An array of naturals

(generated by a permutation of the prime numbers)

Hello SeqFans,

Jean-Marc Falcoz has computed 70 terms of the first line hereunder -- and the resulting array (see end of page).

The constraints were:

1) the first line of the array must be a permutation of the primes;

2) the array, seen as a whole, must be a permutation of the naturals;

3) any two neighboring integers have their absolute first difference

written on the line below, between them.

2  3   13  47   197   11  29   443  397   1321  4831   15559    211     5      19    41   293   113   971 ...

1  10  34  150  186   18  414   46   924   3510  10728   15348    206    14     22   252   180   858 ...

9  24  116  36   168  396  368  878   2586  7218    4620   15142    192     8    230   72   678 ...

15  92   80  132   228   28  510  1708   4632  2598   10522   14950    184   222   158  606 ...

77   12  52    96   200  482 1198  2924   2034   7924    4428   14766    38    64   448 ...

65  40   44   104  282  716  1726   890   5890    3496   10338   14728   26   384 ...

25   4    60   178  434 1010   836   5000   2394    6842   4390    14702  358 ...

21  56   118   256 576   174   4164   2606   4448   2452   10312   14344 ...

35   62   138   320  402  3990  1558   1842    1996   7860    4032  ...

27   76   182   82  3588  2432   284    154    5864    3828 ...

49   106  100  3506  1156  2148    130    5710   2036 ...

57   6   3406  2350   992   2018   5580   3674 ...

51  3400  1056  1358  1026   3562   1906 ...

3349   2344  302  332    2536  1656 ...

1005   2042  30    2204   880 ...

1037  2012  2174  1324 ...

975   162   850 ...

813   688 ...

125 ...

After 70 terms (first line), the smallest missing prime is 17 and the smallest missing non-prime is 39.

The first line is the lexicographically first one, as the building method forced the next prime to be the smallest available one, not yet present and not leading to a contradiction.

All odd non-primes are on the first descending diagonal from the left, and only there.

Many thanks to Jean-Marc Falcoz for his computer skills, to Maximilian Hasler and Alexandre Wajnberg (for their support).

This is now http://oeis.org/A203985 and http://oeis.org/A204137

É.

__________

[French explanation]:

1) la première ligne est une permutation des nombres premiers;

2) la différence absolue entre deux nombres voisins du tableau figure à la ligne du dessous, entre eux;

3) l’ensemble du tableau est une permutation des naturels.

Tableau de _70_ lignes (justifié à gauche) :

{2,3,13,47,197,11,29,443,397,1321,4831,15559,211,5,19,41,293,113,971,419,2687,1087,1709,5851,23629,83,17341,65171,268969,20753,690607,4273,1289,81931,56267,3025961,6343,41927,1455241,14255011,21557,733,44351,7,12347,131,199,757,1021,2837,337,6481,191,5849,7489,26119,1151,24239,76231,262049,607,9341,727427,37,5189,210809,1873441,44017,373049,6102023}

{1,10,34,150,186,18,414,46,924,3510,10728,15348,206,14,22,252,180,858,552,2268,1600,622,4142,17778,23546,17258,47830,203798,248216,669854,686334,2984,80642,25664,2969694,3019618,35584,1413314,12799770,14233454,20824,43618,44344,12340,12216,68,558,264,1816,2500,6144,6290,5658,1640,18630,24968,23088,51992,185818,261442,8734,718086,727390,5152,205620,1662632,1829424,329032,5728974}

{9,24,116,36,168,396,368,878,2586,7218,4620,15142,192,8,230,72,678,306,1716,668,978,3520,13636,5768,6288,30572,155968,44418,421638,16480,683350,77658,54978,2944030,49924,2984034,1377730,11386456,1433684,14212630,22794,726,32004,124,12148,490,294,1552,684,3644,146,632,4018,16990,6338,1880,28904,133826,75624,252708,709352,9304,722238,200468,1457012,166792,1500392,5399942}

{15,92,80,132,228,28,510,1708,4632,2598,10522,14950,184,222,158,606,372,1410,1048,310,2542,10116,7868,520,24284,125396,111550,377220,405158,666870,605692,22680,2889052,2894106,2934110,1606304,10008726,9952772,12778946,14189836,22068,31278,31880,12024,11658,196,1258,868,2960,3498,486,3386,12972,10652,4458,27024,104922,58202,177084,456644,700048,712934,521770,1256544,1290220,1333600,3899550}

{77,12,52,96,200,482,1198,2924,2034,7924,4428,14766,38,64,448,234,1038,362,738,2232,7574,2248,7348,23764,101112,13846,265670,27938,261712,61178,583012,2866372,5054,40004,1327806,8402422,55954,2826174,1410890,14167768,9210,602,19856,366,11462,1062,390,2092,538,3012,2900,9586,2320,6194,22566,77898,46720,118882,279560,243404,12886,191164,734774,33676,43380,2565950}

{65,40,44,104,282,716,1726,890,5890,3496,10338,14728,26,384,214,804,676,376,1494,5342,5326,5100,16416,77348,87266,251824,237732,233774,200534,521834,2283360,2861318,34950,1287802,7074616,8346468,2770220,1415284,12756878,14158558,8608,19254,19490,11096,10400,672,1702,1554,2474,112,6686,7266,3874,16372,55332,31178,72162,160678,36156,230518,178278,543610,701098,9704,2522570}

{25,4,60,178,434,1010,836,5000,2394,6842,4390,14702,358,170,590,128,300,1118,3848,16,226,11316,60932,9918,164558,14092,3958,33240,321300,1761526,577958,2826368,1252852,5786814,1271852,5576248,1354936,11341594,1401680,14149950,10646,236,8394,696,9728,1030,148,920,2362,6574,580,3392,12498,38960,24154,40984,88516,124522,194362,52240,365332,157488,691394,2512866}

{21,56,118,256,576,174,4164,2606,4448,2452,10312,14344,188,420,462,172,818,2730,3832,210,11090,49616,51014,154640,150466,10134,29282,288060,1440226,1183568,2248410,1573516,4533962,4514962,4304396,4221312,9986658,9939914,12748270,14139304,10410,8158,7698,9032,8698,882,772,1442,4212,5994,2812,9106,26462,14806,16830,47532,36006,69840,142122,313092,207844,533906,1821472}

{35,62,138,320,402,3990,1558,1842,1996,7860,4032,14156,232,42,290,646,1912,1102,3622,10880,38526,1398,103626,4174,140332,19148,258778,1152166,256658,1064842,674894,2960446,19000,210566,83084,5765346,46744,2808356,1391034,14128894,2252,460,1334,334,7816,110,670,2770,1782,3182,6294,17356,11656,2024,30702,11526,33834,72282,170970,105248,326062,1287566}

{27,76,182,82,3588,2432,284,154,5864,3828,10124,13924,190,248,356,1266,810,2520,7258,27646,37128,102228,99452,136158,121184,239630,893388,895508,808184,389948,2285552,2941446,191566,127482,5682262,5718602,2761612,1417322,12737860,14126642,1792,874,1000,7482,7706,560,2100,988,1400,3112,11062,5700,9632,28678,19176,22308,38448,98688,65722,220814,961504}

{49,106,100,3506,1156,2148,130,5710,2036,6296,3800,13734,58,108,910,456,1710,4738,20388,9482,65100,2776,36706,14974,118446,653758,2120,87324,418236,1895604,655894,2749880,64084,5554780,36340,2956990,1344290,11320538,1388782,14124850,918,126,6482,224,7146,1540,1112,412,1712,7950,5362,3932,19046,9502,3132,16140,60240,32966,155092,740690}

{57,6,3406,2350,992,2018,5580,3674,4260,2496,9934,13676,50,802,454,1254,3028,15650,10906,55618,62324,33930,21732,103472,535312,651638,85204,330912,1477368,1239710,2093986,2685796,5490696,5518440,2920650,1612700,9976248,9931756,12736068,14123932,792,6356,6258,6922,5606,428,700,1300,6238,2588,1430,15114,9544,6370,13008,44100,27274,122126,585598}

{51,3400,1056,1358,1026,3562,1906,586,1764,7438,3742,13626,752,348,800,1774,12622,4744,44712,6706,28394,12198,81740,431840,116326,566434,245708,1146456,237658,854276,591810,2804900,27744,2597790,1307950,8363548,44492,2804312,1387864,14123140,5564,98,664,1316,5178,272,600,4938,3650,1158,13684,5570,3174,6638,31092,16826,94852,463472}

{3349,2344,302,332,2536,1656,1320,1178,5674,3696,9884,12874,404,452,974,10848,7878,39968,38006,21688,16196,69542,350100,315514,450108,320726,900748,908798,616618,262466,2213090,2777156,2570046,1289840,7055598,8319056,2759820,1416448,12735276,14117576,5466,566,652,3862,4906,328,4338,1288,2492,12526,8114,2396,3464,24454,14266,78026,368620}

{1005,2042,30,2204,880,336,142,4496,1978,6188,2990,12470,48,522,9874,2970,32090,1962,16318,5492,53346,280558,34586,134594,129382,580022,8050,292180,354152,1950624,564066,207110,1280206,5765758,1263458,5559236,1343372,11318828,1382300,14112110,4900,86,3210,1044,4578,4010,3050,1204,10034,4412,5718,1068,20990,10188,63760,290594}

{1037,2012,2174,1324,544,194,4354,2518,4210,3198,9480,12422,474,9352,6904,29120,30128,14356,10826,47854,227212,245972,100008,5212,450640,571972,284130,61972,1596472,1386558,356956,1073096,4485552,4502300,4295778,4215864,9975456,9936528,12729810,14107210,4814,3124,2166,3534,568,960,1846,8830,5622,1306,4650,19922,10802,53572,226834}

{975,162,850,780,350,4160,1836,1692,1012,6282,2942,11948,8878,2448,22216,1008,15772,3530,37028,179358,18760,145964,94796,445428,121332,287842,222158,1534500,209914,1029602,716140,3412456,16748,206522,79914,5759592,38928,2793282,1377400,14102396,1690,958,1368,2966,392,886,6984,3208,4316,3344,15272,9120,42770,173262}

{813,688,70,430,3810,2324,144,680,5270,3340,9006,3070,6430,19768,21208,14764,12242,33498,142330,160598,127204,51168,350632,324096,166510,65684,1312342,1324586,819688,313462,2696316,3395708,189774,126608,5679678,5720664,2754354,1415882,12724996,14100706,732,410,1598,2574,494,6098,3776,1108,972,11928,6152,33650,130492}

{125,618,360,3380,1486,2180,536,4590,1930,5666,5936,3360,13338,1440,6444,2522,21256,108832,18268,33394,76036,299464,26536,157586,100826,1246658,12244,504898,506226,2382854,699392,3205934,63166,5553070,40986,2966310,1338472,11309114,1375710,14099974,322,1188,976,2080,5604,2322,2668,136,10956,5776,27498,96842}

{493,258,3020,1894,694,1644,4054,2660,3736,270,2576,9978,11898,5004,3922,18734,87576,90564,15126,42642,223428,272928,131050,56760,1145832,1234414,492654,1328,1876628,1683462,2506542,3142768,5489904,5512084,2925324,1627838,9970642,9933404,12724264,14099652,866,212,1104,3524,3282,346,2532,10820,5180,21722,69344}

{235,2762,1126,1200,950,2410,1394,1076,3466,2306,7402,1920,6894,1082,14812,68842,2988,75438,27516,180786,49500,141878,74290,1089072,88582,741760,491326,1875300,193166,823080,636226,2347136,22180,2586760,1297486,8342804,37238,2790860,1375388,14098786,654,892,2420,242,2936,2186,8288,5640,16542,47622}

{2527,1636,74,250,1460,1016,318,2390,1160,5096,5482,4974,5812,13730,54030,65854,72450,47922,153270,131286,92378,67588,1014782,1000490,653178,250434,1383974,1682134,629914,186854,1710910,2324956,2564580,1289274,7045318,8305566,2753622,1415472,12723398,14098132,238,1528,2178,2694,750,6102,2648,10902,31080}

{891,1562,176,1210,444,698,2072,1230,3936,386,508,838,7918,40300,11824,6596,24528,105348,21984,38908,24790,947194,14292,347312,402744,1133540,298160,1052220,443060,1524056,614046,239624,1275306,5756044,1260248,5551944,1338150,11307926,1374734,14097894,1290,650,516,1944,5352,3454,8254,20178}

{671,1386,1034,766,254,1374,842,2706,3550,122,330,7080,32382,28476,5228,17932,80820,83364,16924,14118,922404,932902,333020,55432,730796,835380,754060,609160,1080996,910010,374422,1035682,4480738,4495796,4291696,4213794,9969776,9933192,12723160,14096604,640,134,1428,3408,1898,4800,11924}

{715,352,268,512,1120,532,1864,844,3428,208,6750,25302,3906,23248,12704,62888,2544,66440,2806,908286,10498,599882,277588,675364,104584,81320,144900,471836,170986,535588,661260,3445056,15058,204100,77902,5755982,36584,2789968,1373444,14095964,506,1294,1980,1510,2902,7124}

{363,84,244,608,588,1332,1020,2584,3220,6542,18552,21396,19342,10544,50184,60344,63896,63634,905480,897788,589384,322294,397776,570780,23264,63580,326936,300850,364602,125672,2783796,3429998,189042,126198,5678080,5719398,2753384,1416524,12722520,14095458,788,686,470,1392,4222}

{279,160,364,20,744,312,1564,636,3322,12010,2844,2054,8798,39640,10160,3552,262,841846,7692,308404,267090,75482,173004,547516,40316,263356,26086,63752,238930,2658124,646202,3240956,62844,5551882,41318,2966014,1336860,11305996,1372938,14094670,102,216,922,2830}

{119,204,344,724,432,1252,928,2686,8688,9166,790,6744,30842,29480,6608,3290,841584,834154,300712,41314,191608,97522,374512,507200,223040,237270,37666,175178,2419194,2011922,2594754,3178112,5489038,5510564,2924696,1629154,9969136,9933058,12721732,14094568,114,706,1908}

{85,140,380,292,820,324,1758,6002,478,8376,5954,24098,1362,22872,3318,838294,7430,533442,259398,150294,94086,276990,132688,284160,14230,199604,137512,2244016,407272,582832,583358,2310926,21526,2585868,1295542,8339982,36078,2788674,1372836,14094454,592,1202}

{55,240,88,528,496,1434,4244,5524,7898,2422,18144,22736,21510,19554,834976,830864,526012,274044,109104,56208,182904,144302,151472,269930,185374,62092,2106504,1836744,175560,526,1727568,2289400,2564342,1290326,7044440,8303904,2752596,1415838,12721618,14093862,610}

{185,152,440,32,938,2810,1280,2374,5476,15722,4592,1226,1956,815422,4112,304852,251968,164940,52896,126696,38602,7170,118458,84556,123282,2044412,269760,1661184,175034,1727042,561832,274942,1274016,5754114,1259464,5551308,1336758,11305780,1372244,14093252}

{33,288,408,906,1872,1530,1094,3102,10246,11130,3366,730,813466,811310,300740,52884,87028,112044,73800,88094,31432,111288,33902,38726,1921130,1774652,1391424,1486150,1552008,1165210,286890,999074,4480098,4494650,4291844,4214550,9969022,9933536,12721008}

{255,120,498,966,342,436,2008,7144,884,7764,2636,812736,2156,510570,247856,34144,25016,38244,14294,56662,79856,77386,4824,1882404,146478,383228,94726,65858,386798,878320,712184,3481024,14552,202806,77294,5754472,35486,2787472}

{135,378,468,624,94,1572,5136,6260,6880,5128,810100,810580,508414,262714,213712,9128,13228,23950,42368,23194,2470,72562,1877580,1735926,236750,288502,28868,320940,491522,166136,2768840,3466472,188254,125512,5677178,5718986,2751986}

{243,90,156,530,1478,3564,1124,620,1752,804972,480,302166,245700,49002,204584,4100,10722,18418,19174,20724,70092,1805018,141654,1499176,51752,259634,292072,170582,325386,2602704,697632,3278218,62742,5551666,41808,2967000}

{153,66,374,948,2086,2440,504,1132,803220,804492,301686,56466,196698,155582,200484,6622,7696,756,1550,49368,1734926,1663364,1357522,1447424,207882,32438,121490,154804,2277318,1905072,2580586,3215476,5488924,5509858,2925192}

{87,308,574,1138,354,1936,628,802088,1272,502806,245220,140232,41116,44902,193862,1074,6940,794,47818,1685558,71562,305842,89902,1239542,175444,89052,33314,2122514,372246,675514,634890,2273448,20934,2584666}

{221,266,564,784,1582,1308,801460,800816,501534,257586,104988,99116,3786,148960,192788,5866,6146,47024,1637740,1613996,234280,215940,1149640,1064098,86392,55738,2089200,1750268,303268,40624,1638558,2252514,2563732}

{45,298,220,798,274,800152,644,299282,243948,152598,5872,95330,145174,43828,186922,280,40878,1590716,23744,1379716,18340,933700,85542,977706,30654,2033462,338932,1447000,262644,1597934,613956,311218}

{253,78,578,524,799878,799508,298638,55334,91350,146726,89458,49844,101346,143094,186642,40598,1549838,1566972,1355972,1361376,915360,848158,892164,947052,2002808,1694530,1108068,1184356,1335290,983978,302738}

{175,500,54,799354,370,500870,243304,36016,55376,57268,39614,51502,41748,43548,146044,1509240,17134,211000,5404,446016,67202,44006,54888,1055756,308278,586462,76288,150934,351312,681240}

{325,446,799300,798984,500500,257566,207288,19360,1892,17654,11888,9754,1800,102496,1363196,1492106,193866,205596,440612,378814,23196,10882,1000868,747478,278184,510174,74646,200378,329928}

{121,798854,316,298484,242934,50278,187928,17468,15762,5766,2134,7954,100696,1260700,128910,1298240,11730,235016,61798,355618,12314,989986,253390,469294,231990,435528,125732,129550}

{798733,798538,298168,55550,192656,137650,170460,1706,9996,3632,5820,92742,1160004,1131790,1169330,1286510,223286,173218,293820,343304,977672,736596,215904,237304,203538,309796,3818}

{195,500370,242618,137106,55006,32810,168754,8290,6364,2188,86922,1067262,28214,37540,117180,1063224,50068,120602,49484,634368,241076,520692,21400,33766,106258,305978}

{500175,257752,105512,82100,22196,135944,160464,1926,4176,84734,980340,1039048,9326,79640,946044,1013156,70534,71118,584884,393292,279616,499292,12366,72492,199720}

{242423,152240,23412,59904,113748,24520,158538,2250,80558,895606,58708,1029722,70314,866404,67112,942622,584,513766,191592,113676,219676,486926,60126,127228}

{90183,128828,36492,53844,89228,134018,156288,78308,815048,836898,971014,959408,796090,799292,875510,942038,513182,322174,77916,106000,267250,426800,67102}

{38645,92336,17352,35384,44790,22270,77980,736740,21850,134116,11606,163318,3202,76218,66528,428856,191008,244258,28084,161250,159550,359698}

{53691,74984,18032,9406,22520,55710,658760,714890,112266,122510,151712,160116,73016,9690,362328,237848,53250,216174,133166,1700,200148}

{21293,56952,8626,13114,33190,603050,56130,602624,10244,29202,8404,87100,63326,352638,124480,184598,162924,83008,131466,198448}

{35659,48326,4488,20076,569860,546920,546494,592380,18958,20798,78696,23774,289312,228158,60118,21674,79916,48458,66982}

{12667,43838,15588,549784,22940,426,45886,573422,1840,57898,54922,265538,61154,168040,38444,58242,31458,18524}

{31171,28250,534196,526844,22514,45460,527536,571582,56058,2976,210616,204384,106886,129596,19798,26784,12934}

{2921,505946,7352,504330,22946,482076,44046,515524,53082,207640,6232,97498,22710,109798,6986,13850}

{503025,498594,496978,481384,459130,438030,471478,462442,154558,201408,91266,74788,87088,102812,6864}

{4431,1616,15594,22254,21100,33448,9036,307884,46850,110142,16478,12300,15724,95948}

{2815,13978,6660,1154,12348,24412,298848,261034,63292,93664,4178,3424,80224}

{11163,7318,5506,11194,12064,274436,37814,197742,30372,89486,754,76800}

{3845,1812,5688,870,262372,236622,159928,167370,59114,88732,76046}

{2033,3876,4818,261502,25750,76694,7442,108256,29618,12686}

{1843,942,256684,235752,50944,69252,100814,78638,16932}

{901,255742,20932,184808,18308,31562,22176,61706}

{254841,234810,163876,166500,13254,9386,39530}

{20031,70934,2624,153246,3868,30144}

{50903,68310,150622,149378,26276}

{17407,82312,1244,123102}

{64905,81068,121858}

{16163,40790}

{24627}

{}

Plus petit premier manquant : _17

Plus petit non-premier manquant : _39

Jean-Marc:

J’ai essayé de commencer le tableau autrement, juste pour voir.

J’ai commencé arbitrairement par {2,11}, et après environ 3 heures de calcul (à cause du 66e nb premier de la première ligne, qui vaut plus de 13000000), j’ai aussi un tableau de 83 lignes avec un plus petit premier manquant égal à 13 et un plus petit composite manquant valant 69, ce qui me semble ne pas infirmer la conjecture qu’on obtient tous les naturels.

Tableau (bis) de _83_ lignes (justifié à gauche) :

{2,11,3,37,19,113,71,293,331,821,2789,7723,2707,14983,2459,947,5471,43,24359,1523,74861,15683,51431,190261,3739,11971,537769,2675587,467,7963,1538893,7333,2531,23761,5,197,1013,5861,7,149,719,1931,449,5399,30881,509,83047,15217,212423,6997,53,5987,227,1453,827,21757,2099,97961,6733,633001,139,227191,17401,147283,1958029,13630621,191,8689,1187,2711,6791,619,12241,42437,521,1429,38167,3251,13003,143779,810493,24337,2300719}

{9,8,34,18,94,42,222,38,490,1968,4934,5016,12276,12524,1512,4524,5428,24316,22836,73338,59178,35748,138830,186522,8232,525798,2137818,2675120,7496,1530930,1531560,4802,21230,23756,192,816,4848,5854,142,570,1212,1482,4950,25482,30372,82538,67830,197206,205426,6944,5934,5760,1226,626,20930,19658,95862,91228,626268,632862,227052,209790,129882,1810746,11672592,13630430,8498,7502,1524,4080,6172,11622,30196,41916,908,36738,34916,9752,130776,666714,786156,2276382}

{1,26,16,76,52,180,184,452,1478,2966,82,7260,248,11012,3012,904,18888,1480,50502,14160,23430,103082,47692,178290,517566,1612020,537302,2667624,1523434,630,1526758,16428,2526,23564,624,4032,1006,5712,428,642,270,3468,20532,4890,52166,14708,129376,8220,198482,1010,174,4534,600,20304,1272,76204,4634,535040,6594,405810,17262,79908,1680864,9861846,1957838,13621932,996,5978,2556,2092,5450,18574,11720,41008,35830,1822,25164,121024,535938,119442,1490226}

{25,10,60,24,128,4,268,1026,1488,2884,7178,7012,10764,8000,2108,17984,17408,49022,36342,9270,79652,55390,130598,339276,1094454,1074718,2130322,1144190,1522804,1526128,1510330,13902,21038,22940,3408,3026,4706,5284,214,372,3198,17064,15642,47276,37458,114668,121156,190262,197472,836,4360,3934,19704,19032,74932,71570,530406,528446,399216,388548,62646,1600956,8180982,7904008,11664094,13620936,4982,3422,464,3358,13124,6854,29288,5178,34008,23342,95860,414914,416496,1370784}

{15,50,36,104,124,264,758,462,1396,4294,166,3752,2764,5892,15876,576,31614,12680,27072,70382,24262,75208,208678,755178,19736,1055604,986132,378614,3324,15798,1496428,7136,1902,19532,382,1680,578,5070,158,2826,13866,1422,31634,9818,77210,6488,69106,7210,196636,3524,426,15770,672,55900,3362,458836,1960,129230,10668,325902,1538310,6580026,276974,3760086,1956842,13615954,1560,2958,2894,9766,6270,22434,24110,28830,10666,72518,319054,1582,954288}

{35,14,68,20,140,494,296,934,2898,4128,3586,988,3128,9984,15300,31038,18934,14392,43310,46120,50946,133470,546500,735442,1035868,69472,607518,375290,12474,1480630,1489292,5234,17630,19150,1298,1102,4492,4912,2668,11040,12444,30212,21816,67392,70722,62618,61896,189426,193112,3098,15344,15098,55228,52538,455474,456876,127270,118562,315234,1212408,5041716,6303052,3483112,1803244,11659112,13614394,1398,64,6872,3496,16164,1676,4720,18164,61852,246536,317472,952706}

{21,54,48,120,354,198,638,1964,1230,542,2598,2140,6856,5316,15738,12104,4542,28918,2810,4826,82524,413030,188942,300426,966396,538046,232228,362816,1468156,8662,1484058,12396,1520,17852,196,3390,420,2244,8372,1404,17768,8396,45576,3330,8104,722,127530,3686,190014,12246,246,40130,2690,402936,1402,329606,8708,196672,897174,3829308,1261336,2819940,1679868,9855868,1955282,13612996,1334,6808,3376,12668,14488,3044,13444,43688,184684,70936,635234}

{33,6,72,234,156,440,1326,734,688,2056,458,4716,1540,10422,3634,7562,24376,26108,2016,77698,330506,224088,111484,665970,428350,305818,130588,1105340,1459494,1475396,1471662,10876,16332,17656,3194,2970,1824,6128,6968,16364,9372,37180,42246,4774,7382,126808,123844,186328,177768,12000,39884,37440,400246,401534,328204,320898,187964,700502,2932134,2567972,1558604,1140072,8176000,7900586,11657714,13611662,5474,3432,9292,1820,11444,10400,30244,140996,113748,564298}

{27,66,162,78,284,886,592,46,1368,1598,4258,3176,8882,6788,3928,16814,1732,24092,75682,252808,106418,112604,554486,237620,122532,175230,974752,354154,15902,3734,1460786,5456,1324,14462,224,1146,4304,840,9396,6992,27808,5066,37472,2608,119426,2964,62484,8560,165768,27884,2444,362806,1288,73330,7306,132934,512538,2231632,364162,1009368,418532,7035928,275414,3757128,1953948,13606188,2042,5860,7472,9624,1044,19844,110752,27248,450550}

{39,96,84,206,602,294,546,1322,230,2660,1082,5706,2094,2860,12886,15082,22360,51590,177126,146390,6186,441882,316866,115088,52698,799522,620598,338252,12168,1457052,1455330,4132,13138,14238,922,3158,3464,8556,2404,20816,22742,32406,34864,116818,116462,59520,53924,157208,137884,25440,360362,361518,72042,66024,125628,379604,1719094,1867470,645206,590836,6617396,6760514,3481714,1803180,11652240,13604146,3818,1612,2152,8580,18800,90908,83504,423302}

{57,12,122,396,308,252,776,1092,2430,1578,4624,3612,766,10026,2196,7278,29230,125536,30736,140204,435696,125016,201778,62390,746824,178924,282346,326084,1444884,1722,1451198,9006,1100,13316,2236,306,5092,6152,18412,1926,9664,2458,81954,356,56942,5596,103284,19324,112444,334922,1156,289476,6018,59604,253976,1339490,148376,1222264,54370,6026560,143118,3278800,1678534,9849060,1951906,13600328,2206,540,6428,10220,72108,7404,339798}

{45,110,274,88,56,524,316,1338,852,3046,1012,2846,9260,7830,5082,21952,96306,94800,109468,295492,310680,76762,139388,684434,567900,103422,43738,1118800,1443162,1449476,1442192,7906,12216,11080,1930,4786,1060,12260,16486,7738,7206,79496,81598,56586,51346,97688,83960,93120,222478,333766,288320,283458,53586,194372,1085514,1191114,1073888,1167894,5972190,5883442,3135682,1600266,8170526,7897154,11648422,13598122,1666,5888,3792,61888,64704,332394}

{65,164,186,32,468,208,1022,486,2194,2034,1834,6414,1430,2748,16870,74354,1506,14668,186024,15188,233918,62626,545046,116534,464478,59684,1075062,324362,6314,7284,1434286,4310,1136,9150,2856,3726,11200,4226,8748,532,72290,2102,25012,5240,46342,13728,9160,129358,111288,45446,4862,229872,140786,891142,105600,117226,94006,4804296,88748,2747760,1535416,6570260,273372,3751268,1949700,13596456,4222,2096,58096,2816,267690}

{99,22,154,436,260,814,536,1708,160,200,4580,4984,1318,14122,57484,72848,13162,171356,170836,218730,171292,482420,428512,347944,404794,1015378,750700,318048,970,1427002,1429976,3174,8014,6294,870,7474,6974,4522,8216,71758,70188,22910,19772,41102,32614,4568,120198,18070,65842,40584,225010,89086,750356,785542,11626,23220,4710290,4715548,2659012,1212344,5034844,6296888,3477896,1801568,11646756,13592234,2126,56000,55280,264874}

{77,132,282,176,554,278,1172,1548,40,4380,404,3666,12804,43362,15364,59686,158194,520,47894,47438,311128,53908,80568,56850,610584,264678,432652,317078,1426032,2974,1426802,4840,1720,5424,6604,500,2452,3694,63542,1570,47278,3138,21330,8488,28046,115630,102128,47772,25258,184426,135924,661270,35186,773916,11594,4687070,5258,2056536,1446668,3822500,1262044,2818992,1676328,9845188,1945478,13590108,53874,720,209594}

{55,150,106,378,276,894,376,1508,4340,3976,3262,9138,30558,27998,44322,98508,157674,47374,456,263690,257220,26660,23718,553734,345906,167974,115574,1108954,1423058,1423828,1421962,3120,3704,1180,6104,1952,1242,59848,61972,45708,44140,18192,12842,19558,87584,13502,54356,22514,159168,48502,525346,626084,738730,762322,4675476,4681812,2051278,609868,2375832,2560456,1556948,1142664,8168860,7899710,11644630,13536234,53154,208874}

{95,44,272,102,618,518,1132,2832,364,714,5876,21420,2560,16324,54186,59166,110300,46918,263234,6470,230560,2942,530016,207828,177932,52400,993380,314104,770,1866,1418842,584,2524,4924,4152,710,58606,2124,16264,1568,25948,5350,6716,68026,74082,40854,31842,136654,110666,476844,100738,112646,23592,3913154,6336,2630534,1441410,1765964,184624,1003508,414284,7026196,269150,3744920,1891604,13483080,155720}

{51,228,170,516,100,614,1700,2468,350,5162,15544,18860,13764,37862,4980,51134,63382,216316,256764,224090,227618,527074,322188,29896,125532,940980,679276,313334,1096,1416976,1418258,1940,2400,772,3442,57896,56482,14140,14696,24380,20598,1366,61310,6056,33228,9012,104812,25988,366178,376106,11908,89054,3889562,3906818,2624198,1189124,324554,1581340,818884,589224,6611912,6757046,3475770,1853316,11591476,13327360}

{177,58,346,416,514,1086,768,2118,4812,10382,3316,5096,24098,32882,46154,12248,152934,40448,32674,3528,299456,204886,292292,95636,815448,261704,365942,312238,1415880,1282,1416318,460,1628,2670,54454,1414,42342,556,9684,3782,19232,59944,55254,27172,24216,95800,78824,340190,9928,364198,77146,3800508,17256,1282620,1435074,864570,1256786,762456,229660,6022688,145134,3281276,1622454,9738160,1735884}

{119,288,70,98,572,318,1350,2694,5570,7066,1780,19002,8784,13272,33906,140686,112486,7774,29146,295928,94570,87406,196656,719812,553744,104238,53704,1103642,1414598,1415036,1415858,1168,1042,51784,53040,40928,41786,9128,5902,15450,40712,4690,28082,2956,71584,16976,261366,330262,354270,287052,3723362,3783252,1265364,152454,570504,392216,494330,532796,5793028,5877554,3136142,1658822,8115706,8002276}

{169,218,28,474,254,1032,1344,2876,1496,5286,17222,10218,4488,20634,106780,28200,104712,21372,266782,201358,7164,109250,523156,166068,449506,50534,1049938,310956,438,822,1414690,126,50742,1256,12112,858,32658,3226,9548,25262,36022,23392,25126,68628,54608,244390,68896,24008,67218,3436310,59890,2517888,1112910,418050,178288,102114,38466,5260232,84526,2741412,1477320,6456884,113430}

{49,190,446,220,778,312,1532,1380,3790,11936,7004,5730,16146,86146,78580,76512,83340,245410,65424,194194,102086,413906,357088,283438,398972,999404,738982,310518,384,1413868,1414564,50616,49486,10856,11254,31800,29432,6322,15714,10760,12630,1734,43502,14020,189782,175494,44888,43210,3369092,3376420,2457998,1404978,694860,239762,76174,63648,5221766,5175706,2656886,1264092,4979564,6343454}

{141,256,226,558,466,1220,152,2410,8146,4932,1274,10416,70000,7566,2068,6828,162070,179986,128770,92108,311820,56818,73650,115534,600432,260422,428464,310134,1413484,696,1363948,1130,38630,398,20546,2368,23110,9392,4954,1870,10896,41768,29482,175762,14288,130606,1678,3325882,7328,918422,1053020,710118,455098,163588,12526,5158118,46060,2518820,1392794,3715472,1363890}

{115,30,332,92,754,1068,2258,5736,3214,3658,9142,59584,62434,5498,4760,155242,17916,51216,36662,219712,255002,16832,41884,484898,340010,168042,118330,1103350,1412788,1363252,1362818,37500,38232,20148,18178,20742,13718,4438,3084,9026,30872,12286,146280,161474,116318,128928,3324204,3318554,911094,134598,342902,255020,291510,151062,5145592,5112058,2472760,1126026,2322678,2351582}

{85,302,240,662,314,1190,3478,2522,444,5484,50442,2850,56936,738,150482,137326,33300,14554,183050,35290,238170,25052,443014,144888,171968,49712,985020,309438,49536,434,1325318,732,18084,1970,2564,7024,9280,1354,5942,21846,18586,133994,15194,45156,12610,3195276,5650,2407460,776496,208304,87882,36490,140448,4994530,33534,2639298,1346734,1196652,28904}

{217,62,422,348,876,2288,956,2078,5040,44958,47592,54086,56198,149744,13156,104026,18746,168496,147760,202880,213118,417962,298126,27080,122256,935308,675582,259902,49102,1324884,1324586,17352,16114,594,4460,2256,7926,4588,15904,3260,115408,118800,29962,32546,3182666,3189626,2401810,1630964,568192,120422,51392,103958,4854082,4960996,2605764,1292564,150082,1167748}

{155,360,74,528,1412,1332,1122,2962,39918,2634,6494,2112,93546,136588,90870,85280,149750,20736,55120,10238,204844,119836,271046,95176,813052,259726,415680,210800,1275782,298,1307234,1238,15520,3866,2204,5670,3338,11316,12644,112148,3392,88838,2584,3150120,6960,787816,770846,1062772,447770,69030,52566,4750124,106914,2355232,1313200,1142482,1017666}

{205,286,454,884,80,210,1840,36956,37284,3860,4382,91434,43042,45718,5590,64470,129014,34384,44882,194606,85008,151210,175870,717876,553326,155954,204880,1064982,1275484,1306936,1305996,14282,11654,1662,3466,2332,7978,1328,99504,108756,85446,86254,3147536,3143160,780856,16970,291926,615002,378740,16464,4697558,4643210,2248318,1042032,170718,124816}

{81,168,430,804,130,1630,35116,328,33424,522,87052,48392,2676,40128,58880,64544,94630,10498,149724,109598,66202,24660,542006,164550,397372,48926,860102,210502,31452,940,1291714,2628,9992,1804,1134,5646,6650,98176,9252,23310,808,3061282,4376,2362304,763886,274956,323076,236262,362276,4681094,54348,2394892,1206286,871314,45902}

{87,262,374,674,1500,33486,34788,33096,32902,86530,38660,45716,37452,18752,5664,30086,84132,139226,40126,43396,41542,517346,377456,232822,348446,811176,649600,179050,30512,1290774,1289086,7364,8188,670,4512,1004,91526,88924,14058,22502,3060474,3056906,2357928,1598418,488930,48120,86814,126014,4318818,4626746,2340544,1188606,334972,825412}

{175,112,300,826,31986,1302,1692,194,53628,47870,7056,8264,18700,13088,24422,54046,55094,99100,3270,1854,475804,139890,144634,115624,462730,161576,470550,148538,1260262,1688,1281722,824,7518,3842,3508,90522,2602,74866,8444,3037972,3568,698978,759510,1109488,440810,38694,39200,4192804,307928,2286202,1151938,853634,490440}

{63,188,526,31160,30684,390,1498,53434,5758,40814,1208,10436,5612,11334,29624,1048,44006,95830,1416,473950,335914,4744,29010,347106,301154,308974,322012,1111724,1258574,1280034,1280898,6694,3676,334,87014,87920,72264,66422,3029528,3034404,695410,60532,349978,668678,402116,506,4153604,3884876,1978274,1134264,298304,363194}

{125,338,30634,476,30294,1108,51936,47676,35056,39606,9228,4824,5722,18290,28576,42958,51824,94414,472534,138036,331170,24266,318096,45952,7820,13038,789712,146850,21460,864,1274204,3018,3342,86680,906,15656,5842,2963106,4876,2338994,634878,289446,318700,266562,401610,4153098,268728,1906602,844010,835960,64890}

{213,30296,30158,29818,29186,50828,4260,12620,4550,30378,4404,898,12568,10286,14382,8866,42590,378120,334498,193134,306904,293830,272144,38132,5218,776674,642862,125390,20596,1273340,1271186,324,83338,85774,14750,9814,2957264,2958230,2334118,1704116,345432,29254,52138,135048,3751488,3884370,1637874,1062592,8050,771070}

{30083,138,340,632,21642,46568,8360,8070,25828,25974,3506,11670,2282,4096,5516,33724,335530,43622,141364,113770,13074,21686,234012,32914,771456,133812,517472,104794,1252744,2154,1270862,83014,2436,71024,4936,2947450,966,624112,630002,1358684,316178,22884,82910,3616440,132882,2246496,575282,1054542,763020}

{29945,202,292,21010,24926,38208,290,17758,146,22468,8164,9388,1814,1420,28208,301806,291908,97742,27594,100696,8612,212326,201098,738542,637644,383660,412678,1147950,1250590,1268708,1187848,80578,68588,66088,2942514,2946484,623146,5890,728682,1042506,293294,60026,3533530,3483558,2113614,1671214,479260,291522}

{29743,90,20718,3916,13282,37918,17468,17612,22322,14304,1224,7574,394,26788,273598,9898,194166,70148,73102,92084,203714,11228,537444,100898,253984,29018,735272,102640,18118,80860,1107270,11990,2500,2876426,3970,2323338,617256,722792,313824,749212,233268,3473504,49972,1369944,442400,1191954,187738}

{29653,20628,16802,9366,24636,20450,144,4710,8018,13080,6350,7180,26394,246810,263700,184268,124018,2954,18982,111630,192486,526216,436546,153086,224966,706254,632632,84522,62742,1026410,1095280,9490,2873926,2872456,2319368,1706082,105536,408968,435388,515944,3240236,3423532,1319972,927544,749554,1004216}

{9025,3826,7436,15270,4186,20306,4566,3308,5062,6730,830,19214,220416,16890,79432,60250,121064,16028,92648,80856,333730,89670,283460,71880,481288,73622,548110,21780,963668,68870,1085790,2864436,1470,553088,613286,1600546,303432,26420,80556,2724292,183296,2103560,392428,177990,254662}

{5199,3610,7834,11084,16120,15740,1258,1754,1668,5900,18384,201202,203526,62542,19182,60814,105036,76620,11792,252874,244060,193790,211580,409408,407666,474488,526330,941888,894798,1016920,1778646,2862966,551618,60198,987260,1297114,277012,54136,2643736,2540996,1920264,1711132,214438,76672}

{1589,4224,3250,5036,380,14482,496,86,4232,12484,182818,2324,140984,43360,41632,44222,28416,64828,241082,8814,50270,17790,197828,1742,66822,51842,415558,47090,122122,761726,1084320,2311348,491420,927062,309854,1020102,222876,2589600,102740,620732,209132,1496694,137766}

{2635,974,1786,4656,14102,13986,410,4146,8252,170334,180494,138660,97624,1728,2590,15806,36412,176254,232268,41456,32480,180038,196086,65080,14980,363716,368468,75032,639604,322594,1227028,1819928,435642,617208,710248,797226,2366724,2486860,517992,411600,1287562,1358928}

{1661,812,2870,9446,116,13576,3736,4106,162082,10160,41834,41036,95896,862,13216,20606,139842,56014,190812,8976,147558,16048,131006,50100,348736,4752,293436,564572,317010,904434,592900,1384286,181566,93040,86978,1569498,120136,1968868,106392,875962,71366}

{849,2058,6576,9330,13460,9840,370,157976,151922,31674,798,54860,95034,12354,7390,119236,83828,134798,181836,138582,131510,114958,80906,298636,343984,288684,271136,247562,587424,311534,791386,1202720,88526,6062,1482520,1449362,1848732,1862476,769570,804596}

{1209,4518,2754,4130,3620,9470,157606,6054,120248,30876,54062,40174,82680,4964,111846,35408,50970,47038,43254,7072,16552,34052,217730,45348,55300,17548,23574,339862,275890,479852,411334,1114194,82464,1476458,33158,399370,13744,1092906,35026}

{3309,1764,1376,510,5850,148136,151552,114194,89372,23186,13888,42506,77716,106882,76438,15562,3932,3784,36182,9480,17500,183678,172382,9952,37752,6026,316288,63972,203962,68518,702860,1031730,1393994,1443300,366212,385626,1079162,1057880}

{1545,388,866,5340,142286,3416,37358,24822,66186,9298,28618,35210,29166,30444,60876,11630,148,32398,26702,8020,166178,11296,162430,27800,31726,310262,252316,139990,135444,634342,328870,362264,49306,1077088,19414,693536,21282}

{1157,478,4474,136946,138870,33942,12536,41364,56888,19320,6592,6044,1278,30432,49246,11482,32250,5696,18682,158158,154882,151134,134630,3926,278536,57946,112326,4546,498898,305472,33394,312958,1027782,1057674,674122,672254}

{679,3996,132472,1924,104928,21406,28828,15524,37568,12728,548,4766,29154,18814,37764,20768,26554,12986,139476,3276,3748,16504,130704,274610,220590,54380,107780,494352,193426,272078,279564,714824,29892,383552,1868}

{3317,128476,130548,103004,83522,7422,13304,22044,24840,12180,4218,24388,10340,18950,16996,5786,13568,126490,136200,472,12756,114200,143906,54020,166210,53400,386572,300926,78652,7486,435260,684932,353660,381684}

{125159,2072,27544,19482,76100,5882,8740,2796,12660,7962,20170,14048,8610,1954,11210,7782,112922,9710,135728,12284,101444,29706,89886,112190,112810,333172,85646,222274,71166,427774,249672,331272,28024}

{123087,25472,8062,56618,70218,2858,5944,9864,4698,12208,6122,5438,6656,9256,3428,105140,103212,126018,123444,89160,71738,60180,22304,620,220362,247526,136628,151108,356608,178102,81600,303248}

{97615,17410,48556,13600,67360,3086,3920,5166,7510,6086,684,1218,2600,5828,101712,1928,22806,2574,34284,17422,11558,37876,21684,219742,27164,110898,14480,205500,178506,96502,221648}

{80205,31146,34956,53760,64274,834,1246,2344,1424,5402,534,1382,3228,95884,99784,20878,20232,31710,16862,5864,26318,16192,198058,192578,83734,96418,191020,26994,82004,125146}

{49059,3810,18804,10514,63440,412,1098,920,3978,4868,848,1846,92656,3900,78906,646,11478,14848,10998,20454,10126,181866,5480,108844,12684,94602,164026,55010,43142}

{45249,14994,8290,52926,63028,686,178,3058,890,4020,998,90810,88756,75006,78260,10832,3370,3850,9456,10328,171740,176386,103364,96160,81918,69424,109016,11868}

{30255,6704,44636,10102,62342,508,2880,2168,3130,3022,89812,2054,13750,3254,67428,7462,480,5606,872,161412,4646,73022,7204,14242,12494,39592,97148}

{23551,37932,34534,52240,61834,2372,712,962,108,86790,87758,11696,10496,64174,59966,6982,5126,4734,160540,156766,68376,65818,7038,1748,27098,57556}

{14381,3398,17706,9594,59462,1660,250,854,86682,968,76062,1200,53678,4208,52984,1856,392,155806,3774,88390,2558,58780,5290,25350,30458}

{10983,14308,8112,49868,57802,1410,604,85828,85714,75094,74862,52478,49470,48776,51128,1464,155414,152032,84616,85832,56222,53490,20060,5108}

{3325,6196,41756,7934,56392,806,85224,114,10620,232,22384,3008,694,2352,49664,153950,3382,67416,1216,29610,2732,33430,14952}

{2871,35560,33822,48458,55586,84418,85110,10506,10388,22152,19376,2314,1658,47312,104286,150568,64034,66200,28394,26878,30698,18478}

{32689,1738,14636,7128,28832,692,74604,118,11764,2776,17062,656,45654,56974,46282,86534,2166,37806,1516,3820,12220}

{30951,12898,7508,21704,28140,73912,74486,11646,8988,14286,16406,44998,11320,10692,40252,84368,35640,36290,2304,8400}

{18053,5390,14196,6436,45772,574,62840,2658,5298,2120,28592,33678,628,29560,44116,48728,650,33986,6096}

{12663,8806,7760,39336,45198,62266,60182,2640,3178,26472,5086,33050,28932,14556,4612,48078,33336,27890}

{3857,1046,31576,5862,17068,2084,57542,538,23294,21386,27964,4118,14376,9944,43466,14742,5446}

{2811,30530,25714,11206,14984,55458,57004,22756,1908,6578,23846,10258,4432,33522,28724,9296}

{27719,4816,14508,3778,40474,1546,34248,20848,4670,17268,13588,5826,29090,4798,19428}

{22903,9692,10730,36696,38928,32702,13400,16178,12598,3680,7762,23264,24292,14630}

{13211,1038,25966,2232,6226,19302,2778,3580,8918,4082,15502,1028,9662}

{12173,24928,23734,3994,13076,16524,802,5338,4836,11420,14474,8634}

{12755,1194,19740,9082,3448,15722,4536,502,6584,3054,5840}

{11561,18546,10658,5634,12274,11186,4034,6082,3530,2786}

{6985,7888,5024,6640,1088,7152,2048,2552,744}

{903,2864,1616,5552,6064,5104,504,1808}

{1961,1248,3936,512,960,4600,1304}

{713,2688,3424,448,3640,3296}

{1975,736,2976,3192,344}

{1239,2240,216,2848}

{1001,2024,2632}

{1023,608}

{415}

{}

Plus petit premier manquant : 13

Plus petit non premier manquant : 69

__________

Merci à tous !

É.