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 ?
60014*5^159563-9111531Lelio R Paula11/2014
60025*10^111528-21111529Robert Price12/2021
6003(4^185225+23)/3111517Robert Price10/2018
60042^370393-2797093111500Enzo Doria03/2016
6005(21*2^370382-1)/629111495Lelio R Paula03/2014
6006(2^370371+554)/2111493Stefano Morozzi09/2020
60076^143273-5111489Paul Bourdelais01/2021
60082^370292-2791979111469Enzo Doria03/2016
6009(14*10^111443-11)/3111444Robert Price08/2022
60102^370177-461551111435Enzo Doria07/2015
6011(2^370169+1706)/2111432Stefano Morozzi09/2020
6012109^54683-108111413Norbert Schneider02/2017
6013(83*10^111406-173)/9111407Robert Price04/2021
6014(2^370043+1010)/2111394Stefano Morozzi09/2020
601532961^2396+2396^32961111392Hans Havermann10/2020
6016numbpart(10^10+76282)111391Serge Batalov04/2015
6017(19*10^111385+11)/3111386Robert Price07/2023
6018(23*10^111380-29)/3111381Robert Price03/2022
60192^369974+733111374Lelio R Paula05/2013
6020121^53470+120111367Norbert Schneider10/2018
60212^369915-286267111356Enzo Doria07/2015
6022(62*10^111347-629)/9111348Robert Price07/2021
60232^369855-1615111338Lelio R Paula05/2017
60247*10^111325+3111326Robert Price08/2015
602551^65176+2111293Lelio R Paula08/2013
60262^369643-1865767111274Enzo Doria03/2016
60272^369603+885111262Lelio R Paula05/2017
602825555^22564+22564^25555111252Hans Havermann10/2020
6029L(532277)111240Renaud Lifchitz03/2004
6030105^55033-2111233Lelio R Paula10/2017
6031(35*10^111232-737)/9111233Robert Price07/2018
603226970^13307+13307^26970111227Hans Havermann10/2020
603325419^23716+23716^25419111210Hans Havermann10/2020
60349*10^111201-29111202Robert Price09/2019
60352^369392+29835111199Lelio R Paula05/2017
60363^233059+16111198Robert Price03/2020
60372^369354-3413111187Yves Minet12/2016
60382^369296-27111170Lelio R Paula02/2013
60392^369239-109837111153Enzo Doria05/2014
60402^369224-291839111148Enzo Doria07/2015
60412^369216+2798881111146Enzo Doria04/2016
604226842^13817+13817^26842111137Hans Havermann11/2020
6043(5*10^111119-191)/3111120Robert Price05/2021
6044(29*10^111112-23)/3111113Robert Price03/2022
604510^111111+163849111112Patrick De Geest03/2017
604610^111111-312911111111Patrick De Geest03/2017
60472^369092-216923111108Enzo Doria05/2014
60482^369081-55111105Lelio R Paula02/2013
6049(2^369047+3618)/2111094Stefano Morozzi09/2020
605088^57124-87111077Norbert Schneider11/2015
60512^368980+753111075Lelio R Paula05/2013
60522^368946-3623111064Yves Minet03/2017
60532^368929+29835111059Lelio R Paula05/2017
60544^184463-3^184463111058Jean-Louis Charton12/2004
6055111^54298+110111057Norbert Schneider04/2017
6056(4*10^111032-7)/3111033Ray Chandler04/2011
6057(29*10^111020-41)/3111021Tyler Busby03/2024
605835799^1262+1262^35799111015Hans Havermann10/2020
6059(298*10^111004+11)/3111006Robert Price11/2020
606027648^10349+10349^27648111004Hans Havermann11/2020
606128899^6932+6932^28899110997Hans Havermann11/2020
6062(749^38809+1)/(749^197+1)110990Martin Hopf11/2023
60632^368641-460303110972Enzo Doria06/2015
60642^368619-109087110966Enzo Doria04/2014
6065(74*10^110961+313)/9110962Robert Price06/2019
606625258^24711+24711^25258110956Hans Havermann11/2020
6067(2^368539+1290)/2110941Stefano Morozzi01/2021
60683*2^368489+7110927Lelio R Paula09/2014
6069(14*10^110922+61)/3110923Robert Price12/2018
607097411!4-2110913Robert Price07/2017
6071(301*10^110903+23)/9110905Robert Price06/2021
6072(9179*2^368330-1)/35110881Lelio R Paula05/2015
607325830^19619+19619^25830110880Hans Havermann10/2020
6074(34*10^110882-7)/9/13/29/1019374319110871Makoto Morimoto05/2016
607526022^18191+18191^26022110850Hans Havermann10/2020
6076(2^368211+2250)/2110843Stefano Morozzi01/2021
6077(37*10^110813+251)/9110814Robert Price09/2021
60782^368050-64875110795Lelio R Paula05/2017
60792^368048+25110794Lelio R Paula02/2013
6080(2^368017+2262)/2110784Stefano Morozzi02/2021
608169^60239-2110771Lelio R Paula10/2013
6082(23*2^367952+1)/15717110762Lelio R Paula03/2014
60832^367924-69110757Lelio R Paula02/2013
6084(23*10^110738+61)/3110739Robert Price01/2022
6085(2^367779+3750)/2110713Stefano Morozzi01/2021
60862^367709-109723110692Enzo Doria04/2014
60872^367687+213413110685Enzo Doria09/2023
6088(3*2^367644-1)/107110671Lelio R Paula03/2014
6089(2^367626+3514)/2110667Stefano Morozzi09/2020
6090(1288676*34^72242-455)/33110642Eric Chen03/2023
6091(23*2^367398+1)/57963110595Lelio R Paula03/2014
6092140^51515-139110558Norbert Schneider04/2019
60932^367215+1879223110543Enzo Doria09/2016
609425782^19375+19375^25782110534Hans Havermann10/2020
609526117^17058+17058^26117110526Hans Havermann10/2020
60962^367141+41110521Lelio R Paula02/2013
60972^367126+29835110516Lelio R Paula05/2017
6098(10^110503-1)/9+2*(10^59183-1)/9*10^25660110503Makoto Morimoto09/2020
6099(10^110503-1)/9+2*(10^65511-1)/9*10^22496110503Makoto Morimoto09/2020
6100(10^110503-1)/9+2*10^108327+2*10^2175110503Makoto Morimoto09/2020
6101(10^110503-1)/9+2*10^66251+2*10^44251110503Makoto Morimoto09/2020
6102(10^110503-1)/9+3*(10^28813-1)/9*10^40845110503Makoto Morimoto09/2020
6103(10^110503-1)/9+3*(10^82573-1)/9*10^13965110503Makoto Morimoto09/2020
6104(10^110503-1)/9+4*(10^43305-1)/9*10^33599110503Makoto Morimoto09/2020
6105(10^110503-1)/9+5*10^70327+5*10^40175110503Makoto Morimoto09/2020
6106(10^110503-1)/9+5*10^99423+5*10^11079110503Makoto Morimoto09/2020
6107(10^110503-1)/9+7*(10^23617-1)/9*10^43443110503Makoto Morimoto09/2020
6108(10^110503-1)/9+8*(10^30251-1)/9*10^40126110503Makoto Morimoto09/2020
61093*(10^110503-1)/9+1*10^106036+1*10^4466110503Makoto Morimoto09/2020
61103*(10^110503-1)/9+1*10^58962+1*10^51540110503Makoto Morimoto09/2020
61113*(10^110503-1)/9+1*10^78213+1*10^32289110503Makoto Morimoto09/2020
61123*(10^110503-1)/9+2*10^76898+2*10^33604110503Makoto Morimoto09/2020
61133*(10^110503-1)/9-1*10^100802-1*10^9700110503Makoto Morimoto09/2020
61143*(10^110503-1)/9-1*10^76355-1*10^34147110503Makoto Morimoto09/2020
61153*(10^110503-1)/9-2*10^105704-2*10^4798110503Makoto Morimoto09/2020
61167*(10^110503-1)/9+1*(10^27685-1)/9*10^41409110503Makoto Morimoto09/2020
61177*(10^110503-1)/9+1*(10^91035-1)/9*10^9734110503Makoto Morimoto09/2020
61187*(10^110503-1)/9-1*(10^23717-1)/9*10^43393110503Makoto Morimoto09/2020
61197*(10^110503-1)/9-1*10^57906-1*10^52596110503Makoto Morimoto09/2020
61207*(10^110503-1)/9-1*10^72287-1*10^38215110503Makoto Morimoto09/2020
61217*(10^110503-1)/9-2*(10^53823-1)/9*10^28340110503Makoto Morimoto09/2020
61227*(10^110503-1)/9-2*(10^88659-1)/9*10^10922110503Makoto Morimoto09/2020
61237*(10^110503-1)/9-3*(10^79921-1)/9*10^15291110503Makoto Morimoto09/2020
61247*(10^110503-1)/9-3*10^60024-3*10^50478110503Makoto Morimoto09/2020
61257*(10^110503-1)/9-4*(10^103091-1)/9*10^3706110503Makoto Morimoto09/2020
61267*(10^110503-1)/9-4*10^103658-4*10^6844110503Makoto Morimoto09/2020
61277*(10^110503-1)/9-4*10^78188-4*10^32314110503Makoto Morimoto09/2020
61287*(10^110503-1)/9-5*(10^35035-1)/9*10^37734110503Makoto Morimoto09/2020
61297*(10^110503-1)/9-6*(10^67347-1)/9*10^21578110503Makoto Morimoto09/2020
61307*(10^110503-1)/9-6*10^60391-6*10^50111110503Makoto Morimoto09/2020
6131(10^110503-1)-4*(10^96247-1)/9*10^7128110503Makoto Morimoto09/2020
6132(10^110503-1)-4*10^74037-4*10^36465110503Makoto Morimoto09/2020
6133(10^110503-1)-4*10^77787-4*10^32715110503Makoto Morimoto09/2020
6134(10^110503-1)-4*10^91179-4*10^19323110503Makoto Morimoto09/2020
6135(10^110503-1)-5*(10^99143-1)/9*10^5680110503Makoto Morimoto09/2020
6136(10^110503-1)-7*(10^85075-1)/9*10^12714110503Makoto Morimoto09/2020
6137(10^110503-1)-7*10^100712-7*10^9790110503Makoto Morimoto09/2020
6138(10^110503-1)-7*10^76427-7*10^34075110503Makoto Morimoto09/2020
6139(10^110503-1)-7*10^90451-7*10^20051110503Makoto Morimoto09/2020
6140(10^110503-1)-8*10^106252-8*10^4250110503Makoto Morimoto09/2020
6141(11*10^110496+49)/3110497Robert Price07/2018
614225447^21958+21958^25447110481Hans Havermann11/2020
6143(31*2^366976+1)/7110472Lelio R Paula03/2014
61447*10^110468-23110469Robert Price07/2019
61455*3^231464-2^231464110438Jon Grantham08/2023
61462^366853+5711110434Lelio R Paula05/2017
6147(21181*2^366833+1)/3110432Lelio R Paula07/2014
61482^366816+315110423Lelio R Paula05/2017
61492^366775-2787037110411Enzo Doria03/2016
6150(112*10^110405-1)/3110407Serge Batalov12/2014
61512^366751+2797553110404Enzo Doria03/2016
615225276^23331+23331^25276110404Hans Havermann10/2020
61532^366748+255110403Lelio R Paula05/2017
61542^366738-2985110400Yves Minet09/2014
6155(23*2^366739+1)/74575110396Lelio R Paula03/2014
6156(2^366722+1314)/2110395Stefano Morozzi02/2021
61572^366716+1871791110393Enzo Doria05/2016
6158(239*23^81066-349)/22110391Eric Chen08/2023
61592^366649+1871687110373Enzo Doria05/2016
61602^366629-351205110367Enzo Doria06/2015
6161(31*10^110363+257)/9110364Robert Price12/2021
6162(17*19^86292-215)/18110347Eric Chen01/2023
61642^366558+1874479110345Enzo Doria06/2016
616325132^24581+24581^25132110345Hans Havermann10/2020
6165(2^366539+770)/2110339Stefano Morozzi09/2020
616626368^15285+15285^26368110331Hans Havermann10/2020
6167(23*10^110290+19)/3110291Robert Price07/2019
616818^87853-4409110280Enzo Doria03/2013
616928490^7419+7419^28490110267Hans Havermann11/2020
61702^366218-23110243Lelio R Paula02/2013
6171(21*2^366193-1)/197110235Lelio R Paula03/2014
61722^366178-343991110231Enzo Doria07/2015
617312^102123-11110210Riley Fisher09/2023
617425777^18798+18798^25777110174Hans Havermann10/2020
61752^365944+1871341110161Enzo Doria05/2016
61762^365838-461267110129Enzo Doria07/2015
617730152^4491+4491^30152110126Hans Havermann11/2020
61782^365802+23359110118Enzo Doria10/2023
617910^110111+464019110112Patrick De Geest05/2021
618010^110111-40001110111Robert Price01/2021
61812^365763-6555110106Lelio R Paula04/2017
6182(2^365689+2^182845+1)/511008311/2006
61832^365666-459161110077Enzo Doria05/2015
61843*10^110076-7110077Robert Price08/2015
618513^98785-72110041Lelio R Paula03/2017
6186(25^78707+1)/26110027Robert Price06/2013
6187(7*10^110027-277)/9110027Robert Price02/2022
6188(16*10^110014-73)/3110015Robert Price07/2020
6189(7*10^110006-151)/9110006Robert Price02/2018
61906^141361-7110001Lelio R Paula11/2014
619120^84536+81109984Lelio R Paula03/2017
61925*2^365347-9109982Lelio R Paula09/2014
61939*6^141303+7109957Lelio R Paula11/2014
619427635^9522+9522^27635109953Hans Havermann11/2020
619578^58099+77109929Norbert Schneider02/2015
61962*10^109928-7109929Robert Price10/2015
619730580^3933+3933^30580109927Hans Havermann11/2020
619826380^14689+14689^26380109926Hans Havermann11/2020
6199(2^365161+1130)/2109925Stefano Morozzi09/2020
6200(27*2^365137-1)/2021109916Lelio R Paula03/2014
6201(4441*29^75152-24)/7109905Curtis Bright05/2015
6202(2^365087+7)/6015109899Lelio R Paula01/2014
6203(2^365069+3774)/2109897Stefano Morozzi02/2021
620429652^5083+5083^29652109894Mark Rodenkirch10/2020
6205(2^365049+722)/2109891Stefano Morozzi09/2020
6206(35*10^109888-89)/9109889Robert Price02/2022
620718^87533-11109878Lelio R Paula04/2017
62082^364982-5109871Henri Lifchitz04/2006
62093*10^109861+59109862Robert Price08/2018
62105*10^109860-69109861Robert Price02/2021
62112^364936-1867979109857Enzo Doria04/2016
621227013^11652+11652^27013109846Hans Havermann10/2020
62132^364867-112087109836Enzo Doria06/2014
62144^182415-85061109825Mike Oakes06/2011
6215(2^364809+1034)/2109819Stefano Morozzi09/2020
6216(53*10^109809-287)/9109810Robert Price02/2022
6217(52*10^109807-133)/9109808Robert Price09/2021
621825708^18675+18675^25708109806Hans Havermann10/2020
6219(17^89227+16^89227)/33109788Robert Price08/2013
62202^364687-187109782Lelio R Paula01/2012
62212^364644+67109769Lelio R Paula01/2012
6222(9787*2^364625-1)/24947109763Lelio R Paula05/2015
6223(2^364616+5)/9109760Lelio R Paula01/2014
6224(55*10^109759+89)/9109760Robert Price03/2019
6225(14*32^72921+4171)/31109757Eric Chen04/2023
622612^101694+73109747Lelio R Paula03/2017
622713^98518-66109744Lelio R Paula03/2017
6228(8*10^109721-269)/9109721Robert Price09/2021
62292^364478-113261109719Enzo Doria07/2014
6230(2^364513+1)/(3*44290516579)109719Gord Palameta08/2018
6231(24737*2^364454+1)/3109716Lelio R Paula07/2014
623227814^8777+8777^27814109681Hans Havermann10/2020
6233(62*10^109673+1)/9109674Serge Batalov11/2010
62343^229824+340109654Lelio R Paula03/2017
6235(16623*33^72206-8095)/16109649Eric Chen05/2023
6236(2*10^109645-71)/3109645Robert Price12/2017
62372^364169-112813109626Enzo Doria06/2014
623828822^6359+6359^28822109622Hans Havermann11/2020
623910^109615+21109616Lelio R Paula03/2017
624010^109615-456267109615Patrick De Geest03/2017
62412^364094-113109604Lelio R Paula01/2012
624225251^21898+21898^25251109600Hans Havermann11/2020
6243(4^182026+11)/3109591Robert Price02/2017
62442^364041-6883109588Lelio R Paula09/2011
624512^101545+11109586Lelio R Paula03/2017
624626536^13475+13475^26536109582Hans Havermann11/2020
62472^363842-2787101109528Enzo Doria03/2016
6248(2^363812+3570)/2109519Stefano Morozzi09/2020
6249(22699*2^363782+1)/763109511Lelio R Paula07/2014
62502^363769+5711109506Lelio R Paula04/2017


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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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