PRP Records

Probable Primes Top 10000

(301429 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 ?
60012^395018-224141118913Harrison Mesh06/2022
6002(2^395011+2526)/2118910Stefano Morozzi09/2020
6003(2^394918+78557)/3118882Lelio R Paula01/2015
600425771^26948-26948^25771118872Frank Doornink02/2024
6005374^46201-46201^374118870Norman Luhn09/2024
6006(2^394858+1018)/2118864Stefano Morozzi09/2020
6007(77*10^118862-149)/9118863Robert Price03/2022
6008(16*10^118852+77)/3118853Robert Price03/2019
6009fibonacci(568658)-2118843Jon Grantham08/2023
6010(2^394739+3)/1883118826Lelio R Paula04/2014
601110^118772+163599118773Patrick De Geest02/2021
601310^118772-40000000001118772Robert Price09/2020
601210^118772-207603118772Patrick De Geest02/2021
601426842^26577+26577^26842118763Hans Havermann02/2021
6015(2^394513+2034)/2118760Stefano Morozzi09/2020
6016(2^394473+2774)/2118748Stefano Morozzi02/2021
601727949^17710+17710^27949118734Hans Havermann02/2021
60182^394266+71389118686Enzo Doria04/2016
6019(10^118681-3^118681)/7118681Jon Grantham08/2023
60202^394215-51261118671Tony Prest / Never Odd Or Even04/2018
6021(2^394215-48793)/5/5118670Tony Prest / Never Odd Or Even04/2018
6022(2^394215-17063)/3/3/5118669Tony Prest / Never Odd Or Even04/2018
6023(2^394215-24393)/5/5/5/5/5118668Tony Prest / Never Odd Or Even04/2018
6024(2^394215-35885)/3/71/173118666Tony Prest / Never Odd Or Even04/2018
6025(2^394215-47925)/353/2269118665Tony Prest / Never Odd Or Even04/2018
602629201^11568+11568^29201118652Hans Havermann02/2021
6027(2^394215-62819)/3/3/3/3/3/3/3/7/21737/1082153/1953673118650Tony Prest / Never Odd Or Even04/2018
6028(2^394131+2214)/2118645Stefano Morozzi09/2020
6029(17*10^118635+13)/3118636Robert Price01/2019
60305^169727+2118635Lelio R Paula08/2013
60312^394034-3118617M. Frind & P. Underwood09/2002
6032(7*10^118607+179)/3118608Robert Price09/2018
60333^248572-6242118599Enzo Doria05/2014
6034(3*2^393964-1)/181118594Lelio R Paula04/2014
6035(49*10^118576-319)/9118577Robert Price10/2021
60367^140303-6118570Robert Price11/2014
6037(2^393864+2686)/2118565Stefano Morozzi09/2020
6038(2^393862+3150)/2118564Stefano Morozzi09/2020
6039(2^393849+3762)/2118561Stefano Morozzi01/2021
6040(529*10^118554-7)/9118556Robert Price08/2021
604126712^26777-26777^26712118534Norbert Schneider07/2021
6042(2^393661+2666)/2118504Stefano Morozzi09/2020
6043(2^393650+1614)/2118501Stefano Morozzi09/2020
604427655^19264+19264^27655118495Hans Havermann02/2021
604510^118485+469413118486Patrick De Geest05/2021
604610^118485-50001118485Robert Price08/2020
6047(2^393528+1030)/2118464Stefano Morozzi09/2020
60482^393427+75683118434Enzo Doria04/2016
60492^393376-114749118418Enzo Doria04/2015
6050(65*10^118417+493)/9118418Robert Price08/2021
605130960^6671+6671^30960118397Hans Havermann02/2021
6052(2^393234+2010)/2118375Stefano Morozzi09/2020
6053(2^393205+3030)/2118367Stefano Morozzi09/2020
6054(2^393191+2174)/2118362Stefano Morozzi09/2020
60552^393180+73118359Lelio R Paula04/2013
60563*2^393125+5118343Jon Grantham07/2023
605727546^19771+19771^27546118339Hans Havermann02/2021
6058822^40595-40595^822118330Norman Luhn09/2024
6059p(23881)#/2+256118328Robert Price05/2017
6060(10^118324+359)/9118324Serge Batalov12/2014
6061(2^393048+570)/2118319Stefano Morozzi09/2020
6062p(23879)#/2+64118317Robert Price03/2017
60632^393033+20147118315Enzo Doria08/2023
60648*10^118308+59118309Robert Price11/2021
60659*10^118282+29118283Robert Price03/2022
6066(238*10^118265-1)/3118267Robert Price04/2020
6068(53*10^118216+1)/9118217Serge Batalov11/2010
6067(2^392707+1710)/2118217Stefano Morozzi09/2020
6069(7*2^392697+1)/15118214Renaud Lifchitz03/2011
6070(157^53819-1)/156118179Alexander Zhirkov06/2016
6071(2^392567+2750)/2118175Stefano Morozzi01/2021
607255*10^118172+3118174Robert Price07/2022
6073(19*2^392551+1)/3118171Lelio R Paula04/2014
607427185^22222+22222^27185118168Hans Havermann01/2021
60752^392516-29219118160Enzo Doria07/2015
607666*10^118155+7118157Robert Price07/2020
6077Phi(177231,10)118152Maksym Voznyy09/2015
60782^392413-112123118129Enzo Doria06/2014
607927491^19798+19798^27491118119Hans Havermann02/2021
6080(49*10^118109-319)/9118110Robert Price10/2021
6081(2^392342+5)/27118106Lelio R Paula04/2014
6082(2^392333+1782)/2118104Stefano Morozzi01/2021
60832^392300-1841429118095Enzo Doria06/2015
60843*2^392260-5118083Jon Grantham07/2023
60852^392220+75241118070Enzo Doria04/2016
608627836^17409+17409^27836118047Hans Havermann02/2021
6087(13^118026)%(10^118026)118026Henri Lifchitz05/2025
608810^118009+664447118010Patrick De Geest07/2018
608910^118009-20001118009Robert Price01/2018
6090(14*10^117991+61)/3117992Robert Price12/2018
60912^391933+5897117984Yves Minet02/2011
60922^391912-1849259117978Enzo Doria08/2015
6093(2*34^77029+1043)/11117968Eric Chen08/2023
60945*2^391836-3117956Jon Grantham07/2023
609528357^14440+14440^28357117953Hans Havermann02/2021
6096(2^391812+5)/14181117944Lelio R Paula04/2014
609785^61124-61124^85117934Norman Luhn09/2024
6098(7*10^117930-79)/9117930Robert Price01/2021
609927531^19168+19168^27531117904Hans Havermann02/2021
6100(46*10^117902+683)/9117903Robert Price03/2019
610126349^26668-26668^26349117893Frank Doornink03/2024
610227670^18189+18189^27670117869Hans Havermann02/2021
6103(7*2^391521+1)/285117858Lelio R Paula04/2014
6104(56*10^117856+583)/9117857Robert Price08/2021
610532169^4606+4606^32169117846Hans Havermann02/2021
6106(71*10^117803-143)/9117804Robert Price10/2021
61072^391324+90901117801Yves Minet02/2011
61082^391301-1859923117794Enzo Doria03/2016
61092^391261-4131117782Yves Minet02/2018
6110(2^391211+554)/2117766Stefano Morozzi09/2020
6111816^40445-40445^816117764Norman Luhn09/2024
611238434^1157+1157^38434117737Hans Havermann01/2021
6113(2^391115-7)/11791117734Lelio R Paula04/2014
6114(85*10^117719+473)/9117720Robert Price01/2020
6115(2^391049+582)/2117718Stefano Morozzi09/2020
6116(21*23^86445-197)/22117715Eric Chen08/2023
611731083^6122+6122^31083117709Hans Havermann02/2021
61182^390960+1880881117691Enzo Doria11/2016
6119(71*10^117685+91)/9117686Robert Price04/2022
61212^390897-1860553117672Enzo Doria11/2015
6120(61*10^117671+47)/9117672Robert Price07/2022
61222^390889-115003117670Enzo Doria06/2015
612312^109010+35117642Riley Fisher08/2023
61242^390779-30337117637Paul Bourdelais02/2012
6125(2^390735+378)/2117623Stefano Morozzi02/2021
612611^112916-780117590Enzo Doria12/2012
612727641^17916+17916^27641117564Hans Havermann02/2021
612827906^16321+16321^27906117561Hans Havermann02/2021
612927294^20275+20275^27294117555Hans Havermann02/2021
6130(2^390473+1002)/2117544Stefano Morozzi09/2020
613135912^1875+1875^35912117541Hans Havermann02/2021
6132(16^97613-5^97613)/11117537Robert Price07/2013
6133(2^390438+1774)/2117534Stefano Morozzi01/2021
6134(2^390418+1722)/2117528Stefano Morozzi09/2020
6135(2^390403+654)/2117523Stefano Morozzi09/2020
6136(2^390343+2246)/2117505Stefano Morozzi01/2021
613728043^15478+15478^28043117493Hans Havermann02/2021
6138(17*2^390272+1)/1983117482Lelio R Paula04/2014
613937077^1474+1474^37077117479Hans Havermann01/2021
614031^78759-30117459Theodore Burton02/2007
6141(2^390176+1222)/2117455Stefano Morozzi09/2020
6142(2^390133+1242)/2117442Stefano Morozzi09/2020
6143(2^390013+2634)/2117406Stefano Morozzi09/2020
61443*10^117402+61117403Robert Price09/2020
61452^389998+37117402Lelio R Paula03/2013
6146(2^389977+314)/2117395Stefano Morozzi09/2020
6147(2^389921+342)/2117378Stefano Morozzi01/2021
614871830^43+43^71830117333Hans Havermann01/2021
6149(2^389768+1582)/2117332Stefano Morozzi09/2020
615033802^2951+2951^33802117292Hans Havermann02/2021
615126789^23866+23866^26789117277Hans Havermann02/2021
615229^80192-1*80192^29117273Dylan Delgado12/2019
6153(101*10^117260+7)/9117262Robert Price02/2022
6154(13*10^117249+161)/3117250Robert Price11/2018
61552^389478+43117245Lelio R Paula03/2013
6156(298*10^117229-7)/3117231Robert Price06/2020
6157(2^389416+342)/2117226Stefano Morozzi01/2021
6158(29*2^389351-1)/9117207Lelio R Paula04/2014
61595*10^117205+23117206Robert Price03/2019
6160(2^389341-7)/3865117200Lelio R Paula03/2014
616127272^19827+19827^27272117195Hans Havermann01/2021
6162(2^389276+2650)/2117184Stefano Morozzi09/2020
6163(844*10^117175-7)/9117177Robert Price05/2021
616410^117142+209223117143Patrick De Geest04/2018
616610^117142-1000000001117142Robert Price03/2018
616510^117142-966057117142Patrick De Geest04/2018
616710^117135+360577117136Patrick De Geest07/2018
616810^117135-401117135Robert Price01/2018
616926415^26488-26488^26415117126Norbert Schneider05/2021
61704*10^117123+79117124Robert Price08/2018
61712^389033-12797413117111Enzo Doria04/2016
6172(2^388987+2634)/2117097Stefano Morozzi09/2020
61732^388960-109505117089Enzo Doria04/2014
61747*10^117082-57117083Robert Price06/2020
6175791^40398-40398^791117081Norman Luhn09/2024
6176(2^388928-5)/569117077Lelio R Paula03/2014
61772^388888-1529117067Yves Minet01/2013
617810^117059+28879117060Patrick De Geest05/2016
6179(10^117059-71)/1117059Serge Batalov12/2014
6180(2^388854+3630)/2117057Stefano Morozzi09/2020
6181(2^388842+2098)/2117053Stefano Morozzi09/2020
6182(2^388789+3150)/2117037Stefano Morozzi09/2020
6183(2^388748+378)/2117025Stefano Morozzi02/2021
6184(693^41189-1)/692117005Michael Stocker05/2020
6185(26*10^116999-503)/9117000Robert Price07/2018
618620^89917-21116985Anonymous09/2024
6187(2^388609+1554)/2116983Stefano Morozzi09/2020
618838496^1093+1093^38496116975Hans Havermann02/2021
61893^245154-6256116969Enzo Doria05/2014
61905*10^116966-43116967Robert Price01/2019
61912^388536-113495116961Enzo Doria08/2014
6192(2^388512+382)/2116954Stefano Morozzi02/2021
6193(8*32^77701+271)/31116952Eric Chen11/2023
61942^388469-43116941Lelio R Paula03/2013
619527417^18416+18416^27417116939Hans Havermann02/2021
6196(2^388438+1842)/2116932Stefano Morozzi02/2021
6197(7*2^388372-1)/111116911Lelio R Paula04/2014
6198(7*2^388335-1)/25116900Lelio R Paula04/2014
61992^388180+93116854Donovan Johnson07/2008
6200(2^388167+2510)/2116850Stefano Morozzi09/2020
6201(85*10^116842+293)/9116843Robert Price12/2019
620235296^2043+2043^35296116840Hans Havermann02/2021
6203(2^388081+7)/1179116821Lelio R Paula03/2014
620438633^1056+1056^38633116814Hans Havermann02/2021
62052^387946-113261116784Enzo Doria07/2014
620628*36^75009+305116739Eric Chen12/2022
620728363^13056+13056^28363116737Hans Havermann02/2021
62082^387745+75557116723Enzo Doria04/2016
6209(29*10^116719+313)/9116720Robert Price04/2021
621029622^8699+8699^29622116695Hans Havermann02/2021
6211(206*10^116687-17)/9116689Robert Price01/2020
6212(7*10^116684+179)/3116685Robert Price09/2018
62132^387554+71455116666Enzo Doria04/2016
6214(602*10^116647-71)/9116649Robert Price12/2021
62153^244461-10116638Tyler NeSmith09/2022
6216(2^387447+78557)/365116631Lelio R Paula12/2014
6217(2*10^116620+43)/9116620Serge Batalov11/2022
6218(19*10^116617+287)/9/12893116614Alfred Reich11/2022
6219(145*10^116610-1)/9116612Serge Batalov12/2014
6220(25*10^116601-331)/9116602Robert Price08/2018
622125791^26428-26428^25791116587Frank Doornink03/2024
6223(17*2^387284-1)/59116584Lelio R Paula04/2014
6222(2^387284+3726)/2116584Stefano Morozzi09/2020
62242^387211+111546435116563Paul Bourdelais10/2021
622510^116557+987654321116558Robert Price12/2019
622610^116557+9141116558Patrick De Geest02/2020
622710^116557-609431116557Patrick De Geest02/2020
6228209^50234-50234^209116551Norman Luhn09/2024
6229(28*10^116546+41)/3116547Robert Price07/2021
6230(2^387123+1814)/2116536Stefano Morozzi02/2021
6231(2^387076+2046)/2116522Stefano Morozzi09/2020
6232(2^387073+2570)/2116521Stefano Morozzi09/2020
6233(7*10^116514-1)/3116515Robert Price08/2022
6234(26*32^77406-390071011)/31116508Eric Chen11/2023
623528846^10931+10931^28846116500Hans Havermann02/2021
623610^116496+3593037116497Paul Bourdelais10/2021
6237272^47851-47851^272116497Norman Luhn09/2024
6238(31*2^386968+1)/7116490Lelio R Paula03/2014
6239(944^39157+1)/945116489Jinyuan Wang12/2024
62402^386947+1869143116483Enzo Doria05/2016
6241(30^78857-1)/29116480Robert Price12/2011
6242(2^386903-3)/5116469Lelio R Paula03/2014
624328107^13892+13892^28107116441Hans Havermann02/2021
624429110^9957+9957^29110116386Hans Havermann02/2021
624526469^24838+24838^26469116335Hans Havermann01/2021
62462^386389-1864783116315Enzo Doria03/2016
6247(8*32^77250-163)/31116273Eric Chen11/2023
6248(31*2^386231-1)/1711116266Lelio R Paula03/2014
6249297^47012+47012^297116250Norbert Schneider07/2018
6250(35*10^116223-341)/9116224Robert Price08/2021


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 21 2025 13:33 (Time in France)

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