prime_signature.cc

// Copyright 2011-2024 Google LLC
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//     https://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.

#include "third_party/zynamics/bindiff/prime_signature.h"

#include <cassert>

#include "third_party/absl/base/macros.h"

namespace security::bindiff {

uint32_t IPow32(uint32_t base, uint32_t exp) {
  // Lifted from TensorFlow's math_util.h. This is the squared exponentiation
  // method (a.k.a. double-and-add).
  for (uint32_t result = 1;; base *= base) {
    if ((exp & 1) != 0) {
      result *= base;
    }
    exp >>= 1;
    if (exp == 0) {
      return result;
    }
  }
}

namespace {

static constexpr uint32_t kPrimes[] = {
    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,   16747,
    16759,   16763,   16787,   16811,   16823,   16829,   16831,   16843,
    16871,   16879,   16883,   16889,   16901,   16903,   16921,   16927,
    16931,   16937,   16943,   16963,   16979,   16981,   16987,   16993,
    17011,   17021,   17027,   17029,   17033,   17041,   17047,   17053,
    17077,   17093,   17099,   17107,   17117,   17123,   17137,   17159,
    17167,   17183,   17189,   17191,   17203,   17207,   17209,   17231,
    17239,   17257,   17291,   17293,   17299,   17317,   17321,   17327,
    17333,   17341,   17351,   17359,   17377,   17383,   17387,   17389,
    17393,   17401,   17417,   17419,   17431,   17443,   17449,   17467,
    17471,   17477,   17483,   17489,   17491,   17497,   17509,   17519,
    17539,   17551,   17569,   17573,   17579,   17581,   17597,   17599,
    17609,   17623,   17627,   17657,   17659,   17669,   17681,   17683,
    17707,   17713,   17729,   17737,   17747,   17749,   17761,   17783,
    17789,   17791,   17807,   17827,   17837,   17839,   17851,   17863,
    17881,   17891,   17903,   17909,   17911,   17921,   17923,   17929,
    17939,   17957,   17959,   17971,   17977,   17981,   17987,   17989,
    18013,   18041,   18043,   18047,   18049,   18059,   18061,   18077,
    18089,   18097,   18119,   18121,   18127,   18131,   18133,   18143,
    18149,   18169,   18181,   18191,   18199,   18211,   18217,   18223,
    18229,   18233,   18251,   18253,   18257,   18269,   18287,   18289,
    18301,   18307,   18311,   18313,   18329,   18341,   18353,   18367,
    18371,   18379,   18397,   18401,   18413,   18427,   18433,   18439,
    18443,   18451,   18457,   18461,   18481,   18493,   18503,   18517,
    18521,   18523,   18539,   18541,   18553,   18583,   18587,   18593,
    18617,   18637,   18661,   18671,   18679,   18691,   18701,   18713,
    18719,   18731,   18743,   18749,   18757,   18773,   18787,   18793,
    18797,   18803,   18839,   18859,   18869,   18899,   18911,   18913,
    18917,   18919,   18947,   18959,   18973,   18979,   19001,   19009,
    19013,   19031,   19037,   19051,   19069,   19073,   19079,   19081,
    19087,   19121,   19139,   19141,   19157,   19163,   19181,   19183,
    19207,   19211,   19213,   19219,   19231,   19237,   19249,   19259,
    19267,   19273,   19289,   19301,   19309,   19319,   19333,   19373,
    19379,   19381,   19387,   19391,   19403,   19417,   19421,   19423,
    19427,   19429,   19433,   19441,   19447,   19457,   19463,   19469,
    19471,   19477,   19483,   19489,   19501,   19507,   19531,   19541,
    19543,   19553,   19559,   19571,   19577,   19583,   19597,   19603,
    19609,   19661,   19681,   19687,   19697,   19699,   19709,   19717,
    19727,   19739,   19751,   19753,   19759,   19763,   19777,   19793,
    19801,   19813,   19819,   19841,   19843,   19853,   19861,   19867,
    19889,   19891,   19913,   19919,   19927,   19937,   19949,   19961,
    19963,   19973,   19979,   19991,   19993,   19997,   20011,   20021,
    20023,   20029,   20047,   20051,   20063,   20071,   20089,   20101,
    20107,   20113,   20117,   20123,   20129,   20143,   20147,   20149,
    20161,   20173,   20177,   20183,   20201,   20219,   20231,   20233,
    20249,   20261,   20269,   20287,   20297,   20323,   20327,   20333,
    20341,   20347,   20353,   20357,   20359,   20369,   20389,   20393,
    20399,   20407,   20411,   20431,   20441,   20443,   20477,   20479,
    20483,   20507,   20509,   20521,   20533,   20543,   20549,   20551,
    20563,   20593,   20599,   20611,   20627,   20639,   20641,   20663,
    20681,   20693,   20707,   20717,   20719,   20731,   20743,   20747,
    20749,   20753,   20759,   20771,   20773,   20789,   20807,   20809,
    20849,   20857,   20873,   20879,   20887,   20897,   20899,   20903,
    20921,   20929,   20939,   20947,   20959,   20963,   20981,   20983,
    21001,   21011,   21013,   21017,   21019,   21023,   21031,   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,   22453,
    22469,   22481,   22483,   22501,   22511,   22531,   22541,   22543,
    22549,   22567,   22571,   22573,   22613,   22619,   22621,   22637,
    22639,   22643,   22651,   22669,   22679,   22691,   22697,   22699,
    22709,   22717,   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,   23459,   23473,   23497,   23509,   23531,   23537,
    23539,   23549,   23557,   23561,   23563,   23567,   23581,   23593,
    23599,   23603,   23609,   23623,   23627,   23629,   23633,   23663,
    23669,   23671,   23677,   23687,   23689,   23719,   23741,   23743,
    23747,   23753,   23761,   23767,   23773,   23789,   23801,   23813,
    23819,   23827,   23831,   23833,   23857,   23869,   23873,   23879,
    23887,   23893,   23899,   23909,   23911,   23917,   23929,   23957,
    23971,   23977,   23981,   23993,   24001,   24007,   24019,   24023,
    24029,   24043,   24049,   24061,   24071,   24077,   24083,   24091,
    24097,   24103,   24107,   24109,   24113,   24121,   24133,   24137,
    24151,   24169,   24179,   24181,   24197,   24203,   24223,   24229,
    24239,   24247,   24251,   24281,   24317,   24329,   24337,   24359,
    24371,   24373,   24379,   24391,   24407,   24413,   24419,   24421,
    24439,   24443,   24469,   24473,   24481,   24499,   24509,   24517,
    24527,   24533,   24547,   24551,   24571,   24593,   24611,   24623,
    24631,   24659,   24671,   24677,   24683,   24691,   24697,   24709,
    24733,   24749,   24763,   24767,   24781,   24793,   24799,   24809,
    24821,   24841,   24847,   24851,   24859,   24877,   24889,   24907,
    24917,   24919,   24923,   24943,   24953,   24967,   24971,   24977,
    24979,   24989,   25013,   25031,   25033,   25037,   25057,   25073,
    25087,   25097,   25111,   25117,   25121,   25127,   25147,   25153,
    25163,   25169,   25171,   25183,   25189,   25219,   25229,   25237,
    25243,   25247,   25253,   25261,   25301,   25303,   25307,   25309,
    25321,   25339,   25343,   25349,   25357,   25367,   25373,   25391,
    25409,   25411,   25423,   25439,   25447,   25453,   25457,   25463,
    25469,   25471,   25523,   25537,   25541,   25561,   25577,   25579,
    25583,   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,   26731,   26737,
    26759,   26777,   26783,   26801,   26813,   26821,   26833,   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,
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    39551,   39563,   39569,   39581,   39607,   39619,   39623,   39631,
    39659,   39667,   39671,   39679,   39703,   39709,   39719,   39727,
    39733,   39749,   39761,   39769,   39779,   39791,   39799,   39821,
    39827,   39829,   39839,   39841,   39847,   39857,   39863,   39869,
    39877,   39883,   39887,   39901,   39929,   39937,   39953,   39971,
    39979,   39983,   39989,   40009,   40013,   40031,   40037,   40039,
    40063,   40087,   40093,   40099,   40111,   40123,   40127,   40129,
    40151,   40153,   40163,   40169,   40177,   40189,   40193,   40213,
    40231,   40237,   40241,   40253,   40277,   40283,   40289,   40343,
    40351,   40357,   40361,   40387,   40423,   40427,   40429,   40433,
    40459,   40471,   40483,   40487,   40493,   40499,   40507,   40519,
    40529,   40531,   40543,   40559,   40577,   40583,   40591,   40597,
    40609,   40627,   40637,   40639,   40693,   40697,   40699,   40709,
    40739,   40751,   40759,   40763,   40771,   40787,   40801,   40813,
    40819,   40823,   40829,   40841,   40847,   40849,   40853,   40867,
    40879,   40883,   40897,   40903,   40927,   40933,   40939,   40949,
    40961,   40973,   40993,   41011,   41017,   41023,   41039,   41047,
    41051,   41057,   41077,   41081,   41113,   41117,   41131,   41141,
    41143,   41149,   41161,   41177,   41179,   41183,   41189,   41201,
    41203,   41213,   41221,   41227,   41231,   41233,   41243,   41257,
    41263,   41269,   41281,   41299,   41333,   41341,   41351,   41357,
    41381,   41387,   41389,   41399,   41411,   41413,   41443,   41453,
    41467,   41479,   41491,   41507,   41513,   41519,   41521,   41539,
    41543,   41549,   41579,   41593,   41597,   41603,   41609,   41611,
    41617,   41621,   41627,   41641,   41647,   41651,   41659,   41669,
    41681,   41687,   41719,   41729,   41737,   41759,   41761,   41771,
    41777,   41801,   41809,   41813,   41843,   41849,   41851,   41863,
    41879,   41887,   41893,   41897,   41903,   41911,   41927,   41941,
    41947,   41953,   41957,   41959,   41969,   41981,   41983,   41999,
    42013,   42017,   42019,   42023,   42043,   42061,   42071,   42073,
    42083,   42089,   42101,   42131,   42139,   42157,   42169,   42179,
    42181,   42187,   42193,   42197,   42209,   42221,   42223,   42227,
    42239,   42257,   42281,   42283,   42293,   42299,   42307,   42323,
    42331,   42337,   42349,   42359,   42373,   42379,   42391,   42397,
    42403,   42407,   42409,   42433,   42437,   42443,   42451,   42457,
    42461,   42463,   42467,   42473,   42487,   42491,   42499,   42509,
    42533,   42557,   42569,   42571,   42577,   42589,   42611,   42641,
    42643,   42649,   42667,   42677,   42683,   42689,   42697,   42701,
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    43543,   43573,   43577,   43579,   43591,   43597,   43607,   43609,
    43613,   43627,   43633,   43649,   43651,   43661,   43669,   43691,
    43711,   43717,   43721,   43753,   43759,   43777,   43781,   43783,
    43787,   43789,   43793,   43801,   43853,   43867,   43889,   43891,
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    44647,   44651,   44657,   44683,   44687,   44699,   44701,   44711,
    44729,   44741,   44753,   44771,   44773,   44777,   44789,   44797,
    44809,   44819,   44839,   44843,   44851,   44867,   44879,   44887,
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    44971,   44983,   44987,   45007,   45013,   45053,   45061,   45077,
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    45179,   45181,   45191,   45197,   45233,   45247,   45259,   45263,
    45281,   45289,   45293,   45307,   45317,   45319,   45329,   45337,
    45341,   45343,   45361,   45377,   45389,   45403,   45413,   45427,
    45433,   45439,   45481,   45491,   45497,   45503,   45523,   45533,
    45541,   45553,   45557,   45569,   45587,   45589,   45599,   45613,
    45631,   45641,   45659,   45667,   45673,   45677,   45691,   45697,
    45707,   45737,   45751,   45757,   45763,   45767,   45779,   45817,
    45821,   45823,   45827,   45833,   45841,   45853,   45863,   45869,
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    46687,   46691,   46703,   46723,   46727,   46747,   46751,   46757,
    46769,   46771,   46807,   46811,   46817,   46819,   46829,   46831,
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    47147,   47149,   47161,   47189,   47207,   47221,   47237,   47251,
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    47737,   47741,   47743,   47777,   47779,   47791,   47797,   47807,
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    48473,   48479,   48481,   48487,   48491,   48497,   48523,   48527,
    48533,   48539,   48541,   48563,   48571,   48589,   48593,   48611,
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    48731,   48733,   48751,   48757,   48761,   48767,   48779,   48781,
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    49199,   49201,   49207,   49211,   49223,   49253,   49261,   49277,
    49279,   49297,   49307,   49331,   49333,   49339,   49363,   49367,
    49369,   49391,   49393,   49409,   49411,   49417,   49429,   49433,
    49451,   49459,   49463,   49477,   49481,   49499,   49523,   49529,
    49531,   49537,   49547,   49549,   49559,   49597,   49603,   49613,
    49627,   49633,   49639,   49663,   49667,   49669,   49681,   49697,
    49711,   49727,   49739,   49741,   49747,   49757,   49783,   49787,
    49789,   49801,   49807,   49811,   49823,   49831,   49843,   49853,
    49871,   49877,   49891,   49919,   49921,   49927,   49937,   49939,
    49943,   49957,   49991,   49993,   49999,   50021,   50023,   50033,
    50047,   50051,   50053,   50069,   50077,   50087,   50093,   50101,
    50111,   50119,   50123,   50129,   50131,   50147,   50153,   50159,
    50177,   50207,   50221,   50227,   50231,   50261,   50263,   50273,
    50287,   50291,   50311,   50321,   50329,   50333,   50341,   50359,
    50363,   50377,   50383,   50387,   50411,   50417,   50423,   50441,
    50459,   50461,   50497,   50503,   50513,   50527,   50539,   50543,
    50549,   50551,   50581,   50587,   50591,   50593,   50599,   50627,
    50647,   50651,   50671,   50683,   50707,   50723,   50741,   50753,
    50767,   50773,   50777,   50789,   50821,   50833,   50839,   50849,
    50857,   50867,   50873,   50891,   50893,   50909,   50923,   50929,
    50951,   50957,   50969,   50971,   50989,   50993,   51001,   51031,
    51043,   51047,   51059,   51061,   51071,   51109,   51131,   51133,
    51137,   51151,   51157,   51169,   51193,   51197,   51199,   51203,
    51217,   51229,   51239,   51241,   51257,   51263,   51283,   51287,
    51307,   51329,   51341,   51343,   51347,   51349,   51361,   51383,
    51407,   51413,   51419,   51421,   51427,   51431,   51437,   51439,
    51449,   51461,   51473,   51479,   51481,   51487,   51503,   51511,
    51517,   51521,   51539,   51551,   51563,   51577,   51581,   51593,
    51599,   51607,   51613,   51631,   51637,   51647,   51659,   51673,
    51679,   51683,   51691,   51713,   51719,   51721,   51749,   51767,
    51769,   51787,   51797,   51803,   51817,   51827,   51829,   51839,
    51853,   51859,   51869,   51871,   51893,   51899,   51907,   51913,
    51929,   51941,   51949,   51971,   51973,   51977,   51991,   52009,
    52021,   52027,   52051,   52057,   52067,   52069,   52081,   52103,
    52121,   52127,   52147,   52153,   52163,   52177,   52181,   52183,
    52189,   52201,   52223,   52237,   52249,   52253,   52259,   52267,
    52289,   52291,   52301,   52313,   52321,   52361,   52363,   52369,
    52379,   52387,   52391,   52433,   52453,   52457,   52489,   52501,
    52511,   52517,   52529,   52541,   52543,   52553,   52561,   52567,
    52571,   52579,   52583,   52609,   52627,   52631,   52639,   52667,
    52673,   52691,   52697,   52709,   52711,   52721,   52727,   52733,
    52747,   52757,   52769,   52783,   52807,   52813,   52817,   52837,
    52859,   52861,   52879,   52883,   52889,   52901,   52903,   52919,
    52937,   52951,   52957,   52963,   52967,   52973,   52981,   52999,
    53003,   53017,   53047,   53051,   53069,   53077,   53087,   53089,
    53093,   53101,   53113,   53117,   53129,   53147,   53149,   53161,
    53171,   53173,   53189,   53197,   53201,   53231,   53233,   53239,
    53267,   53269,   53279,   53281,   53299,   53309,   53323,   53327,
    53353,   53359,   53377,   53381,   53401,   53407,   53411,   53419,
    53437,   53441,   53453,   53479,   53503,   53507,   53527,   53549,
    53551,   53569,   53591,   53593,   53597,   53609,   53611,   53617,
    53623,   53629,   53633,   53639,   53653,   53657,   53681,   53693,
    53699,   53717,   53719,   53731,   53759,   53773,   53777,   53783,
    53791,   53813,   53819,   53831,   53849,   53857,   53861,   53881,
    53887,   53891,   53897,   53899,   53917,   53923,   53927,   53939,
    53951,   53959,   53987,   53993,   54001,   54011,   54013,   54037,
    54049,   54059,   54083,   54091,   54101,   54121,   54133,   54139,
    54151,   54163,   54167,   54181,   54193,   54217,   54251,   54269,
    54277,   54287,   54293,   54311,   54319,   54323,   54331,   54347,
    54361,   54367,   54371,   54377,   54401,   54403,   54409,   54413,
    54419,   54421,   54437,   54443,   54449,   54469,   54493,   54497,
    54499,   54503,   54517,   54521,   54539,   54541,   54547,   54559,
    54563,   54577,   54581,   54583,   54601,   54617,   54623,   54629,
    54631,   54647,   54667,   54673,   54679,   54709,   54713,   54721,
    54727,   54751,   54767,   54773,   54779,   54787,   54799,   54829,
    54833,   54851,   54869,   54877,   54881,   54907,   54917,   54919,
    54941,   54949,   54959,   54973,   54979,   54983,   55001,   55009,
    55021,   55049,   55051,   55057,   55061,   55073,   55079,   55103,
    55109,   55117,   55127,   55147,   55163,   55171,   55201,   55207,
    55213,   55217,   55219,   55229,   55243,   55249,   55259,   55291,
    55313,   55331,   55333,   55337,   55339,   55343,   55351,   55373,
    55381,   55399,   55411,   55439,   55441,   55457,   55469,   55487,
    55501,   55511,   55529,   55541,   55547,   55579,   55589,   55603,
    55609,   55619,   55621,   55631,   55633,   55639,   55661,   55663,
    55667,   55673,   55681,   55691,   55697,   55711,   55717,   55721,
    55733,   55763,   55787,   55793,   55799,   55807,   55813,   55817,
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    1017847, 1017851, 1017857, 1017859, 1017881, 1017889, 1017923, 1017953,
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    1021577, 1021621, 1021627, 1021651, 1021661, 1021663, 1021673, 1021697,
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    1021831, 1021837, 1021849, 1021861, 1021879, 1021897, 1021907, 1021919,
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    1022629, 1022633, 1022639, 1022653, 1022677, 1022683, 1022689, 1022701,
    1022719, 1022729, 1022761, 1022773, 1022797, 1022821, 1022837, 1022843,
    1022849, 1022869, 1022881, 1022891, 1022899, 1022911, 1022929, 1022933,
    1022963, 1022977, 1022981, 1023019, 1023037, 1023041, 1023047, 1023067,
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    1024277, 1024307, 1024313, 1024319, 1024321, 1024327, 1024337, 1024339,
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    1024843, 1024853, 1024871, 1024883, 1024901, 1024909, 1024921, 1024931,
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    1033517, 1033537, 1033541, 1033559, 1033567, 1033601, 1033603, 1033631,
    1033661, 1033663, 1033667, 1033679, 1033687, 1033693, 1033741, 1033751,
    1033759, 1033777, 1033783, 1033789, 1033793, 1033801, 1033807, 1033829,
    1033841, 1033843, 1033867, 1033927, 1033951, 1033987, 1034003, 1034009,
    1034027, 1034029, 1034069, 1034071, 1034101, 1034119, 1034123, 1034147,
    1034167, 1034171, 1034177, 1034183, 1034197, 1034207, 1034219, 1034221,
    1034233, 1034237, 1034239, 1034249, 1034251, 1034281, 1034309, 1034317,
    1034323, 1034339, 1034353, 1034357, 1034359, 1034381, 1034387, 1034419,
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    1034651, 1034653, 1034659, 1034707, 1034729, 1034731, 1034767, 1034771,
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    1034959, 1034983, 1034989, 1034993, 1035007, 1035019, 1035043, 1035061,
    1035077, 1035107, 1035131, 1035163, 1035187, 1035191, 1035197, 1035211,
    1035241, 1035247, 1035257, 1035263, 1035277, 1035301, 1035313, 1035323,
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    1036027, 1036039, 1036067, 1036069, 1036073, 1036093, 1036109, 1036117,
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    1036307, 1036319, 1036327, 1036331, 1036339, 1036349, 1036351, 1036363,
    1036367, 1036369, 1036391, 1036411, 1036459, 1036471, 1036493, 1036499,
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    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};

constexpr size_t GetPrimeTableSize() {
  static_assert(100003 <= ABSL_ARRAYSIZE(kPrimes),
                "Table size should be prime to avoid collisions");
  // There are 100008 primes in the table, the largest prime < 100008 is 100003.
  // 100003 is at index 9592.
  return 100003;
}

}  // namespace

uint32_t GetPrime(const std::string& mnemonic) {
  assert(mnemonic.size() < GetPrimeTableSize());
  constexpr char kAsciiSpace = 32;
  uint32_t id = 1;
  for (uint32_t i = 0; i < mnemonic.size(); ++i) {
    const char c = mnemonic[i];
    if (c <= kAsciiSpace) {  // Skip unprintable characters
      continue;
    }
    // Compute a variant of Gödel number to uniquely identify a mnemonic string:
    //   prime[character_value] ^ character_position
    // The substraction below is to make better use of the kPrimes table.
    id *= IPow32(kPrimes[c - kAsciiSpace], i + 1);
  }
  return id;
}

}  // namespace security::bindiff