PRP Records

Probable Primes Top 10000

(295461 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 50000) Who ? When ?
62512^366649+1871687110373Enzo Doria05/2016
62522^366629-351205110367Enzo Doria06/2015
6253(31*10^110363+257)/9110364Robert Price12/2021
6254(17*19^86292-215)/18110347Eric Chen01/2023
62562^366558+1874479110345Enzo Doria06/2016
625525132^24581+24581^25132110345Hans Havermann10/2020
6257(2^366539+770)/2110339Stefano Morozzi09/2020
625826368^15285+15285^26368110331Hans Havermann10/2020
6259(23*10^110290+19)/3110291Robert Price07/2019
626018^87853-4409110280Enzo Doria03/2013
626128490^7419+7419^28490110267Hans Havermann11/2020
62622^366218-23110243Lelio R Paula02/2013
6263(21*2^366193-1)/197110235Lelio R Paula03/2014
62642^366178-343991110231Enzo Doria07/2015
626512^102123-11110210Riley Fisher09/2023
626625777^18798+18798^25777110174Hans Havermann10/2020
62672^365944+1871341110161Enzo Doria05/2016
62682^365838-461267110129Enzo Doria07/2015
626930152^4491+4491^30152110126Hans Havermann11/2020
62702^365802+23359110118Enzo Doria10/2023
627110^110111+464019110112Patrick De Geest05/2021
627210^110111-40001110111Robert Price01/2021
62732^365763-6555110106Lelio R Paula04/2017
6274(2^365689+2^182845+1)/511008311/2006
62752^365666-459161110077Enzo Doria05/2015
62763*10^110076-7110077Robert Price08/2015
627713^98785-72110041Lelio R Paula03/2017
6278(25^78707+1)/26110027Robert Price06/2013
6279(7*10^110027-277)/9110027Robert Price02/2022
6280(16*10^110014-73)/3110015Robert Price07/2020
6281(7*10^110006-151)/9110006Robert Price02/2018
62826^141361-7110001Lelio R Paula11/2014
628320^84536+81109984Lelio R Paula03/2017
62845*2^365347-9109982Lelio R Paula09/2014
62859*6^141303+7109957Lelio R Paula11/2014
628627635^9522+9522^27635109953Hans Havermann11/2020
628778^58099+77109929Norbert Schneider02/2015
62882*10^109928-7109929Robert Price10/2015
628930580^3933+3933^30580109927Hans Havermann11/2020
629026380^14689+14689^26380109926Hans Havermann11/2020
6291(2^365161+1130)/2109925Stefano Morozzi09/2020
6292(27*2^365137-1)/2021109916Lelio R Paula03/2014
6293(4441*29^75152-24)/7109905Curtis Bright05/2015
6294(2^365087+7)/6015109899Lelio R Paula01/2014
6295(2^365069+3774)/2109897Stefano Morozzi02/2021
629629652^5083+5083^29652109894Mark Rodenkirch10/2020
6297(2^365049+722)/2109891Stefano Morozzi09/2020
6298(35*10^109888-89)/9109889Robert Price02/2022
629918^87533-11109878Lelio R Paula04/2017
63002^364982-5109871Henri Lifchitz04/2006
63013*10^109861+59109862Robert Price08/2018
63025*10^109860-69109861Robert Price02/2021
63032^364936-1867979109857Enzo Doria04/2016
630427013^11652+11652^27013109846Hans Havermann10/2020
63052^364867-112087109836Enzo Doria06/2014
63064^182415-85061109825Mike Oakes06/2011
6307(2^364809+1034)/2109819Stefano Morozzi09/2020
6308(53*10^109809-287)/9109810Robert Price02/2022
6309(52*10^109807-133)/9109808Robert Price09/2021
631025708^18675+18675^25708109806Hans Havermann10/2020
6311(17^89227+16^89227)/33109788Robert Price08/2013
63122^364687-187109782Lelio R Paula01/2012
63132^364644+67109769Lelio R Paula01/2012
6314(9787*2^364625-1)/24947109763Lelio R Paula05/2015
6315(2^364616+5)/9109760Lelio R Paula01/2014
6316(55*10^109759+89)/9109760Robert Price03/2019
6317(14*32^72921+4171)/31109757Eric Chen04/2023
631812^101694+73109747Lelio R Paula03/2017
631913^98518-66109744Lelio R Paula03/2017
6320(8*10^109721-269)/9109721Robert Price09/2021
63212^364478-113261109719Enzo Doria07/2014
6322(2^364513+1)/(3*44290516579)109719Gord Palameta08/2018
6323(24737*2^364454+1)/3109716Lelio R Paula07/2014
632427814^8777+8777^27814109681Hans Havermann10/2020
6325(62*10^109673+1)/9109674Serge Batalov11/2010
63263^229824+340109654Lelio R Paula03/2017
6327(16623*33^72206-8095)/16109649Eric Chen05/2023
6328(2*10^109645-71)/3109645Robert Price12/2017
63292^364169-112813109626Enzo Doria06/2014
633028822^6359+6359^28822109622Hans Havermann11/2020
633110^109615+21109616Lelio R Paula03/2017
633210^109615-456267109615Patrick De Geest03/2017
63332^364094-113109604Lelio R Paula01/2012
633425251^21898+21898^25251109600Hans Havermann11/2020
6335(4^182026+11)/3109591Robert Price02/2017
63362^364041-6883109588Lelio R Paula09/2011
633712^101545+11109586Lelio R Paula03/2017
633826536^13475+13475^26536109582Hans Havermann11/2020
63392^363842-2787101109528Enzo Doria03/2016
6340(2^363812+3570)/2109519Stefano Morozzi09/2020
6341(22699*2^363782+1)/763109511Lelio R Paula07/2014
63422^363769+5711109506Lelio R Paula04/2017
6343(31*2^363748+1)/49109499Lelio R Paula03/2014
6344(2^363670+100280245065)109476Paul Bourdelais05/2022
6345p(22245)#/2-8109462Robert Price01/2017
63462^363556+55109442Lelio R Paula01/2012
6347(509*10^109414+31)/9109416Robert Price08/2022
6348(2^363437+1682)/2109406Stefano Morozzi09/2020
6349(55459*2^363411+1)/81109401Lelio R Paula07/2014
63502^363406+1871569109397Enzo Doria05/2016
6351(129^51829-1)/128109388Anonymous06/2024
6352(2^363370+1338)/2109385Stefano Morozzi02/2021
6353(2^363349+7)/9109378Lelio R Paula01/2014
6354(13869^26569-1)/(13869^163-1)109375Ryan Propper11/2023
63553^229236+100109374Lelio R Paula03/2017
6356(2^363315+3258)/2109369Stefano Morozzi02/2021
63572^363268-58695109355Lelio R Paula04/2017
63582^363191-112321109332Enzo Doria06/2014
635926231^14718+14718^26231109327Hans Havermann10/2020
636025461^19672+19672^25461109326Hans Havermann10/2020
63614*10^109316-63109317Robert Price10/2018
63622^363120+3109311Donovan Johnson04/2006
6363(10^109297-1)/9109297Paul Bourdelais, Harvey Dubner04/2007
63642^363042-114641109287Enzo Doria04/2015
63652^363020-112793109280Enzo Doria06/2014
6366(8732^27889-1)/(8732^167-1)109256Ryan Propper11/2023
6367(85*10^109253+203)/9109254Robert Price09/2020
636824990^23431+23431^24990109202Hans Havermann10/2020
6369(2^362746+3738)/2109198Stefano Morozzi09/2020
6370(2^362716+1282)/2109189Stefano Morozzi01/2021
6371(67607*2^362695+1)/70499109183Lelio R Paula07/2014
637225060^22737+22737^25060109180Hans Havermann10/2020
6373(9*2^362644+1)/5109167Lelio R Paula03/2014
63745^156181+38109166Lelio R Paula02/2017
6375(2^362623+3618)/2109161Stefano Morozzi09/2020
637625138^21993+21993^25138109157Hans Havermann10/2020
63774*10^109142+91109143Robert Price08/2018
63783^228750+68109142Lelio R Paula03/2017
6379(2^362561+786)/2109142Stefano Morozzi09/2020
6380(23*10^109113+61)/3109114Robert Price01/2022
63812*10^109100-49109101Robert Price09/2020
6382(10223*2^362376+1)/9109090Lelio R Paula07/2014
638365^60167-64^60167109078Robert Price08/2013
63847*3^228589-2109066Lelio R Paula09/2014
638524874^24243+24243^24874109063Hans Havermann11/2020
6386(17*10^109059-161)/9109060Robert Price02/2021
638729158^5495+5495^29158109050Hans Havermann11/2020
6388(78557*2^362188+1)/189109033Lelio R Paula07/2014
63892*7^129008+9109025Lelio R Paula11/2014
639088*10^109022+7109024Robert Price03/2020
639128194^7337+7337^28194108985Hans Havermann10/2020
6392(5*10^108960+91)/3108961Robert Price04/2018
63932^361957+76367108960Enzo Doria05/2016
63942^361873-1411108935Yves Minet01/2013
6395(24737*2^361857+1)/35108933Lelio R Paula07/2014
6396115^52842-114108892Norbert Schneider07/2018
639713^97745-24108883Lelio R Paula03/2017
6398(2^361696+2562)/2108882Stefano Morozzi09/2020
639917^88475+8108864Lelio R Paula04/2017
64002^361567+51108843Lelio R Paula01/2012
64012^361563-109501108842Enzo Doria04/2014
640212^100852+83108838Lelio R Paula03/2017
64032^361497+767108822Lelio R Paula01/2012
6404L(520691)/78103651/1057002731/42794551909108791Serge Batalov07/2024
640528019^7630+7630^28019108785Hans Havermann10/2020
640624723^24758-24758^24723108765Norbert Schneider11/2020
64072^361280-112349108757Enzo Doria06/2014
64082^361271-5955108754Lelio R Paula04/2017
640912^100757+19108736Lelio R Paula03/2017
641025368^19333+19333^25368108735Hans Havermann11/2020
6411(2^361195+3618)/2108731Stefano Morozzi09/2020
64122^361153-111546435108718Paul Bourdelais10/2021
641314^94849-61108710Lelio R Paula05/2017
641427267^9700+9700^27267108708Hans Havermann11/2020
6415(19^85009-5^85009)/14108705Robert Price07/2013
641624832^23853+23853^24832108704Hans Havermann11/2020
641727502^8963+8963^27502108701Hans Havermann11/2020
6418(130^51419-1)/129108695Anonymous06/2024
641925807^16278+16278^25807108689Hans Havermann11/2020
6420(11*2^361027+1)/40463108677Lelio R Paula03/2014
64212^360973+1299108664Lelio R Paula04/2017
64222^360959-109101108660Enzo Doria04/2014
64236*5^155454+7108659Lelio R Paula11/2014
642410^108656+79108657Lelio R Paula02/2017
642510^108656-50001108656Patrick De Geest03/2017
64262^360918-35108648Lelio R Paula01/2012
64274*10^108646-47108647Robert Price10/2021
6428(11*2^360886-1)/7108638Lelio R Paula03/2014
64293*10^108624-49108625Robert Price07/2018
6430(2^360831+666)/2108621Stefano Morozzi09/2020
6431(134*10^108610+7)/3108612Robert Price02/2020
64322*10^108609+29108610Robert Price02/2021
6433(10^108604+7)/71/191108600Alfred Reich06/2021
6434(2^360742+3222)/2108594Stefano Morozzi09/2020
64352^360706-458903108584Enzo Doria04/2015
643631112^3087+3087^31112108567Hans Havermann11/2020
64372^360641-113185108564Enzo Doria07/2014
6438(29*10^108559-71)/3108560Robert Price07/2021
64392^360618+75019108557Enzo Doria04/2016
64402^360607-216367108554Harrison Mesh06/2022
6441(14*10^108545-221)/9108546Robert Price04/2018
6442(44*10^108544-233)/9108545Robert Price01/2019
64433*5^155286+2108541Lelio R Paula11/2014
64447^128422+4108530Lelio R Paula11/2014
64457^128421-80108529Lelio R Paula03/2017
64462^360497+53807108521Yves Minet07/2010
64472^360468-4559108512Yves Minet03/2019
6448(2^360451+578)/2108507Stefano Morozzi09/2020
64492^360366+1459108481Lelio R Paula09/2011
64502^360364-1499108481Yves Minet05/2013
645125662^16871+16871^25662108477Hans Havermann10/2020
645225009^21748+21748^25009108475Hans Havermann10/2020
645314^94642-23108472Lelio R Paula05/2017
6454(197*10^108446-11)/3108448Robert Price03/2020
6455(2^360229+1290)/2108440Stefano Morozzi01/2021
64564*10^108412+9108413Robert Price05/2015
6457(259*10^108409-1)/3108411Robert Price12/2020
6458(2^360122+1194)/2108408Stefano Morozzi09/2020
6459133^51042-132108406Norbert Schneider02/2019
64602^360093-351103108399Enzo Doria06/2015
64612^360042+723108384Lelio R Paula01/2012
646285^56164-2108364Lelio R Paula10/2013
64632^359937-29323108352Enzo Doria07/2015
6464(2^359922+1762)/2108348Stefano Morozzi09/2020
6465(2^359903+758)/2108342Stefano Morozzi09/2020
64662^359898-19997108341Enzo Doria06/2013
6467(2^359886+2122)/2108337Stefano Morozzi09/2020
64682*5^154948-7108305Lelio R Paula11/2014
646910^108303+13108304Lelio R Paula02/2017
647010^108303-207959108303Patrick De Geest03/2017
64717*10^108300+69108301Robert Price07/2019
64722^359730+753108290Lelio R Paula12/2011
6473(8*10^108273+13)/3108274Robert Price06/2018
64742^359650-19797108266Enzo Doria06/2013
6475(47*10^108261+259)/9108262Robert Price03/2022
647691^55259-90^55259108255Robert Price07/2015
647710^108251+85749108252Patrick De Geest02/2021
647810^108251-50000000001108251Robert Price12/2020
647910^108251-252081108251Patrick De Geest02/2021
64804*10^108238-71108239Robert Price12/2018
64813^226845+68108233Lelio R Paula03/2017
648231836^2509+2509^31836108227Hans Havermann10/2020
64835^154822-12866108216Enzo Doria05/2014
6484(9*2^359480+1)/5108215Lelio R Paula03/2014
64852^359454-177108207Lelio R Paula12/2011
6486(19*10^108184+191)/3108185Robert Price05/2019
64876^139022-59108181Lelio R Paula02/2017
6488(19*10^108176-43)/3108177Robert Price05/2019
64892^359352-179108176Lelio R Paula12/2011
64902^359338-1858781108172Enzo Doria04/2016
649112^100230-97108167Lelio R Paula03/2017
649227028^10043+10043^27028108163Hans Havermann11/2020
6493(25*2^359297-1)/137108159Lelio R Paula03/2014
6494(2^359262-509203)/9108148Lelio R Paula12/2013
649526583^11702+11702^26583108147Hans Havermann11/2020
6496(3^226648-8)/352715633108131Lelio R Paula12/2013
64976^138956-59108129Lelio R Paula02/2017
64982^359184+30285108126Lelio R Paula04/2017
649913^97059+10108119Lelio R Paula03/2017
65002^359137-81108112Lelio R Paula12/2011


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 19 2024 15:29 (Time in France)

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