diagnostics: calculate prime number list for prime_search
Previously, a very large list of known prime numbers was used to verify
calculated prime numbers. This list of numbers took up a significant
amount of space on the rootfs (300kb).
Now, the known list of prime numbers is calculated using a sieve and
compared to the other method of calculating prime numbers. This
exercises the CPU in two different ways and ensures the results are the
same. The test is also modified to return on the first error, instead of
completing all prime calculations for simplicity.
BUG=chromium:1106852
TEST=FEATURES=test emerge-sarien diagnostics && cros deploy dut
diagnostics;
(dut) cros-health-tool diag --action=run_routine --routine=prime_search
Change-Id: Ib6138b80fde720bed4c8df4531912ad2247652b6
Reviewed-on: https://chromium-review.googlesource.com/c/chromiumos/platform2/+/2308050
Reviewed-by: Paul Moy <pmoy@chromium.org>
Tested-by: Trent Begin <tbegin@chromium.org>
Commit-Queue: Trent Begin <tbegin@chromium.org>
diff --git a/diagnostics/routines/prime_search/main.cc b/diagnostics/routines/prime_search/main.cc
index 357cab8..a4d93e5 100644
--- a/diagnostics/routines/prime_search/main.cc
+++ b/diagnostics/routines/prime_search/main.cc
@@ -11,19 +11,12 @@
#include "diagnostics/routines/prime_search/prime_number_search.h"
-namespace {
-
-// Largest number that routine will calculate prime numbers up to.
-constexpr uint64_t kMaxNumber = 1000000;
-
-} // namespace
-
// 'prime_search' command-line tool:
// Calculates prime number between 2 to max_num and verifies the calculation
// repeatedly within a duration.
int main(int argc, char** argv) {
DEFINE_uint64(time, 10, "duration in seconds to run routine for.");
- DEFINE_uint64(max_num, kMaxNumber,
+ DEFINE_uint64(max_num, diagnostics::kMaxPrimeNumber,
"search for prime number less or equal to max_num. "
"Max and default is 1000000");
brillo::FlagHelper::Init(argc, argv, "prime_search - diagnostic routine.");
@@ -31,8 +24,8 @@
base::TimeTicks end_time =
base::TimeTicks::Now() + base::TimeDelta::FromSeconds(FLAGS_time);
- uint64_t max_num = kMaxNumber;
- if (FLAGS_max_num <= kMaxNumber && FLAGS_max_num >= 2)
+ uint64_t max_num = diagnostics::kMaxPrimeNumber;
+ if (FLAGS_max_num <= diagnostics::kMaxPrimeNumber && FLAGS_max_num >= 2)
max_num = FLAGS_max_num;
auto prime_number_search =
diff --git a/diagnostics/routines/prime_search/prime_number_list.h b/diagnostics/routines/prime_search/prime_number_list.h
deleted file mode 100644
index bfcdf4b..0000000
--- a/diagnostics/routines/prime_search/prime_number_list.h
+++ /dev/null
@@ -1,8737 +0,0 @@
-// Copyright 2020 The Chromium OS Authors. All rights reserved.
-// Use of this source code is governed by a BSD-style license that can be
-// found in the LICENSE file.
-
-#ifndef DIAGNOSTICS_ROUTINES_PRIME_SEARCH_PRIME_NUMBER_LIST_H_
-#define DIAGNOSTICS_ROUTINES_PRIME_SEARCH_PRIME_NUMBER_LIST_H_
-
-#include <cstdint>
-
-namespace diagnostics {
-
-constexpr uint32_t kPrimeNumberList[] = {
- 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, 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,
- 36107, 36109, 36131, 36137, 36151, 36161, 36187, 36191, 36209,
- 36217, 36229, 36241, 36251, 36263, 36269, 36277, 36293, 36299,
- 36307, 36313, 36319, 36341, 36343, 36353, 36373, 36383, 36389,
- 36433, 36451, 36457, 36467, 36469, 36473, 36479, 36493, 36497,
- 36523, 36527, 36529, 36541, 36551, 36559, 36563, 36571, 36583,
- 36587, 36599, 36607, 36629, 36637, 36643, 36653, 36671, 36677,
- 36683, 36691, 36697, 36709, 36713, 36721, 36739, 36749, 36761,
- 36767, 36779, 36781, 36787, 36791, 36793, 36809, 36821, 36833,
- 36847, 36857, 36871, 36877, 36887, 36899, 36901, 36913, 36919,
- 36923, 36929, 36931, 36943, 36947, 36973, 36979, 36997, 37003,
- 37013, 37019, 37021, 37039, 37049, 37057, 37061, 37087, 37097,
- 37117, 37123, 37139, 37159, 37171, 37181, 37189, 37199, 37201,
- 37217, 37223, 37243, 37253, 37273, 37277, 37307, 37309, 37313,
- 37321, 37337, 37339, 37357, 37361, 37363, 37369, 37379, 37397,
- 37409, 37423, 37441, 37447, 37463, 37483, 37489, 37493, 37501,
- 37507, 37511, 37517, 37529, 37537, 37547, 37549, 37561, 37567,
- 37571, 37573, 37579, 37589, 37591, 37607, 37619, 37633, 37643,
- 37649, 37657, 37663, 37691, 37693, 37699, 37717, 37747, 37781,
- 37783, 37799, 37811, 37813, 37831, 37847, 37853, 37861, 37871,
- 37879, 37889, 37897, 37907, 37951, 37957, 37963, 37967, 37987,
- 37991, 37993, 37997, 38011, 38039, 38047, 38053, 38069, 38083,
- 38113, 38119, 38149, 38153, 38167, 38177, 38183, 38189, 38197,
- 38201, 38219, 38231, 38237, 38239, 38261, 38273, 38281, 38287,
- 38299, 38303, 38317, 38321, 38327, 38329, 38333, 38351, 38371,
- 38377, 38393, 38431, 38447, 38449, 38453, 38459, 38461, 38501,
- 38543, 38557, 38561, 38567, 38569, 38593, 38603, 38609, 38611,
- 38629, 38639, 38651, 38653, 38669, 38671, 38677, 38693, 38699,
- 38707, 38711, 38713, 38723, 38729, 38737, 38747, 38749, 38767,
- 38783, 38791, 38803, 38821, 38833, 38839, 38851, 38861, 38867,
- 38873, 38891, 38903, 38917, 38921, 38923, 38933, 38953, 38959,
- 38971, 38977, 38993, 39019, 39023, 39041, 39043, 39047, 39079,
- 39089, 39097, 39103, 39107, 39113, 39119, 39133, 39139, 39157,
- 39161, 39163, 39181, 39191, 39199, 39209, 39217, 39227, 39229,
- 39233, 39239, 39241, 39251, 39293, 39301, 39313, 39317, 39323,
- 39341, 39343, 39359, 39367, 39371, 39373, 39383, 39397, 39409,
- 39419, 39439, 39443, 39451, 39461, 39499, 39503, 39509, 39511,
- 39521, 39541, 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,
- 42703, 42709, 42719, 42727, 42737, 42743, 42751, 42767, 42773,
- 42787, 42793, 42797, 42821, 42829, 42839, 42841, 42853, 42859,
- 42863, 42899, 42901, 42923, 42929, 42937, 42943, 42953, 42961,
- 42967, 42979, 42989, 43003, 43013, 43019, 43037, 43049, 43051,
- 43063, 43067, 43093, 43103, 43117, 43133, 43151, 43159, 43177,
- 43189, 43201, 43207, 43223, 43237, 43261, 43271, 43283, 43291,
- 43313, 43319, 43321, 43331, 43391, 43397, 43399, 43403, 43411,
- 43427, 43441, 43451, 43457, 43481, 43487, 43499, 43517, 43541,
- 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, 43913, 43933, 43943, 43951,
- 43961, 43963, 43969, 43973, 43987, 43991, 43997, 44017, 44021,
- 44027, 44029, 44041, 44053, 44059, 44071, 44087, 44089, 44101,
- 44111, 44119, 44123, 44129, 44131, 44159, 44171, 44179, 44189,
- 44201, 44203, 44207, 44221, 44249, 44257, 44263, 44267, 44269,
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- 987911, 987913, 987929, 987941, 987971, 987979, 987983, 987991, 987997,
- 988007, 988021, 988033, 988051, 988061, 988067, 988069, 988093, 988109,
- 988111, 988129, 988147, 988157, 988199, 988213, 988217, 988219, 988231,
- 988237, 988243, 988271, 988279, 988297, 988313, 988319, 988321, 988343,
- 988357, 988367, 988409, 988417, 988439, 988453, 988459, 988483, 988489,
- 988501, 988511, 988541, 988549, 988571, 988577, 988579, 988583, 988591,
- 988607, 988643, 988649, 988651, 988661, 988681, 988693, 988711, 988727,
- 988733, 988759, 988763, 988783, 988789, 988829, 988837, 988849, 988859,
- 988861, 988877, 988901, 988909, 988937, 988951, 988963, 988979, 989011,
- 989029, 989059, 989071, 989081, 989099, 989119, 989123, 989171, 989173,
- 989231, 989239, 989249, 989251, 989279, 989293, 989309, 989321, 989323,
- 989327, 989341, 989347, 989353, 989377, 989381, 989411, 989419, 989423,
- 989441, 989467, 989477, 989479, 989507, 989533, 989557, 989561, 989579,
- 989581, 989623, 989629, 989641, 989647, 989663, 989671, 989687, 989719,
- 989743, 989749, 989753, 989761, 989777, 989783, 989797, 989803, 989827,
- 989831, 989837, 989839, 989869, 989873, 989887, 989909, 989917, 989921,
- 989929, 989939, 989951, 989959, 989971, 989977, 989981, 989999, 990001,
- 990013, 990023, 990037, 990043, 990053, 990137, 990151, 990163, 990169,
- 990179, 990181, 990211, 990239, 990259, 990277, 990281, 990287, 990289,
- 990293, 990307, 990313, 990323, 990329, 990331, 990349, 990359, 990361,
- 990371, 990377, 990383, 990389, 990397, 990463, 990469, 990487, 990497,
- 990503, 990511, 990523, 990529, 990547, 990559, 990589, 990593, 990599,
- 990631, 990637, 990643, 990673, 990707, 990719, 990733, 990761, 990767,
- 990797, 990799, 990809, 990841, 990851, 990881, 990887, 990889, 990893,
- 990917, 990923, 990953, 990961, 990967, 990973, 990989, 991009, 991027,
- 991031, 991037, 991043, 991057, 991063, 991069, 991073, 991079, 991091,
- 991127, 991129, 991147, 991171, 991181, 991187, 991201, 991217, 991223,
- 991229, 991261, 991273, 991313, 991327, 991343, 991357, 991381, 991387,
- 991409, 991427, 991429, 991447, 991453, 991483, 991493, 991499, 991511,
- 991531, 991541, 991547, 991567, 991579, 991603, 991607, 991619, 991621,
- 991633, 991643, 991651, 991663, 991693, 991703, 991717, 991723, 991733,
- 991741, 991751, 991777, 991811, 991817, 991867, 991871, 991873, 991883,
- 991889, 991901, 991909, 991927, 991931, 991943, 991951, 991957, 991961,
- 991973, 991979, 991981, 991987, 991999, 992011, 992021, 992023, 992051,
- 992087, 992111, 992113, 992129, 992141, 992153, 992179, 992183, 992219,
- 992231, 992249, 992263, 992267, 992269, 992281, 992309, 992317, 992357,
- 992359, 992363, 992371, 992393, 992417, 992429, 992437, 992441, 992449,
- 992461, 992513, 992521, 992539, 992549, 992561, 992591, 992603, 992609,
- 992623, 992633, 992659, 992689, 992701, 992707, 992723, 992737, 992777,
- 992801, 992809, 992819, 992843, 992857, 992861, 992863, 992867, 992891,
- 992903, 992917, 992923, 992941, 992947, 992963, 992983, 993001, 993011,
- 993037, 993049, 993053, 993079, 993103, 993107, 993121, 993137, 993169,
- 993197, 993199, 993203, 993211, 993217, 993233, 993241, 993247, 993253,
- 993269, 993283, 993287, 993319, 993323, 993341, 993367, 993397, 993401,
- 993407, 993431, 993437, 993451, 993467, 993479, 993481, 993493, 993527,
- 993541, 993557, 993589, 993611, 993617, 993647, 993679, 993683, 993689,
- 993703, 993763, 993779, 993781, 993793, 993821, 993823, 993827, 993841,
- 993851, 993869, 993887, 993893, 993907, 993913, 993919, 993943, 993961,
- 993977, 993983, 993997, 994013, 994027, 994039, 994051, 994067, 994069,
- 994073, 994087, 994093, 994141, 994163, 994181, 994183, 994193, 994199,
- 994229, 994237, 994241, 994247, 994249, 994271, 994297, 994303, 994307,
- 994309, 994319, 994321, 994337, 994339, 994363, 994369, 994391, 994393,
- 994417, 994447, 994453, 994457, 994471, 994489, 994501, 994549, 994559,
- 994561, 994571, 994579, 994583, 994603, 994621, 994657, 994663, 994667,
- 994691, 994699, 994709, 994711, 994717, 994723, 994751, 994769, 994793,
- 994811, 994813, 994817, 994831, 994837, 994853, 994867, 994871, 994879,
- 994901, 994907, 994913, 994927, 994933, 994949, 994963, 994991, 994997,
- 995009, 995023, 995051, 995053, 995081, 995117, 995119, 995147, 995167,
- 995173, 995219, 995227, 995237, 995243, 995273, 995303, 995327, 995329,
- 995339, 995341, 995347, 995363, 995369, 995377, 995381, 995387, 995399,
- 995431, 995443, 995447, 995461, 995471, 995513, 995531, 995539, 995549,
- 995551, 995567, 995573, 995587, 995591, 995593, 995611, 995623, 995641,
- 995651, 995663, 995669, 995677, 995699, 995713, 995719, 995737, 995747,
- 995783, 995791, 995801, 995833, 995881, 995887, 995903, 995909, 995927,
- 995941, 995957, 995959, 995983, 995987, 995989, 996001, 996011, 996019,
- 996049, 996067, 996103, 996109, 996119, 996143, 996157, 996161, 996167,
- 996169, 996173, 996187, 996197, 996209, 996211, 996253, 996257, 996263,
- 996271, 996293, 996301, 996311, 996323, 996329, 996361, 996367, 996403,
- 996407, 996409, 996431, 996461, 996487, 996511, 996529, 996539, 996551,
- 996563, 996571, 996599, 996601, 996617, 996629, 996631, 996637, 996647,
- 996649, 996689, 996703, 996739, 996763, 996781, 996803, 996811, 996841,
- 996847, 996857, 996859, 996871, 996881, 996883, 996887, 996899, 996953,
- 996967, 996973, 996979, 997001, 997013, 997019, 997021, 997037, 997043,
- 997057, 997069, 997081, 997091, 997097, 997099, 997103, 997109, 997111,
- 997121, 997123, 997141, 997147, 997151, 997153, 997163, 997201, 997207,
- 997219, 997247, 997259, 997267, 997273, 997279, 997307, 997309, 997319,
- 997327, 997333, 997343, 997357, 997369, 997379, 997391, 997427, 997433,
- 997439, 997453, 997463, 997511, 997541, 997547, 997553, 997573, 997583,
- 997589, 997597, 997609, 997627, 997637, 997649, 997651, 997663, 997681,
- 997693, 997699, 997727, 997739, 997741, 997751, 997769, 997783, 997793,
- 997807, 997811, 997813, 997877, 997879, 997889, 997891, 997897, 997933,
- 997949, 997961, 997963, 997973, 997991, 998009, 998017, 998027, 998029,
- 998069, 998071, 998077, 998083, 998111, 998117, 998147, 998161, 998167,
- 998197, 998201, 998213, 998219, 998237, 998243, 998273, 998281, 998287,
- 998311, 998329, 998353, 998377, 998381, 998399, 998411, 998419, 998423,
- 998429, 998443, 998471, 998497, 998513, 998527, 998537, 998539, 998551,
- 998561, 998617, 998623, 998629, 998633, 998651, 998653, 998681, 998687,
- 998689, 998717, 998737, 998743, 998749, 998759, 998779, 998813, 998819,
- 998831, 998839, 998843, 998857, 998861, 998897, 998909, 998917, 998927,
- 998941, 998947, 998951, 998957, 998969, 998983, 998989, 999007, 999023,
- 999029, 999043, 999049, 999067, 999083, 999091, 999101, 999133, 999149,
- 999169, 999181, 999199, 999217, 999221, 999233, 999239, 999269, 999287,
- 999307, 999329, 999331, 999359, 999371, 999377, 999389, 999431, 999433,
- 999437, 999451, 999491, 999499, 999521, 999529, 999541, 999553, 999563,
- 999599, 999611, 999613, 999623, 999631, 999653, 999667, 999671, 999683,
- 999721, 999727, 999749, 999763, 999769, 999773, 999809, 999853, 999863,
- 999883, 999907, 999917, 999931, 999953, 999959, 999961, 999979, 999983};
-} // namespace diagnostics
-
-#endif // DIAGNOSTICS_ROUTINES_PRIME_SEARCH_PRIME_NUMBER_LIST_H_
diff --git a/diagnostics/routines/prime_search/prime_number_search.cc b/diagnostics/routines/prime_search/prime_number_search.cc
index 5eca6cb..39bc1b4 100644
--- a/diagnostics/routines/prime_search/prime_number_search.cc
+++ b/diagnostics/routines/prime_search/prime_number_search.cc
@@ -8,37 +8,33 @@
#include <base/stl_util.h>
-#include "diagnostics/routines/prime_search/prime_number_list.h"
-
namespace diagnostics {
PrimeNumberSearch::PrimeNumberSearch(uint64_t max_num) : max_num_(max_num) {
- expected_prime_num_count_ = 0;
- for (auto prime : diagnostics::kPrimeNumberList) {
- if (prime <= max_num_)
- expected_prime_num_count_++;
- else
- break;
+ // Create a Sieve of Eratosthenes. This creates a bitfield of prime numbers
+ // from 0 - |max_number|.
+ // https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes
+ for (uint64_t i = 2;
+ i <= static_cast<uint64_t>(std::sqrt(static_cast<double>(max_num_)));
+ i++) {
+ if (prime_sieve_[i]) {
+ for (uint64_t j = (i * i); j <= max_num_; j += i)
+ prime_sieve_[j] = 0;
+ }
}
}
bool PrimeNumberSearch::Run() {
- uint64_t prime_num_count = 0;
for (uint64_t num = 2; num <= max_num_; num++) {
- if (!IsPrime(num)) {
- continue;
- }
- if (prime_num_count >= base::size(diagnostics::kPrimeNumberList) ||
- kPrimeNumberList[prime_num_count++] != num) {
- LOG(ERROR) << "incorrect number " << num << " is calculated as "
- << prime_num_count << "th prime number";
+ bool sieve_prime = prime_sieve_[num];
+ bool func_prime = IsPrime(num);
+
+ if (sieve_prime != func_prime) {
+ LOG(ERROR) << "prime number mismatch: " << num
+ << ". sieve: " << sieve_prime << " IsPrime(): " << func_prime;
return false;
}
}
- if (prime_num_count != expected_prime_num_count_) {
- LOG(ERROR) << "incorrect total calculated prime number amount";
- return false;
- }
return true;
}
diff --git a/diagnostics/routines/prime_search/prime_number_search.h b/diagnostics/routines/prime_search/prime_number_search.h
index eaddd78..5171eff 100644
--- a/diagnostics/routines/prime_search/prime_number_search.h
+++ b/diagnostics/routines/prime_search/prime_number_search.h
@@ -5,10 +5,14 @@
#ifndef DIAGNOSTICS_ROUTINES_PRIME_SEARCH_PRIME_NUMBER_SEARCH_H_
#define DIAGNOSTICS_ROUTINES_PRIME_SEARCH_PRIME_NUMBER_SEARCH_H_
+#include <bitset>
#include <cstdint>
namespace diagnostics {
+// Largest number that routine will calculate prime numbers up to.
+constexpr uint64_t kMaxPrimeNumber = 1000000;
+
class PrimeNumberSearch {
public:
explicit PrimeNumberSearch(uint64_t max_num);
@@ -24,8 +28,8 @@
private:
const uint64_t max_num_ = 0;
-
- uint64_t expected_prime_num_count_ = 0;
+ std::bitset<kMaxPrimeNumber + 1> prime_sieve_ =
+ std::bitset<kMaxPrimeNumber + 1>().set();
};
} // namespace diagnostics
diff --git a/diagnostics/routines/prime_search/prime_number_search_test.cc b/diagnostics/routines/prime_search/prime_number_search_test.cc
index ac8a258..0267a6b 100644
--- a/diagnostics/routines/prime_search/prime_number_search_test.cc
+++ b/diagnostics/routines/prime_search/prime_number_search_test.cc
@@ -29,6 +29,7 @@
} // namespace
+// Tests if different numbers are prime by using the IsPrime() calculation.
TEST(PrimeNumberSearchTest, IsPrime) {
PrimeNumberSearch prime_search(4);
@@ -37,6 +38,7 @@
EXPECT_TRUE(prime_search.IsPrime(2));
EXPECT_TRUE(prime_search.IsPrime(3));
EXPECT_FALSE(prime_search.IsPrime(4));
+ EXPECT_TRUE(prime_search.IsPrime(5));
EXPECT_TRUE(prime_search.IsPrime(999983));
EXPECT_FALSE(prime_search.IsPrime(999984));
EXPECT_TRUE(prime_search.IsPrime(360289));
@@ -49,6 +51,12 @@
EXPECT_FALSE(prime_search.IsPrime(87120));
}
+// Test that all values under kMaxPrimeNumber are calculated correctly.
+TEST(PrimeNumbersSearchTest, RunFull) {
+ PrimeNumberSearch prime_search(kMaxPrimeNumber);
+ EXPECT_TRUE(prime_search.Run());
+}
+
// Test Run() returns true when IsPrime() calculates
// correctly.
TEST(PrimeNumberSearchTest, RunPass) {
@@ -65,10 +73,8 @@
EXPECT_TRUE(prime_search.Run());
}
-// Test Run() returns false when IsPrime() miscalculate a prime number as
-// nonprime when no more prime number between miscalculated number to max_num.
-// The error will be discovered by unexpected amount of calculated prime numbers
-// when Run() finished the traversing of the whole number sequences.
+// Test Run() returns false when IsPrime() miscalculates a prime number as
+// nonprime.
TEST(PrimeNumberSearchTest,
RunFailUnexpectedPrimeNumberFollowedWithNoMorePrime) {
MockPrimeNumberSearchTest prime_search(6);
@@ -78,45 +84,6 @@
EXPECT_CALL(prime_search, IsPrime(4)).WillOnce(Return(false));
// 5 should be prime number and is miscalcuated here.
EXPECT_CALL(prime_search, IsPrime(5)).WillOnce(Return(false));
- EXPECT_CALL(prime_search, IsPrime(6)).WillOnce(Return(false));
-
- EXPECT_FALSE(prime_search.Run());
-}
-
-// Test Run() returns false when IsPrime() miscalculate a prime number as
-// nonprime when there is still some prime numbers between miscalculate number
-// to max_num. The error will be discovered by detecting the next correctedly
-// calculated prime number's misposistioning in the prime number table.
-TEST(PrimeNumberSearchTest, RunFailUnexpectedPrimeNumberFollowedWithPrime) {
- MockPrimeNumberSearchTest prime_search(8);
-
- EXPECT_CALL(prime_search, IsPrime(2)).WillOnce(Return(true));
- EXPECT_CALL(prime_search, IsPrime(3)).WillOnce(Return(true));
- EXPECT_CALL(prime_search, IsPrime(4)).WillOnce(Return(false));
- // 5 should be prime number and is miscalcuated here.
- EXPECT_CALL(prime_search, IsPrime(5)).WillOnce(Return(false));
- EXPECT_CALL(prime_search, IsPrime(6)).WillOnce(Return(false));
- EXPECT_CALL(prime_search, IsPrime(7)).WillOnce(Return(true));
- // Run() shall stop when mispositioned prime number is discovered.
- EXPECT_CALL(prime_search, IsPrime(8)).Times(0);
-
- EXPECT_FALSE(prime_search.Run());
-}
-
-// Test Run() returns false when IsPrime() miscalculate a nonprime number as
-// prime. The error will be discovered by detecting the inequality between this
-// miscalculated prime number and the expected value in prime number table.
-TEST(PrimeNumberSearchTest, RunFailUnexpectedNonPrimeNumber) {
- MockPrimeNumberSearchTest prime_search(7);
-
- EXPECT_CALL(prime_search, IsPrime(2)).WillOnce(Return(true));
- EXPECT_CALL(prime_search, IsPrime(3)).WillOnce(Return(true));
- EXPECT_CALL(prime_search, IsPrime(4)).WillOnce(Return(false));
- EXPECT_CALL(prime_search, IsPrime(5)).WillOnce(Return(true));
- // 6 should be nonprime number and is miscalcuated here.
- EXPECT_CALL(prime_search, IsPrime(6)).WillOnce(Return(true));
- // Run() shall stop when unequal prime number value is discovered.
- EXPECT_CALL(prime_search, IsPrime(7)).Times(0);
EXPECT_FALSE(prime_search.Run());
}
