PRP Records

Probable Primes Top 10000

(295148 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 ?
52512^398877+105120074Donovan Johnson01/2006
5252(88^61751+1)/89120072Paul Bourdelais09/2017
52532^398710+57120024Lelio R Paula04/2013
5254(2^398698+1138)/2120020Stefano Morozzi09/2020
52552^398691-115057120018Enzo Doria06/2015
5256L(574219)120005Renaud Lifchitz03/2004
52572^398571+60413119982Yves Minet03/2011
525828623^15538+15538^28623119971Hans Havermann02/2021
5259p(24179)#/2-64119949Robert Price04/2017
52602^398448+1872001119945Enzo Doria05/2016
5261(10^119946*19-91)/6093119944Alfred Reich10/2023
5262(19*10^119946-91)/9/677119944Alfred Reich11/2023
5263(191*10^119941-17)/3119943Robert Price11/2021
5264634^42803+42803^634119938Norbert Schneider07/2019
526531083^7220+7220^31083119935Hans Havermann01/2021
5266(68*10^119931-11)/3119933Robert Price01/2020
52678*10^119930-3119931Ray Chandler04/2011
5268(2^398398+774)/2119930Stefano Morozzi09/2020
5269(10^119880+179)/9119880Serge Batalov12/2014
5270(9*2^398145+1)/73119853Lelio R Paula04/2014
5271(10^119836+77)/3119836Robert Price01/2018
527226681^27074-27074^26681119835Frank Doornink03/2024
527328179^17870+17870^28179119821Hans Havermann02/2021
52742^398029+1872527119819Enzo Doria05/2016
527533142^4119+4119^33142119802Hans Havermann01/2021
52762^397897-113541119779Enzo Doria08/2014
527728636^15171+15171^28636119728Hans Havermann02/2021
5278(10556^29929-1)/(10556^173-1)119724Ryan Propper11/2023
5279(2^397696+1042)/2119719Stefano Morozzi09/2020
5280(19*10^119716+101)/3119717Robert Price09/2019
528129563^11208+11208^29563119717Hans Havermann02/2021
52822^397655-933075119707Paul Bourdelais06/2021
5283(21*2^397661-1)/27593119705Lelio R Paula04/2014
528428243^17308+17308^28243119701Hans Havermann02/2021
528577*10^119688+3119690Robert Price06/2020
5286586*25^85601+3717119668Eric Chen10/2023
5287(2^397504+1698)/2119661Stefano Morozzi09/2020
5288(58^67853-1)/57119653Paul Bourdelais09/2017
52892^397426+73849119638Enzo Doria04/2016
52908*10^119509+29119510Robert Price11/2021
52912^396933-112723119489Enzo Doria06/2014
529211^114738-150119488Enzo Doria10/2012
5293(4*10^119474+149)/9119474Robert Price04/2018
52942^396790-21119446Lelio R Paula04/2013
529532061^5300+5300^32061119405Hans Havermann01/2021
5296(2^396633-7)/5119398Lelio R Paula04/2014
529727382^22913+22913^27382119388Hans Havermann03/2021
5298(2^396577+2522)/2119382Stefano Morozzi09/2020
5299(2^396492+2230)/2119356Stefano Morozzi01/2021
5300(47*10^119354+259)/9119355Robert Price03/2022
5302105^59050+104119352Norbert Schneider11/2016
5301126^56824-125119352Norbert Schneider12/2018
53032^396469+111546435119350Paul Bourdelais10/2021
5304139^55690-138119345Norbert Schneider04/2019
5305790^41179+41179^790119322Norbert Schneider04/2019
53062^396374+73729119321Enzo Doria04/2016
530788*10^119295+3119297Robert Price05/2020
53082^396258-459491119286Enzo Doria05/2015
5309(2^396248+3126)/2119283Stefano Morozzi09/2020
53102^396128-396128-1119247Karsten Bonath06/2018
5311(893*10^119228+7)/9119230Robert Price06/2021
5312(31*10^119229+257)/9119230Robert Price12/2021
5313(28*10^119206-67)/3119207Robert Price10/2020
5314(2^395986+5)/76881119199Lelio R Paula04/2014
531511^114458+6119196Paul Bourdelais02/2021
5316(23*2^395942-1)/91119190Lelio R Paula04/2014
5317(2^395902+202)/2119179Stefano Morozzi09/2020
5318(2^395825+582)/2119155Stefano Morozzi09/2020
5319(2^395733+1130)/2119128Stefano Morozzi09/2020
532029548^10725+10725^29548119091Hans Havermann02/2021
5321(11*2^395548+1)/3119073Lelio R Paula04/2014
5322(30^80599+1)/31119054Robert Price07/2013
5323(232*10^119047+17)/3119049Robert Price04/2021
5324(43*10^119024-403)/9119025Robert Price01/2019
5325(4*10^119021+47)/3119022Robert Price01/2022
5326fibonacci(569433)+3119005Jon Grantham08/2023
532726603^26888-26888^26603118978Norbert Schneider07/2021
53286*10^118964+43118965Robert Price07/2020
5329(8*10^118960+49)/3118961Robert Price05/2020
533031253^6402+6402^31253118959Hans Havermann02/2021
5331(194*10^118925-17)/3118927Robert Price09/2020
53322^395062-109121118926Enzo Doria04/2014
53332^395055-4627118924Yves Minet05/2019
5334(2^395054+702)/2118923Stefano Morozzi09/2020
53352^395018-224141118913Harrison Mesh06/2022
5336(2^395011+2526)/2118910Stefano Morozzi09/2020
5337(2^394918+78557)/3118882Lelio R Paula01/2015
533825771^26948-26948^25771118872Frank Doornink02/2024
5339(2^394858+1018)/2118864Stefano Morozzi09/2020
5340(77*10^118862-149)/9118863Robert Price03/2022
5341(16*10^118852+77)/3118853Robert Price03/2019
5342fibonacci(568658)-2118843Jon Grantham08/2023
5343(2^394739+3)/1883118826Lelio R Paula04/2014
534410^118772+163599118773Patrick De Geest02/2021
534610^118772-40000000001118772Robert Price09/2020
534510^118772-207603118772Patrick De Geest02/2021
534726842^26577+26577^26842118763Hans Havermann02/2021
5348(2^394513+2034)/2118760Stefano Morozzi09/2020
5349(2^394473+2774)/2118748Stefano Morozzi02/2021
535027949^17710+17710^27949118734Hans Havermann02/2021
53512^394266+71389118686Enzo Doria04/2016
5352(10^118681-3^118681)/7118681Jon Grantham08/2023
53532^394215-51261118671Tony Prest / Never Odd Or Even04/2018
5354(2^394215-48793)/5/5118670Tony Prest / Never Odd Or Even04/2018
5355(2^394215-17063)/3/3/5118669Tony Prest / Never Odd Or Even04/2018
5356(2^394215-24393)/5/5/5/5/5118668Tony Prest / Never Odd Or Even04/2018
5357(2^394215-35885)/3/71/173118666Tony Prest / Never Odd Or Even04/2018
5358(2^394215-47925)/353/2269118665Tony Prest / Never Odd Or Even04/2018
535929201^11568+11568^29201118652Hans Havermann02/2021
5360(2^394215-62819)/3/3/3/3/3/3/3/7/21737/1082153/1953673118650Tony Prest / Never Odd Or Even04/2018
5361(2^394131+2214)/2118645Stefano Morozzi09/2020
5362(17*10^118635+13)/3118636Robert Price01/2019
53635^169727+2118635Lelio R Paula08/2013
53642^394034-3118617M. Frind & P. Underwood09/2002
5365(7*10^118607+179)/3118608Robert Price09/2018
53663^248572-6242118599Enzo Doria05/2014
5367(3*2^393964-1)/181118594Lelio R Paula04/2014
5368(49*10^118576-319)/9118577Robert Price10/2021
53697^140303-6118570Robert Price11/2014
5370(2^393864+2686)/2118565Stefano Morozzi09/2020
5371(2^393862+3150)/2118564Stefano Morozzi09/2020
5372(2^393849+3762)/2118561Stefano Morozzi01/2021
5373(529*10^118554-7)/9118556Robert Price08/2021
537426712^26777-26777^26712118534Norbert Schneider07/2021
5375(2^393661+2666)/2118504Stefano Morozzi09/2020
5376(2^393650+1614)/2118501Stefano Morozzi09/2020
537727655^19264+19264^27655118495Hans Havermann02/2021
537810^118485+469413118486Patrick De Geest05/2021
537910^118485-50001118485Robert Price08/2020
5380(2^393528+1030)/2118464Stefano Morozzi09/2020
53812^393427+75683118434Enzo Doria04/2016
53822^393376-114749118418Enzo Doria04/2015
5383(65*10^118417+493)/9118418Robert Price08/2021
538430960^6671+6671^30960118397Hans Havermann02/2021
5385(2^393234+2010)/2118375Stefano Morozzi09/2020
5386(2^393205+3030)/2118367Stefano Morozzi09/2020
5387(2^393191+2174)/2118362Stefano Morozzi09/2020
53882^393180+73118359Lelio R Paula04/2013
53893*2^393125+5118343Jon Grantham07/2023
539027546^19771+19771^27546118339Hans Havermann02/2021
5391p(23881)#/2+256118328Robert Price05/2017
5392(10^118324+359)/9118324Serge Batalov12/2014
5393(2^393048+570)/2118319Stefano Morozzi09/2020
5394p(23879)#/2+64118317Robert Price03/2017
53952^393033+20147118315Enzo Doria08/2023
53968*10^118308+59118309Robert Price11/2021
53979*10^118282+29118283Robert Price03/2022
5398(238*10^118265-1)/3118267Robert Price04/2020
5400(53*10^118216+1)/9118217Serge Batalov11/2010
5399(2^392707+1710)/2118217Stefano Morozzi09/2020
5401(7*2^392697+1)/15118214Renaud Lifchitz03/2011
5402(157^53819-1)/156118179Alexander Zhirkov06/2016
5403(2^392567+2750)/2118175Stefano Morozzi01/2021
540455*10^118172+3118174Robert Price07/2022
5405(19*2^392551+1)/3118171Lelio R Paula04/2014
540627185^22222+22222^27185118168Hans Havermann01/2021
54072^392516-29219118160Enzo Doria07/2015
540866*10^118155+7118157Robert Price07/2020
5409Phi(177231,10)118152Maksym Voznyy09/2015
54102^392413-112123118129Enzo Doria06/2014
541127491^19798+19798^27491118119Hans Havermann02/2021
5412(49*10^118109-319)/9118110Robert Price10/2021
5413(2^392342+5)/27118106Lelio R Paula04/2014
5414(2^392333+1782)/2118104Stefano Morozzi01/2021
54152^392300-1841429118095Enzo Doria06/2015
54163*2^392260-5118083Jon Grantham07/2023
54172^392220+75241118070Enzo Doria04/2016
541827836^17409+17409^27836118047Hans Havermann02/2021
541910^118009+664447118010Patrick De Geest07/2018
542010^118009-20001118009Robert Price01/2018
5421(14*10^117991+61)/3117992Robert Price12/2018
54222^391933+5897117984Yves Minet02/2011
54232^391912-1849259117978Enzo Doria08/2015
5424(2*34^77029+1043)/11117968Eric Chen08/2023
54255*2^391836-3117956Jon Grantham07/2023
542628357^14440+14440^28357117953Hans Havermann02/2021
5427(2^391812+5)/14181117944Lelio R Paula04/2014
5428(7*10^117930-79)/9117930Robert Price01/2021
542927531^19168+19168^27531117904Hans Havermann02/2021
5430(46*10^117902+683)/9117903Robert Price03/2019
543126349^26668-26668^26349117893Frank Doornink03/2024
543227670^18189+18189^27670117869Hans Havermann02/2021
5433(7*2^391521+1)/285117858Lelio R Paula04/2014
5434(56*10^117856+583)/9117857Robert Price08/2021
543532169^4606+4606^32169117846Hans Havermann02/2021
5436(71*10^117803-143)/9117804Robert Price10/2021
54372^391324+90901117801Yves Minet02/2011
54382^391301-1859923117794Enzo Doria03/2016
54392^391261-4131117782Yves Minet02/2018
5440(2^391211+554)/2117766Stefano Morozzi09/2020
544138434^1157+1157^38434117737Hans Havermann01/2021
5442(2^391115-7)/11791117734Lelio R Paula04/2014
5443(85*10^117719+473)/9117720Robert Price01/2020
5444(2^391049+582)/2117718Stefano Morozzi09/2020
5445(21*23^86445-197)/22117715Eric Chen08/2023
544631083^6122+6122^31083117709Hans Havermann02/2021
54472^390960+1880881117691Enzo Doria11/2016
5448(71*10^117685+91)/9117686Robert Price04/2022
54502^390897-1860553117672Enzo Doria11/2015
5449(61*10^117671+47)/9117672Robert Price07/2022
54512^390889-115003117670Enzo Doria06/2015
545212^109010+35117642Riley Fisher08/2023
54532^390779-30337117637Paul Bourdelais02/2012
5454(2^390735+378)/2117623Stefano Morozzi02/2021
545511^112916-780117590Enzo Doria12/2012
545627641^17916+17916^27641117564Hans Havermann02/2021
545727906^16321+16321^27906117561Hans Havermann02/2021
545827294^20275+20275^27294117555Hans Havermann02/2021
5459(2^390473+1002)/2117544Stefano Morozzi09/2020
546035912^1875+1875^35912117541Hans Havermann02/2021
5461(16^97613-5^97613)/11117537Robert Price07/2013
5462(2^390438+1774)/2117534Stefano Morozzi01/2021
5463(2^390418+1722)/2117528Stefano Morozzi09/2020
5464(2^390403+654)/2117523Stefano Morozzi09/2020
5465(2^390343+2246)/2117505Stefano Morozzi01/2021
546628043^15478+15478^28043117493Hans Havermann02/2021
5467(17*2^390272+1)/1983117482Lelio R Paula04/2014
546837077^1474+1474^37077117479Hans Havermann01/2021
546931^78759-30117459Theodore Burton02/2007
5470(2^390176+1222)/2117455Stefano Morozzi09/2020
5471(2^390133+1242)/2117442Stefano Morozzi09/2020
5472(2^390013+2634)/2117406Stefano Morozzi09/2020
54733*10^117402+61117403Robert Price09/2020
54742^389998+37117402Lelio R Paula03/2013
5475(2^389977+314)/2117395Stefano Morozzi09/2020
5476(2^389921+342)/2117378Stefano Morozzi01/2021
547771830^43+43^71830117333Hans Havermann01/2021
5478(2^389768+1582)/2117332Stefano Morozzi09/2020
547933802^2951+2951^33802117292Hans Havermann02/2021
548026789^23866+23866^26789117277Hans Havermann02/2021
548129^80192-1*80192^29117273Dylan Delgado12/2019
5482(101*10^117260+7)/9117262Robert Price02/2022
5483(13*10^117249+161)/3117250Robert Price11/2018
54842^389478+43117245Lelio R Paula03/2013
5485(298*10^117229-7)/3117231Robert Price06/2020
5486(2^389416+342)/2117226Stefano Morozzi01/2021
5487(29*2^389351-1)/9117207Lelio R Paula04/2014
54885*10^117205+23117206Robert Price03/2019
5489(2^389341-7)/3865117200Lelio R Paula03/2014
549027272^19827+19827^27272117195Hans Havermann01/2021
5491(2^389276+2650)/2117184Stefano Morozzi09/2020
5492(844*10^117175-7)/9117177Robert Price05/2021
549310^117142+209223117143Patrick De Geest04/2018
549510^117142-1000000001117142Robert Price03/2018
549410^117142-966057117142Patrick De Geest04/2018
549610^117135+360577117136Patrick De Geest07/2018
549710^117135-401117135Robert Price01/2018
549826415^26488-26488^26415117126Norbert Schneider05/2021
54994*10^117123+79117124Robert Price08/2018
55002^389033-12797413117111Enzo Doria04/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 20 2024 09:22 (Time in France)

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