The first 50,000 prime numbers, enjoy :)

1,2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131 ,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, 1511,1523,1531,1543,154
9,1553,1559,1567,1571,1579,1583,1597,1601,1607,1609,1613,1619,1621,1627,1637,1657,1663,1667,1669,169 3,1697,1699,1709,1721,1723,1733,1741,1747,1753,1759,1777,1783,1787,1789,1801,1811,1823,1831,1847,186 1,1867,1871,1873,1877,1879,1889,1901,1907,1913,1931,1933,1949,1951,1973,1979,1987,1993,1997,1999,200 3,2011,2017,2027,2029,2039,2053,2063,2069,2081,2083,2087,2089,2099,2111,2113,2129,2131,2137,2141,214 3,2153,2161,2179,2203,2207,2213,2221,2237,2239,2243,2251,2267,2269,2273,2281,2287,2293,2297,2309,231 1,2333,2339,2341,2347,2351,2357,2371,2377,2381,2383,2389,2393,2399,2411,2417,2423,2437,2441,2447,245 9,2467,2473,2477,2503,2521,2531,2539,2543,2549,2551,2557,2579,2591,2593,2609,2617,2621,2633,2647,265 7,2659,2663,2671,2677,2683,2687,2689,2693,2699,2707,2711,2713,2719,2729,2731,2741,2749,2753,2767,277 7,2789,2791,2797,2801,2803,2819,2833,2837,2843,2851,2857,2861,2879,2887,2897,2903,2909,2917,2927,293 9,2953,2957,2963,2969,2971,2999,3001,3011,3019,3023,3037,3041,3049,3061,3067,3079,3083,3089,3109,311 9,3121,3137,3163,3167,3
169,3181,3187,3191,3203,3209,3217,3221,3229,3251,3253,3257,3259,3271,3299,3301,3307,3313,3319,3323,3 329,3331,3343,3347,3359,3361,3371,3373,3389,3391,3407,3413,3433,3449,3457,3461,3463,3467,3469,3491,3 499,3511,3517,3527,3529,3533,3539,3541,3547,3557,3559,3571,3581,3583,3593,3607,3613,3617,3623,3631,3 637,3643,3659,3671,3673,3677,3691,3697,3701,3709,3719,3727,3733,3739,3761,3767,3769,3779,3793,3797,3 803,3821,3823,3833,3847,3851,3853,3863,3877,3881,3889,3907,3911,3917,3919,3923,3929,3931,3943,3947,3 967,3989,4001,4003,4007,4013,4019,4021,4027,4049,4051,4057,4073,4079,4091,4093,4099,4111,4127,4129,4 133,4139,4153,4157,4159,4177,4201,4211,4217,4219,4229,4231,4241,4243,4253,4259,4261,4271,4273,4283,4 289,4297,4327,4337,4339,4349,4357,4363,4373,4391,4397,4409,4421,4423,4441,4447,4451,4457,4463,4481,4 483,4493,4507,4513,4517,4519,4523,4547,4549,4561,4567,4583,4591,4597,4603,4621,4637,4639,4643,4649,4 651,4657,4663,4673,4679,4691,4703,4721,4723,4729,4733,4751,4759,4783,4787,4789,4793,4799,4801,4813,4 817,4831,4861,4871,4877
,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 ,6607,6619,6637,6653,66
59,6661,6673,6679,6689,6691,6701,6703,6709,6719,6733,6737,6761,6763,6779,6781,6791,6793,6803,6823,68 27,6829,6833,6841,6857,6863,6869,6871,6883,6899,6907,6911,6917,6947,6949,6959,6961,6967,6971,6977,69 83,6991,6997,7001,7013,7019,7027,7039,7043,7057,7069,7079,7103,7109,7121,7127,7129,7151,7159,7177,71 87,7193,7207,7211,7213,7219,7229,7237,7243,7247,7253,7283,7297,7307,7309,7321,7331,7333,7349,7351,73 69,7393,7411,7417,7433,7451,7457,7459,7477,7481,7487,7489,7499,7507,7517,7523,7529,7537,7541,7547,75 49,7559,7561,7573,7577,7583,7589,7591,7603,7607,7621,7639,7643,7649,7669,7673,7681,7687,7691,7699,77 03,7717,7723,7727,7741,7753,7757,7759,7789,7793,7817,7823,7829,7841,7853,7867,7873,7877,7879,7883,79 01,7907,7919,7927,7933,7937,7949,7951,7963,7993,8009,8011,8017,8039,8053,8059,8069,8081,8087,8089,80 93,8101,8111,8117,8123,8147,8161,8167,8171,8179,8191,8209,8219,8221,8231,8233,8237,8243,8263,8269,82 73,8287,8291,8293,8297,8311,8317,8329,8353,8363,8369,8377,8387,8389,8419,8423,8429,8431,8443,8447,84 61,8467,8501,8513,8521,
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 ,10103,10111,10133,10139,10141,10151,10159,10163,10169,10177,10181,10193,10211,10223,10243,10247,102 53,10259,10267,10271,10
273,10289,10301,10303,10313,10321,10331,10333,10337,10343,10357,10369,10391,10399,10427,10429,10433, 10453,10457,10459,10463,10477,10487,10499,10501,10513,10529,10531,10559,10567,10589,10597,10601,1060 7,10613,10627,10631,10639,10651,10657,10663,10667,10687,10691,10709,10711,10723,10729,10733,10739,10 753,10771,10781,10789,10799,10831,10837,10847,10853,10859,10861,10867,10883,10889,10891,10903,10909, 10937,10939,10949,10957,10973,10979,10987,10993,11003,11027,11047,11057,11059,11069,11071,11083,1108 7,11093,11113,11117,11119,11131,11149,11159,11161,11171,11173,11177,11197,11213,11239,11243,11251,11 257,11261,11273,11279,11287,11299,11311,11317,11321,11329,11351,11353,11369,11383,11393,11399,11411, 11423,11437,11443,11447,11467,11471,11483,11489,11491,11497,11503,11519,11527,11549,11551,11579,1158 7,11593,11597,11617,11621,11633,11657,11677,11681,11689,11699,11701,11717,11719,11731,11743,11777,11 779,11783,11789,11801,11807,11813,11821,11827,11831,11833,11839,11863,11867,11887,11897,11903,11909, 11923,11927,11933,11939
,11941,11953,11959,11969,11971,11981,11987,12007,12011,12037,12041,12043,12049,12071,12073,12097,121 01,12107,12109,12113,12119,12143,12149,12157,12161,12163,12197,12203,12211,12227,12239,12241,12251,1 2253,12263,12269,12277,12281,12289,12301,12323,12329,12343,12347,12373,12377,12379,12391,12401,12409 ,12413,12421,12433,12437,12451,12457,12473,12479,12487,12491,12497,12503,12511,12517,12527,12539,125 41,12547,12553,12569,12577,12583,12589,12601,12611,12613,12619,12637,12641,12647,12653,12659,12671,1 2689,12697,12703,12713,12721,12739,12743,12757,12763,12781,12791,12799,12809,12821,12823,12829,12841 ,12853,12889,12893,12899,12907,12911,12917,12919,12923,12941,12953,12959,12967,12973,12979,12983,130 01,13003,13007,13009,13033,13037,13043,13049,13063,13093,13099,13103,13109,13121,13127,13147,13151,1 3159,13163,13171,13177,13183,13187,13217,13219,13229,13241,13249,13259,13267,13291,13297,13309,13313 ,13327,13331,13337,13339,13367,13381,13397,13399,13411,13417,13421,13441,13451,13457,13463,13469,134 77,13487,13499,13513,13
523,13537,13553,13567,13577,13591,13597,13613,13619,13627,13633,13649,13669,13679,13681,13687,13691, 13693,13697,13709,13711,13721,13723,13729,13751,13757,13759,13763,13781,13789,13799,13807,13829,1383 1,13841,13859,13873,13877,13879,13883,13901,13903,13907,13913,13921,13931,13933,13963,13967,13997,13 999,14009,14011,14029,14033,14051,14057,14071,14081,14083,14087,14107,14143,14149,14153,14159,14173, 14177,14197,14207,14221,14243,14249,14251,14281,14293,14303,14321,14323,14327,14341,14347,14369,1438 7,14389,14401,14407,14411,14419,14423,14431,14437,14447,14449,14461,14479,14489,14503,14519,14533,14 537,14543,14549,14551,14557,14561,14563,14591,14593,14621,14627,14629,14633,14639,14653,14657,14669, 14683,14699,14713,14717,14723,14731,14737,14741,14747,14753,14759,14767,14771,14779,14783,14797,1481 3,14821,14827,14831,14843,14851,14867,14869,14879,14887,14891,14897,14923,14929,14939,14947,14951,14 957,14969,14983,15013,15017,15031,15053,15061,15073,15077,15083,15091,15101,15107,15121,15131,15137, 15139,15149,15161,15173
,15187,15193,

15199,15217,15227,15233,15241,15259,15263,15269,15271,15277,15287,15289,15299,15307,15313,15319,1532 9,15331,15349,15359,15361,15373,15377,15383,15391,15401,15413,15427,15439,15443,15451,15461,15467,15 473,15493,15497,15511,15527,15541,15551,15559,15569,15581,15583,15601,15607,15619,15629,15641,15643, 15647,15649,15661,15667,15671,15679,15683,15727,15731,15733,15737,15739,15749,15761,15767,15773,1578 7,15791,15797,15803,15809,15817,15823,15859,15877,15881,15887,15889,15901,15907,15913,15919,15923,15 937,15959,15971,15973,15991,16001,16007,16033,16057,16061,16063,16067,16069,16073,16087,16091,16097, 16103,16111,16127,16139,16141,16183,16187,16189,16193,16217,16223,16229,16231,16249,16253,16267,1627 3,16301,16319,16333,16339,16349,16361,16363,16369,16381,16411,16417,16421,16427,16433,16447,16451,16 453,16477,16481,16487,16493,16519,16529,16547,16553,16561,16567,16573,16603,16607,16619,16631,16633, 16649,16651,16657,16661,16673,16691,16693,16699,16703,16729,16741,16747,16759,16763,16787,16811,1682 3,16829,16
831,16843,16871,16879,16883,16889,16901,16903,16921,16927,16931,16937,16943,16963,16979,16981,16987, 16993,17011,17021,17027,17029,17033,17041,17047,17053,17077,17093,17099,17107,17117,17123,17137,1715 9,17167,17183,17189,17191,17203,17207,17209,17231,17239,17257,17291,17293,17299,17317,17321,17327,17 333,17341,17351,17359,17377,17383,17387,17389,17393,17401,17417,17419,17431,17443,17449,17467,17471, 17477,17483,17489,17491,17497,17509,17519,17539,17551,17569,17573,17579,17581,17597,17599,17609,1762 3,17627,17657,17659,17669,17681,17683,17707,17713,17729,17737,17747,17749,17761,17783,17789,17791,17 807,17827,17837,17839,17851,17863,17881,17891,17903,17909,17911,17921,17923,17929,17939,17957,17959, 17971,17977,17981,17987,17989,18013,18041,18043,18047,18049,18059,18061,18077,18089,18097,18119,1812 1,18127,18131,18133,18143,18149,18169,18181,18191,18199,18211,18217,18223,18229,18233,18251,18253,18 257,18269,18287,18289,18301,18307,18311,18313,18329,18341,18353,18367,18371,18379,18397,18401,18413, 18427,18433,18439,18443
,18451,18457,18461,18481,18493,18503,18517,18521,18523,18539,18541,18553,18583,18587,18593,18617,186 37,18661,18671,18679,18691,18701,18713,18719,18731,18743,18749,18757,18773,18787,18793,18797,18803,1 8839,18859,18869,18899,18911,18913,18917,18919,18947,18959,18973,18979,19001,19009,19013,19031,19037 ,19051,19069,19073,19079,19081,19087,19121,19139,19141,19157,19163,19181,19183,19207,19211,19213,192 19,19231,19237,19249,19259,19267,19273,19289,19301,19309,19319,19333,19373,19379,19381,19387,19391,1 9403,19417,19421,19423,19427,19429,19433,19441,19447,19457,19463,19469,19471,19477,19483,19489,19501 ,19507,19531,19541,19543,19553,19559,19571,19577,19583,19597,19603,19609,19661,19681,19687,19697,196 99,19709,19717,19727,19739,19751,19753,19759,19763,19777,19793,19801,19813,19819,19841,19843,19853,1 9861,19867,19889,19891,19913,19919,19927,19937,19949,19961,19963,19973,19979,19991,19993,19997,20011 ,20021,20023,20029,20047,20051,20063,20071,20089,20101,20107,20113,20117,20123,20129,20143,20147,201 49,20161,20173,20177,20
183,20201,20219,20231,20233,20249,20261,20269,20287,20297,20323,20327,20333,20341,20347,20353,20357, 20359,20369,20389,20393,20399,20407,20411,20431,20441,20443,20477,20479,20483,20507,20509,20521,2053 3,20543,20549,20551,20563,20593,20599,20611,20627,20639,20641,20663,20681,20693,20707,20717,20719,20 731,20743,20747,20749,20753,20759,20771,20773,20789,20807,20809,20849,20857,20873,20879,20887,20897, 20899,20903,20921,20929,20939,20947,20959,20963,20981,20983,21001,21011,21013,21017,21019,21023,2103 1,21059,21061,21067,21089,21101,21107,21121,21139,21143,21149,21157,21163,21169,21179,21187,21191,21 193,21211,21221,21227,21247,21269,21277,21283,21313,21317,21319,21323,21341,21347,21377,21379,21383, 21391,21397,21401,21407,21419,21433,21467,21481,21487,21491,21493,21499,21503,21517,21521,21523,2152 9,21557,21559,21563,21569,21577,21587,21589,21599,21601,21611,21613,21617,21647,21649,21661,21673,21 683,21701,21713,21727,21737,21739,21751,21757,21767,21773,21787,21799,21803,21817,21821,21839,21841, 21851,21859,21863,21871
,21881,21893,21911,21929,21937,21943,21961,21977,21991,21997,22003,22013,22027,22031,22037,22039,220 51,22063,22067,22073,22079,22091,22093,22109,22111,22123,22129,22133,22147,22153,22157,22159,22171,2 2189,22193,22229,22247,22259,22271,22273,22277,22279,22283,22291,22303,22307,22343,22349,22367,22369 ,22381,22391,22397,22409,22433,22441,22447,22453,22469,22481,22483,22501,22511,22531,22541,22543,225 49,22567,22571,22573,22613,22619,22621,22637,22639,22643,22651,22669,22679,22691,22697,22699,22709,2 2717,22721,22727,22739,22741,22751,22769,22777,22783,22787,22807,22811,22817,22853,22859,22861,22871 ,22877,22901,22907,22921,22937,22943,22961,22963,22973,22993,23003,23011,23017,23021,23027,23029,230 39,23041,23053,23057,23059,23063,23071,23081,23087,23099,23117,23131,23143,23159,23167,23173,23189,2 3197,23201,23203,23209,23227,23251,23269,23279,23291,23293,23297,23311,23321,23327,23333,23339,23357 ,23369,23371,23399,23417,23431,23447,23459,23473,23497,23509,23531,23537,23539,23549,23557,23561,235 63,23567,23581,23593,23
599,23603,23609,23623,23627,23629,23633,23663,23669,23671,23677,23687,23689,23719,23741,23743,23747, 23753,23761,23767,23773,23789,23801,23813,23819,23827,23831,23833,23857,23869,23873,23879,23887,2389 3,23899,23909,23911,23917,23929,23957,23971,23977,23981,23993,24001,24007,24019,24023,24029,24043,24 049,24061,24071,24077,24083,24091,24097,24103,24107,24109,24113,24121,24133,24137,24151,24169,24179, 24181,24197,24203,24223,24229,24239,24247,24251,24281,24317,24329,24337,24359,24371,24373,24379,2439 1,24407,24413,24419,24421,24439,24443,24469,24473,24481,24499,24509,24517,24527,24533,24547,24551,24 571,24593,24611,24623,24631,24659,24671,24677,24683,24691,24697,24709,24733,24749,24763,24767,24781, 24793,24799,24809,24821,24841,24847,24851,24859,24877,24889,24907,24917,24919,24923,24943,24953,2496 7,24971,24977,24979,24989,25013,25031,25033,25037,25057,25073,25087,25097,25111,25117,25121,25127,25 147,25153,25163,25169,25171,25183,25189,25219,25229,25237,25243,25247,25253,25261,25301,25303,25307, 25309,25321,25339,25343
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059,27061,27067,27073,27077,27091,27103,27107,27109,27127,27143,27179,27191,27197,27211,27239,27241, 27253,27259,27271,27277,27281,27283,27299,27329,27337,27361,27367,27397,27407,27409,27427,27431,2743 7,27449,27457,27479,27481,27487,27509,27527,27529,27539,27541,27551,27581,27583,27611,27617,27631,27 647,27653,27673,27689,27691,27697,27701,27733,27737,27739,27743,27749,27751,27763,27767,27773,27779, 27791,27793,27799,27803,27809,27817,27823,27827,27847,27851,27883,27893,27901,27917,27919,27941,2794 3,27947,27953,27961,27967,27983,27997,28001,28019,28027,28031,28051,28057,28069,28081,28087,28097,28 099,28109,28111,28123,28151,28163,28181,28183,28201,28211,28219,28229,28277,28279,28283,28289,28297, 28307,28309,28319,28349,28351,28387,28393,28403,28409,28411,28429,28433,28439,28447,28463,28477,2849 3,28499,28513,28517,28537,28541,28547,28549,28559,28571,28573,28579,28591,28597,28603,28607,28619,28 621,28627,28631,28643,28649,28657,28661,28663,28669,28687,28697,28703,28711,28723,28729,28751,28753, 28759,28771,28789,28793
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141,34147,34157,34159,34171,34183,34211,34213,34217,34231,34253,34259,34261,34267,34273,34283,34297, 34301,34303,34313,34319,34327,34337,34351,34361,34367,34369,34381,34403,34421,34429,34439,34457,3446 9,34471,34483,34487,34499,34501,34511,34513,34519,34537,34543,34549,34583,34589,34591,34603,34607,34 613,34631,34649,34651,34667,34673,34679,34687,34693,34703,34721,34729,34739,34747,34757,34759,34763, 34781,34807,34819,34841,34843,34847,34849,34871,34877,34883,34897,34913,34919,34939,34949,34961,3496 3,34981,35023,35027,35051,35053,35059,35069,35081,35083,35089,35099,35107,35111,35117,35129,35141,35 149,35153,35159,35171,35201,35221,35227,35251,35257,35267,35279,35281,35291,35311,35317,35323,35327, 35339,35353,35363,35381,35393,35401,35407,35419,35423,35437,35447,35449,35461,35491,35507,35509,3552 1,35527,35531,35533,35537,35543,35569,35573,35591,35593,35597,35603,35617,35671,35677,35729,35731,35 747,35753,35759,35771,35797,35801,35803,35809,35831,35837,35839,35851,35863,35869,35879,35897,35899, 35911,35923,35933,35951
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657,37663,37691,37693,37699,37717,37747,37781,37783,37799,37811,37813,37831,37847,37853,37861,37871, 37879,37889,37897,37907,37951,37957,37963,37967,37987,37991,37993,37997,38011,38039,38047,38053,3806 9,38083,38113,38119,38149,38153,38167,38177,38183,38189,38197,38201,38219,38231,38237,38239,38261,38 273,38281,38287,38299,38303,38317,38321,38327,38329,38333,38351,38371,38377,38393,38431,38447,38449, 38453,38459,38461,38501,38543,38557,38561,38567,38569,38593,38603,38609,38611,38629,38639,38651,3865 3,38669,38671,38677,38693,38699,38707,38711,38713,38723,38729,38737,38747,38749,38767,38783,38791,38 803,38821,38833,38839,38851,38861,38867,38873,38891,38903,38917,38921,38923,38933,38953,38959,38971, 38977,38993,39019,39023,39041,39043,39047,39079,39089,39097,39103,39107,39113,39119,39133,39139,3915 7,39161,39163,39181,39191,39199,39209,39217,39227,39229,39233,39239,39241,39251,39293,39301,39313,39 317,39323,39341,39343,39359,39367,39371,39373,39383,39397,39409,39419,39439,39443,39451,39461,39499, 39503,39509,39511,39521
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387,41389,41399,41411,41413,41443,41453,41467,41479,41491,41507,41513,41519,41521,41539,41543,41549, 41579,41593,41597,41603,41609,41611,41617,41621,41627,41641,41647,41651,41659,41669,41681,41687,4171 9,41729,41737,41759,41761,41771,41777,41801,41809,41813,41843,41849,41851,41863,41879,41887,41893,41 897,41903,41911,41927,41941,41947,41953,41957,41959,41969,41981,41983,41999,42013,42017,42019,42023, 42043,42061,42071,42073,42083,42089,42101,42131,42139,42157,42169,42179,42181,42187,42193,42197,4220 9,42221,42223,42227,42239,42257,42281,42283,42293,42299,42307,42323,42331,42337,42349,42359,42373,42 379,42391,42397,42403,42407,42409,42433,42437,42443,42451,42457,42461,42463,42467,42473,42487,42491, 42499,42509,42533,42557,42569,42571,42577,42589,42611,42641,42643,42649,42667,42677,42683,42689,4269 7,42701,42703,42709,42719,42727,42737,42743,42751,42767,42773,42787,42793,42797,42821,42829,42839,42 841,42853,42859,42863,42899,42901,42923,42929,42937,42943,42953,42961,42967,42979,42989,43003,43013, 43019,43037,43049,43051
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959,44963,44971,44983,44987,45007,45013,45053,45061,45077,45083,45119,45121,45127,45131,45137,45139, 45161,45179,45181,45191,45197,45233,45247,45259,45263,45281,45289,45293,45307,45317,45319,45329,4533 7,45341,45343,45361,45377,45389,45403,45413,45427,45433,45439,45481,45491,45497,45503,45523,45533,45 541,45553,45557,45569,45587,45589,45599,45613,45631,45641,45659,45667,45673,45677,45691,45697,45707, 45737,45751,45757,45763,45767,45779,45817,45821,45823,45827,45833,45841,45853,45863,45869,45887,4589 3,45943,45949,45953,45959,45971,45979,45989,46021,46027,46049,46051,46061,46073,46091,46093,46099,46 103,46133,46141,46147,46153,46171,46181,46183,46187,46199,46219,46229,46237,46261,46271,46273,46279, 46301,46307,46309,46327,46337,46349,46351,46381,46399,46411,46439,46441,46447,46451,46457,46471,4647 7,46489,46499,46507,46511,46523,46549,46559,46567,46573,46589,46591,46601,46619,46633,46639,46643,46 649,46663,46679,46681,46687,46691,46703,46723,46727,46747,46751,46757,46769,46771,46807,46811,46817, 46819,46829,46831,46853
,

46861,46867,46877,46889,46901,46919,46933,46957,46993,46997,47017,47041,47051,47057,47059,47087,4709 3,47111,47119,47123,47129,47137,47143,47147,47149,47161,47189,47207,47221,47237,47251,47269,47279,47 287,47293,47297,47303,47309,47317,47339,47351,47353,47363,47381,47387,47389,47407,47417,47419,47431, 47441,47459,47491,47497,47501,47507,47513,47521,47527,47533,47543,47563,47569,47581,47591,47599,4760 9,47623,47629,47639,47653,47657,47659,47681,47699,47701,47711,47713,47717,47737,47741,47743,47777,47 779,47791,47797,47807,47809,47819,47837,47843,47857,47869,47881,47903,47911,47917,47933,47939,47947, 47951,47963,47969,47977,47981,48017,48023,48029,48049,48073,48079,48091,48109,48119,48121,48131,4815 7,48163,48179,48187,48193,48197,48221,48239,48247,48259,48271,48281,48299,48311,48313,48337,48341,48 353,48371,48383,48397,48407,48409,48413,48437,48449,48463,48473,48479,48481,48487,48491,48497,48523, 48527,48533,48539,48541,48563,48571,48589,48593,48611,48619,48623,48647,48649,48661,48673,48677,4867 9,48731,48733,48751,48
757,48761,48767,48779,48781,48787,48799,48809,48817,48821,48823,48847,48857,48859,48869,48871,48883, 48889,48907,48947,48953,48973,48989,48991,49003,49009,49019,49031,49033,49037,49043,49057,49069,4908 1,49103,49109,49117,49121,49123,49139,49157,49169,49171,49177,49193,49199,49201,49207,49211,49223,49 253,49261,49277,49279,49297,49307,49331,49333,49339,49363,49367,49369,49391,49393,49409,49411,49417, 49429,49433,49451,49459,49463,49477,49481,49499,49523,49529,49531,49537,49547,49549,49559,49597,4960 3,49613,49627,49633,49639,49663,49667,49669,49681,49697,49711,49727,49739,49741,49747,49757,49783,49 787,49789,49801,49807,49811,49823,49831,49843,49853,49871,49877,49891,49919,49921,49927,49937,49939, 49943,49957,49991,49993,49999,


Thankyou, thankyou very much :)

Hehe, you should have seen the load this put on my CPU to work it all out...

The 234th one looks a bit like Bernard Cribbins.

That should probably take about 0.5 seconds if you do it right..:) I once made a similar app when I had a 120Mhz pc with 64Mb ram...when I came to a file that was 250Mb I gave up...:)

That's fascinating note.

Theres always a better way to do things, i printed these using Debug.Print... which now seems the slower option...

Any hey wossy, i agree the 234th does look a bit like Bernard Cribbins :lol:

You have a lot of spare time.. 8-)

Great :) You have saved me a lot of work, it just so happens that I need the first 50000 crime numbers. Now I can devte my night to guarding my new sun flowers from hungrey slugs. Thanks very much.

Greatone.....get a life, or even better get a girlfriend to keep you occupied ;)

Quote:

---

Originally Posted by visualAd

Great :) You have saved me a lot of work, it just so happens that I need the first 50000 crime numbers. Now I can devte my night to guarding my new sun flowers from hungrey slugs. Thanks very much.

---

Do i detect a hint of sarcasm :P

I have a life, just not a very good one... and i have agirlfriend, problem is shes 46 miles away right now :'(

1 is not prime.

And, since your list ends with 49,999 I think you have less than 50 thousand prime numbers listed.

:wave:

Quote:

---

Originally Posted by NotLKH

1 is not prime.

And, since your list ends with 49,999 I think you have less than 50 thousand prime numbers listed.

:wave:

---

Finall someone notices the blatant mistake with the thread title, as for #1 not being prime could you explain why ? its only divisible by 1 and itself...

Quote:

---

Originally Posted by thegreatone

I have a life, just not a very good one... and i have agirlfriend, problem is shes 46 ...

---

Wossname never saw that as a problem :D

Quote:

---

Originally Posted by thegreatone

Finall someone notices the blatant mistake with the thread title, as for #1 not being prime could you explain why ? its only divisible by 1 and itself...

---

The following site explains why:

http://mathworld.wolfram.com/PrimeNumber.html

Quote:

---

Originally Posted by NotLKH

The following site explains why:

http://mathworld.wolfram.com/PrimeNumber.html

---

Ah, i see why now :) Thankyou so much, this site is really very good, thanks :thumb:

Quote:

---

Originally Posted by thegreatone

I have a life, just not a very good one... and i have a girlfriend, problem is shes 46 miles away right now :'(

---

:eek:

Pity that girlfriend wasn't 1 mile further away then she would be in a prime location.

I wrote an application that counts characters. Your first post has 9,329 characters, 2nd 9,295, 3rd, 9,307 and last 1,769 if you leave out the words. More info that hardly anyone will be interested in. If they allowed posts of 30,000 characters you could have gotten it all in one post.

Quote:

---

Originally Posted by TriLogic

:eek:

Pity that girlfriend wasn't 1 mile further away then she would be in a prime location.

---

:thumb: way to dig up a 4 year old thread

Normally, old threads shouldn't be bumped, but this was well worth it :afrog:

I only regret that it took somebody four years to think up that pun. What is this world coming to?

Quote:

---

Originally Posted by Shaggy Hiker

I only regret that it took somebody four years to think up that pun. What is this world coming to?

---

Yes at this rate Mersenne primes can be calculated faster than prime puns.

Quote:

---

Originally Posted by visualAd

Great :) You have saved me a lot of work, it just so happens that I need the first 50000 crime numbers. Now I can devte my night to guarding my new sun flowers from hungrey slugs. Thanks very much.

---

Yes, in this case they were "50000 crime numbers". I think that if thegreatone is not too busy he should re-align them all properly.

Quote:

---

Originally Posted by mendhak

Normally, old threads shouldn't be bumped, but this was well worth it :afrog:

---

Agreed. Check the Maths threads. Right now there's a guy from Indiana trying to store the first billion or so primes on disk. Storm is creating a storm of followers, including me. I'm guilty as well. :rolleyes:

funny it's all the same ppl talking giberish !!!

maybe in 4 years i will see this again??

It's very important that everyone memorizes the first 50,000 prime numbers. They'll be so many times that that information will be useful to know it will just make your head spin.

Quote:

---

Originally Posted by EntityX

It's very important that everyone memorizes the first 50,000 prime numbers.

---

Lucky I have a photographic memory. :afrog:

Quote:

---

Originally Posted by Valleysboy1978

Greatone.....get a life, or even better get a girlfriend to keep you occupied ;)

---

Not an option for many. :rolleyes:

Quote:

---

Originally Posted by storm5510

Not an option for many. :rolleyes:

---

Hi D,

Fortunately, thegreatone had a partner but he informed us that she was 46 miles away at the time.

Personally I'm too obsessed with prime numbers to have a partner or a life :blush:

Quote:

---

Originally Posted by TriLogic

Personally I'm too obsessed with prime numbers to have a partner or a life :blush:

---

I'm obsessed too. It is sanity maintenance for me. If I couldn't do this, I would be insane by now. I think I already am, a little.

:bigyello:

Is it not true that a prime number appears an average of every 5.8 whole numbers as the whole numbers increase, irrespective of size?

If not, what is the average and how does it fluctuate? :ehh:

At 8.8 billion, the average number is a little over 9%. One would need to collect samples at regular intervals and graph it. Something I could have done, and didn't.

:blush:

Quote:

---

Originally Posted by storm5510

At 8.8 billion, the average number is a little over 9%. One would need to collect samples at regular intervals and graph it. Something I could have done, and didn't.

:blush:

---

Well, Storm, your sample size is rather huge (understatement of the year).

As you have accumulated multitudes of files in sequential order, you can easily obain the average interval between primes as the size of the prime increases. There are 25 primes within the first 97 whole numbers (ratio = 26%), 69 within the first 400 (ratio = 17%) and it appears to drop continuously thereafter.

Plotting individual and cumulative average percentages in 100- or perhaps 1000-number ascending samples could prove interesting. I believe that what you are saying is that it eventually gets down to 9%. Using curvilinear regression, similar to a log curve, we might project a limit of 7% as N --> infinity.

As usual, I'm sure someone has already done this and published it somewhere in the math journals. Years ago I used to dig this stuff up.

Quote:

---

Originally Posted by Code Doc

Plotting individual and cumulative average percentages in 100- or perhaps 1000-number ascending samples could prove interesting. I believe that what you are saying is that it eventually gets down to 9%. Using curvilinear regression, similar to a log curve, we might project a limit of 7% as N --> infinity.

---

As the ratio of prime numbers diminishes in relation to increase in numbers then we would have to project eventual 0% --> infinity. But it is proven that primes are infinite and we have no reason to believe that the ratio will ever become fixed. So what happens after .001% as N --> infinity.

As I have noticed when starting over with nothing, the percentage started out high then drops dramatically. It begins to level out but never quite gets there. Two days ago, I was at magnitude 7.5 billion. The percentage was 9.22. Today, the percentage is 9.14 at magnitude 9.05 billion. This is a 0.08% decrease.

The gaps between the primes widens and occurrences of pairs diminishes greatly. Where this goes, I'm not sure, but maybe I can chart just a tiny fraction of it. I suppose I could go back and dig through the data files. With over 4,700, that seems sort of impractical.

Someone can keep themselves busy by trying to caluculate what percentage of prime numbers there are between gogool (10 ^ 100) and 10 gogool (10 ^ 101).

Quote:

---

Originally Posted by EntityX

Someone can keep themselves busy by trying to caluculate what percentage of prime numbers there are between gogool (10 ^ 100) and 10 gogool (10 ^ 101).

---

You say that like it's a bit funny. It may be just a bit. It is also possible to do...

I don't doubt that it's possible and I would actually be interested to know what the percentage is. I misspelled googol. According to wikipedia

Quote:

---

A googol is greater than the number of atoms in the observable universe, which has been variously estimated from 10 ^ 79 up to 10 ^ 81.

---

Quote:

---

Originally Posted by TriLogic

As the ratio of prime numbers diminishes in relation to increase in numbers then we would have to project eventual 0% --> infinity. But it is proven that primes are infinite and we have no reason to believe that the ratio will ever become fixed. So what happens after .001% as N --> infinity.

---

That may be true as long as the curvilinear function is continuous and you can wait forever. But, let's be realistic. Assume we can calculate primes for several years with today's high speed computers as Storm is doing. Then go up a notch and use a Cray. I have a feeling that you would still never obtain in your lifetime a ratio of (Number of Primes / Largest Prime) that was less than 0.05.

I am judging this based on Storm's findings alone, and that's rather good empirical evidence. Can anyone find a published discussion of this ratio: (Number of Primes / Largest Prime)? If so, what is your conclusion?

This is the straight forward algorithm I can come up with. I am sure there are ingenious algorithms that are super weird, but fast. Does anyone know what kind of algorithm software like mathematica uses?

Code:

---

int* primes = new int[500000];
primes[0] = 2;
int primesCount = 1;
int testNumber = 3;

cout << "Begin." << endl;
while (primesCount < 500000)
{
        int maxTest = (int)sqrt((float)testNumber);
        bool isPrime = true;
        for (int i = 0; primes[i] <= maxTest; i++)
        {
                if (testNumber &#37; primes[i] == 0)
                {
                        isPrime = false;
                        break;
                }
        }
        if (isPrime)
        {
                primes[primesCount] = testNumber;
                primesCount++;
        }
        testNumber += 2;
}
cout << "Last prime calculated: " << primes[499999] << endl;
cin.get();
delete[] primes;

---

My code doesn't do anything with the primes it calculates except show the last one. But it could easily be changed to output the numbers to a file or something.

Quote:

---

Originally Posted by Arrow_Raider

This is the straight forward algorithm I can come up with. I am sure there are ingenious algorithms that are super weird, but fast. Does anyone know what kind of algorithm software like mathematica uses?

Code:

---

int* primes = new int[500000];
primes[0] = 2;
int primesCount = 1;
int testNumber = 3;

cout << "Begin." << endl;
while (primesCount < 500000)
{
        int maxTest = (int)sqrt((float)testNumber);
        bool isPrime = true;
        for (int i = 0; primes[i] <= maxTest; i++)
        {
                if (testNumber % primes[i] == 0)
                {
                        isPrime = false;
                        break;
                }
        }
        if (isPrime)
        {
                primes[primesCount] = testNumber;
                primesCount++;
        }
        testNumber += 2;
}
cout << "Last prime calculated: " << primes[499999] << endl;
cin.get();
delete[] primes;

---

My code doesn't do anything with the primes it calculates except show the last one. But it could easily be changed to output the numbers to a file or something.

---

You're using a memory array. That's fine if you want a short list. Could this array hold over 422 million elements of 64-bit unsigned length? No. So, you see, this is not a practical way.

I have no limit on number size or numbers to find. It's all to infinity.

I can't read C++ very well, and can write none.