_certif_t p;
  certif_t lc;
  char * filename;
 
  mpz_init(t);
  time = 0;
  filename="FirstPrimes.v";
  min = 0;
  max = MAXSIZE;
 
  if (argc <= 1) { 
    fprintf(stdout,"no option given\n");
    fflush(stdout);
    exit(1);
  }

  if (strcmp (argv[1], "-o") == 0) 
    {
      filename = argv[2];
      argv += 2;
      argc -= 2;
    };

  if (strcmp (argv[1], "-base") == 0) 
    {
      max =  atoi(argv[2]);
    
    }
  else if (argc > 2) {
    min = atoi(argv[1]);
    max = atoi(argv[2]);
  } else exit (1);

  if (min < 1) min = 0;
  if (max > MAXSIZE) max = MAXSIZE;

  out = fopen(filename,"w+");
  fprintf(out, "From Coqprime Require Import PocklingtonRefl.\n\n"); 
   
  fprintf(out,"Local Open Scope positive_scope.\n\n");

  char mynum[11];

  for(i = min; i < max; i++) {
    if (i == 0) {
      fprintf(out, "Lemma prime2 : prime 2.\n");
      fprintf(out, "exact prime_2.\n");
      fprintf(out, "Qed.\n\n");
    } else {
      char name[] = "prime";
      sprintf(mynum, "%d", tprimes[i]);
      strcat(name,mynum);
      lc = init_certif();
      mpz_set_ui(t, tprimes[i]);
      c = pock_certif(t);
      extend_lc (lc, c, tprimes[min], tprimes[max]); 
      p = mk_pock_certif(c);
      print_lemma(out,name,p,lc);
    }
  }

  fclose(out);

  exit(0);
}