PRP Records

Probable Primes Top 10000

(300935 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 ?
575128243^17308+17308^28243119701Hans Havermann02/2021
575277*10^119688+3119690Robert Price06/2020
5753586*25^85601+3717119668Eric Chen10/2023
5754(2^397504+1698)/2119661Stefano Morozzi09/2020
5755(58^67853-1)/57119653Paul Bourdelais09/2017
57562^397426+73849119638Enzo Doria04/2016
57578*10^119509+29119510Robert Price11/2021
57582^396933-112723119489Enzo Doria06/2014
575911^114738-150119488Enzo Doria10/2012
5760(4*10^119474+149)/9119474Robert Price04/2018
576126964^26964-13^13119472Henri Lifchitz08/2024
57622^396790-21119446Lelio R Paula04/2013
576332061^5300+5300^32061119405Hans Havermann01/2021
5764(2^396633-7)/5119398Lelio R Paula04/2014
576527382^22913+22913^27382119388Hans Havermann03/2021
5766(2^396577+2522)/2119382Stefano Morozzi09/2020
5767(2^396492+2230)/2119356Stefano Morozzi01/2021
5768(47*10^119354+259)/9119355Robert Price03/2022
5770105^59050+104119352Norbert Schneider11/2016
5769126^56824-125119352Norbert Schneider12/2018
57712^396469+111546435119350Paul Bourdelais10/2021
5772139^55690-138119345Norbert Schneider04/2019
5773790^41179+41179^790119322Norbert Schneider04/2019
57742^396374+73729119321Enzo Doria04/2016
577588*10^119295+3119297Robert Price05/2020
57762^396258-459491119286Enzo Doria05/2015
5777(2^396248+3126)/2119283Stefano Morozzi09/2020
57782^396128-396128-1119247Karsten Bonath06/2018
5779(893*10^119228+7)/9119230Robert Price06/2021
5780(31*10^119229+257)/9119230Robert Price12/2021
5781(28*10^119206-67)/3119207Robert Price10/2020
5782(2^395986+5)/76881119199Lelio R Paula04/2014
578311^114458+6119196Paul Bourdelais02/2021
5784(23*2^395942-1)/91119190Lelio R Paula04/2014
5785(2^395902+202)/2119179Stefano Morozzi09/2020
5786(2^395825+582)/2119155Stefano Morozzi09/2020
5787(2^395733+1130)/2119128Stefano Morozzi09/2020
578829548^10725+10725^29548119091Hans Havermann02/2021
5789(11*2^395548+1)/3119073Lelio R Paula04/2014
5790(30^80599+1)/31119054Robert Price07/2013
5791(232*10^119047+17)/3119049Robert Price04/2021
5792(43*10^119024-403)/9119025Robert Price01/2019
5793(4*10^119021+47)/3119022Robert Price01/2022
5794fibonacci(569433)+3119005Jon Grantham08/2023
579526603^26888-26888^26603118978Norbert Schneider07/2021
5796912^40193-40193^912118972Norman Luhn09/2024
5797681^41992-41992^681118970Norman Luhn09/2024
57986*10^118964+43118965Robert Price07/2020
5799(8*10^118960+49)/3118961Robert Price05/2020
580031253^6402+6402^31253118959Hans Havermann02/2021
5801(194*10^118925-17)/3118927Robert Price09/2020
58022^395062-109121118926Enzo Doria04/2014
58032^395055-4627118924Yves Minet05/2019
5804(2^395054+702)/2118923Stefano Morozzi09/2020
58052^395018-224141118913Harrison Mesh06/2022
5806(2^395011+2526)/2118910Stefano Morozzi09/2020
5807(2^394918+78557)/3118882Lelio R Paula01/2015
580825771^26948-26948^25771118872Frank Doornink02/2024
5809374^46201-46201^374118870Norman Luhn09/2024
5810(2^394858+1018)/2118864Stefano Morozzi09/2020
5811(77*10^118862-149)/9118863Robert Price03/2022
5812(16*10^118852+77)/3118853Robert Price03/2019
5813fibonacci(568658)-2118843Jon Grantham08/2023
5814(2^394739+3)/1883118826Lelio R Paula04/2014
581510^118772+163599118773Patrick De Geest02/2021
581710^118772-40000000001118772Robert Price09/2020
581610^118772-207603118772Patrick De Geest02/2021
581826842^26577+26577^26842118763Hans Havermann02/2021
5819(2^394513+2034)/2118760Stefano Morozzi09/2020
5820(2^394473+2774)/2118748Stefano Morozzi02/2021
582127949^17710+17710^27949118734Hans Havermann02/2021
58222^394266+71389118686Enzo Doria04/2016
5823(10^118681-3^118681)/7118681Jon Grantham08/2023
58242^394215-51261118671Tony Prest / Never Odd Or Even04/2018
5825(2^394215-48793)/5/5118670Tony Prest / Never Odd Or Even04/2018
5826(2^394215-17063)/3/3/5118669Tony Prest / Never Odd Or Even04/2018
5827(2^394215-24393)/5/5/5/5/5118668Tony Prest / Never Odd Or Even04/2018
5828(2^394215-35885)/3/71/173118666Tony Prest / Never Odd Or Even04/2018
5829(2^394215-47925)/353/2269118665Tony Prest / Never Odd Or Even04/2018
583029201^11568+11568^29201118652Hans Havermann02/2021
5831(2^394215-62819)/3/3/3/3/3/3/3/7/21737/1082153/1953673118650Tony Prest / Never Odd Or Even04/2018
5832(2^394131+2214)/2118645Stefano Morozzi09/2020
5833(17*10^118635+13)/3118636Robert Price01/2019
58345^169727+2118635Lelio R Paula08/2013
58352^394034-3118617M. Frind & P. Underwood09/2002
5836(7*10^118607+179)/3118608Robert Price09/2018
58373^248572-6242118599Enzo Doria05/2014
5838(3*2^393964-1)/181118594Lelio R Paula04/2014
5839(49*10^118576-319)/9118577Robert Price10/2021
58407^140303-6118570Robert Price11/2014
5841(2^393864+2686)/2118565Stefano Morozzi09/2020
5842(2^393862+3150)/2118564Stefano Morozzi09/2020
5843(2^393849+3762)/2118561Stefano Morozzi01/2021
5844(529*10^118554-7)/9118556Robert Price08/2021
584526712^26777-26777^26712118534Norbert Schneider07/2021
5846(2^393661+2666)/2118504Stefano Morozzi09/2020
5847(2^393650+1614)/2118501Stefano Morozzi09/2020
584827655^19264+19264^27655118495Hans Havermann02/2021
584910^118485+469413118486Patrick De Geest05/2021
585010^118485-50001118485Robert Price08/2020
5851(2^393528+1030)/2118464Stefano Morozzi09/2020
58522^393427+75683118434Enzo Doria04/2016
58532^393376-114749118418Enzo Doria04/2015
5854(65*10^118417+493)/9118418Robert Price08/2021
585530960^6671+6671^30960118397Hans Havermann02/2021
5856(2^393234+2010)/2118375Stefano Morozzi09/2020
5857(2^393205+3030)/2118367Stefano Morozzi09/2020
5858(2^393191+2174)/2118362Stefano Morozzi09/2020
58592^393180+73118359Lelio R Paula04/2013
58603*2^393125+5118343Jon Grantham07/2023
586127546^19771+19771^27546118339Hans Havermann02/2021
5862822^40595-40595^822118330Norman Luhn09/2024
5863p(23881)#/2+256118328Robert Price05/2017
5864(10^118324+359)/9118324Serge Batalov12/2014
5865(2^393048+570)/2118319Stefano Morozzi09/2020
5866p(23879)#/2+64118317Robert Price03/2017
58672^393033+20147118315Enzo Doria08/2023
58688*10^118308+59118309Robert Price11/2021
58699*10^118282+29118283Robert Price03/2022
5870(238*10^118265-1)/3118267Robert Price04/2020
5872(53*10^118216+1)/9118217Serge Batalov11/2010
5871(2^392707+1710)/2118217Stefano Morozzi09/2020
5873(7*2^392697+1)/15118214Renaud Lifchitz03/2011
5874(157^53819-1)/156118179Alexander Zhirkov06/2016
5875(2^392567+2750)/2118175Stefano Morozzi01/2021
587655*10^118172+3118174Robert Price07/2022
5877(19*2^392551+1)/3118171Lelio R Paula04/2014
587827185^22222+22222^27185118168Hans Havermann01/2021
58792^392516-29219118160Enzo Doria07/2015
588066*10^118155+7118157Robert Price07/2020
5881Phi(177231,10)118152Maksym Voznyy09/2015
58822^392413-112123118129Enzo Doria06/2014
588327491^19798+19798^27491118119Hans Havermann02/2021
5884(49*10^118109-319)/9118110Robert Price10/2021
5885(2^392342+5)/27118106Lelio R Paula04/2014
5886(2^392333+1782)/2118104Stefano Morozzi01/2021
58872^392300-1841429118095Enzo Doria06/2015
58883*2^392260-5118083Jon Grantham07/2023
58892^392220+75241118070Enzo Doria04/2016
589027836^17409+17409^27836118047Hans Havermann02/2021
589110^118009+664447118010Patrick De Geest07/2018
589210^118009-20001118009Robert Price01/2018
5893(14*10^117991+61)/3117992Robert Price12/2018
58942^391933+5897117984Yves Minet02/2011
58952^391912-1849259117978Enzo Doria08/2015
5896(2*34^77029+1043)/11117968Eric Chen08/2023
58975*2^391836-3117956Jon Grantham07/2023
589828357^14440+14440^28357117953Hans Havermann02/2021
5899(2^391812+5)/14181117944Lelio R Paula04/2014
590085^61124-61124^85117934Norman Luhn09/2024
5901(7*10^117930-79)/9117930Robert Price01/2021
590227531^19168+19168^27531117904Hans Havermann02/2021
5903(46*10^117902+683)/9117903Robert Price03/2019
590426349^26668-26668^26349117893Frank Doornink03/2024
590527670^18189+18189^27670117869Hans Havermann02/2021
5906(7*2^391521+1)/285117858Lelio R Paula04/2014
5907(56*10^117856+583)/9117857Robert Price08/2021
590832169^4606+4606^32169117846Hans Havermann02/2021
5909(71*10^117803-143)/9117804Robert Price10/2021
59102^391324+90901117801Yves Minet02/2011
59112^391301-1859923117794Enzo Doria03/2016
59122^391261-4131117782Yves Minet02/2018
5913(2^391211+554)/2117766Stefano Morozzi09/2020
5914816^40445-40445^816117764Norman Luhn09/2024
591538434^1157+1157^38434117737Hans Havermann01/2021
5916(2^391115-7)/11791117734Lelio R Paula04/2014
5917(85*10^117719+473)/9117720Robert Price01/2020
5918(2^391049+582)/2117718Stefano Morozzi09/2020
5919(21*23^86445-197)/22117715Eric Chen08/2023
592031083^6122+6122^31083117709Hans Havermann02/2021
59212^390960+1880881117691Enzo Doria11/2016
5922(71*10^117685+91)/9117686Robert Price04/2022
59242^390897-1860553117672Enzo Doria11/2015
5923(61*10^117671+47)/9117672Robert Price07/2022
59252^390889-115003117670Enzo Doria06/2015
592612^109010+35117642Riley Fisher08/2023
59272^390779-30337117637Paul Bourdelais02/2012
5928(2^390735+378)/2117623Stefano Morozzi02/2021
592911^112916-780117590Enzo Doria12/2012
593027641^17916+17916^27641117564Hans Havermann02/2021
593127906^16321+16321^27906117561Hans Havermann02/2021
593227294^20275+20275^27294117555Hans Havermann02/2021
5933(2^390473+1002)/2117544Stefano Morozzi09/2020
593435912^1875+1875^35912117541Hans Havermann02/2021
5935(16^97613-5^97613)/11117537Robert Price07/2013
5936(2^390438+1774)/2117534Stefano Morozzi01/2021
5937(2^390418+1722)/2117528Stefano Morozzi09/2020
5938(2^390403+654)/2117523Stefano Morozzi09/2020
5939(2^390343+2246)/2117505Stefano Morozzi01/2021
594028043^15478+15478^28043117493Hans Havermann02/2021
5941(17*2^390272+1)/1983117482Lelio R Paula04/2014
594237077^1474+1474^37077117479Hans Havermann01/2021
594331^78759-30117459Theodore Burton02/2007
5944(2^390176+1222)/2117455Stefano Morozzi09/2020
5945(2^390133+1242)/2117442Stefano Morozzi09/2020
5946(2^390013+2634)/2117406Stefano Morozzi09/2020
59473*10^117402+61117403Robert Price09/2020
59482^389998+37117402Lelio R Paula03/2013
5949(2^389977+314)/2117395Stefano Morozzi09/2020
5950(2^389921+342)/2117378Stefano Morozzi01/2021
595171830^43+43^71830117333Hans Havermann01/2021
5952(2^389768+1582)/2117332Stefano Morozzi09/2020
595333802^2951+2951^33802117292Hans Havermann02/2021
595426789^23866+23866^26789117277Hans Havermann02/2021
595529^80192-1*80192^29117273Dylan Delgado12/2019
5956(101*10^117260+7)/9117262Robert Price02/2022
5957(13*10^117249+161)/3117250Robert Price11/2018
59582^389478+43117245Lelio R Paula03/2013
5959(298*10^117229-7)/3117231Robert Price06/2020
5960(2^389416+342)/2117226Stefano Morozzi01/2021
5961(29*2^389351-1)/9117207Lelio R Paula04/2014
59625*10^117205+23117206Robert Price03/2019
5963(2^389341-7)/3865117200Lelio R Paula03/2014
596427272^19827+19827^27272117195Hans Havermann01/2021
5965(2^389276+2650)/2117184Stefano Morozzi09/2020
5966(844*10^117175-7)/9117177Robert Price05/2021
596710^117142+209223117143Patrick De Geest04/2018
596910^117142-1000000001117142Robert Price03/2018
596810^117142-966057117142Patrick De Geest04/2018
597010^117135+360577117136Patrick De Geest07/2018
597110^117135-401117135Robert Price01/2018
597226415^26488-26488^26415117126Norbert Schneider05/2021
59734*10^117123+79117124Robert Price08/2018
59742^389033-12797413117111Enzo Doria04/2016
5975(2^388987+2634)/2117097Stefano Morozzi09/2020
59762^388960-109505117089Enzo Doria04/2014
59777*10^117082-57117083Robert Price06/2020
5978791^40398-40398^791117081Norman Luhn09/2024
5979(2^388928-5)/569117077Lelio R Paula03/2014
59802^388888-1529117067Yves Minet01/2013
598110^117059+28879117060Patrick De Geest05/2016
5982(10^117059-71)/1117059Serge Batalov12/2014
5983(2^388854+3630)/2117057Stefano Morozzi09/2020
5984(2^388842+2098)/2117053Stefano Morozzi09/2020
5985(2^388789+3150)/2117037Stefano Morozzi09/2020
5986(2^388748+378)/2117025Stefano Morozzi02/2021
5987(693^41189-1)/692117005Michael Stocker05/2020
5988(26*10^116999-503)/9117000Robert Price07/2018
598920^89917-21116985Anonymous09/2024
5990(2^388609+1554)/2116983Stefano Morozzi09/2020
599138496^1093+1093^38496116975Hans Havermann02/2021
59923^245154-6256116969Enzo Doria05/2014
59935*10^116966-43116967Robert Price01/2019
59942^388536-113495116961Enzo Doria08/2014
5995(2^388512+382)/2116954Stefano Morozzi02/2021
5996(8*32^77701+271)/31116952Eric Chen11/2023
59972^388469-43116941Lelio R Paula03/2013
599827417^18416+18416^27417116939Hans Havermann02/2021
5999(2^388438+1842)/2116932Stefano Morozzi02/2021
6000(7*2^388372-1)/111116911Lelio R Paula04/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 07 2025 10:37 (Time in France)

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