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 ?
6501(2^370043+1010)/2111394Stefano Morozzi09/2020
650232961^2396+2396^32961111392Hans Havermann10/2020
6503numbpart(10^10+76282)111391Serge Batalov04/2015
6504(19*10^111385+11)/3111386Robert Price07/2023
6505(23*10^111380-29)/3111381Robert Price03/2022
65062^369974+733111374Lelio R Paula05/2013
6507121^53470+120111367Norbert Schneider10/2018
65082^369915-286267111356Enzo Doria07/2015
6509(62*10^111347-629)/9111348Robert Price07/2021
65102^369855-1615111338Lelio R Paula05/2017
65117*10^111325+3111326Robert Price08/2015
651251^65176+2111293Lelio R Paula08/2013
65132^369643-1865767111274Enzo Doria03/2016
65142^369603+885111262Lelio R Paula05/2017
651525555^22564+22564^25555111252Hans Havermann10/2020
6516F(532391)/89441689/1425422598617111243Serge Batalov07/2024
6517L(532277)111240Renaud Lifchitz03/2004
6518105^55033-2111233Lelio R Paula10/2017
6519(35*10^111232-737)/9111233Robert Price07/2018
652026970^13307+13307^26970111227Hans Havermann10/2020
652125419^23716+23716^25419111210Hans Havermann10/2020
65229*10^111201-29111202Robert Price09/2019
65232^369392+29835111199Lelio R Paula05/2017
65243^233059+16111198Robert Price03/2020
65252^369354-3413111187Yves Minet12/2016
65262^369296-27111170Lelio R Paula02/2013
6527(2468^40960+1)/(2468^8192+1)111161Martin Hopf08/2024
65282^369239-109837111153Enzo Doria05/2014
65292^369224-291839111148Enzo Doria07/2015
65302^369216+2798881111146Enzo Doria04/2016
653126842^13817+13817^26842111137Hans Havermann11/2020
6532(5*10^111119-191)/3111120Robert Price05/2021
6533(29*10^111112-23)/3111113Robert Price03/2022
653410^111111+163849111112Patrick De Geest03/2017
653510^111111-312911111111Patrick De Geest03/2017
65362^369092-216923111108Enzo Doria05/2014
65372^369081-55111105Lelio R Paula02/2013
6538(2^369047+3618)/2111094Stefano Morozzi09/2020
653988^57124-87111077Norbert Schneider11/2015
65402^368980+753111075Lelio R Paula05/2013
65412^368946-3623111064Yves Minet03/2017
65422^368929+29835111059Lelio R Paula05/2017
65434^184463-3^184463111058Jean-Louis Charton12/2004
6544111^54298+110111057Norbert Schneider04/2017
6545(4*10^111032-7)/3111033Ray Chandler04/2011
6546(29*10^111020-41)/3111021Tyler Busby03/2024
654735799^1262+1262^35799111015Hans Havermann10/2020
6548(298*10^111004+11)/3111006Robert Price11/2020
654927648^10349+10349^27648111004Hans Havermann11/2020
655028899^6932+6932^28899110997Hans Havermann11/2020
6551(749^38809+1)/(749^197+1)110990Martin Hopf11/2023
65522^368641-460303110972Enzo Doria06/2015
65532^368619-109087110966Enzo Doria04/2014
6554(74*10^110961+313)/9110962Robert Price06/2019
655525258^24711+24711^25258110956Hans Havermann11/2020
6556(2^368539+1290)/2110941Stefano Morozzi01/2021
65573*2^368489+7110927Lelio R Paula09/2014
6558(14*10^110922+61)/3110923Robert Price12/2018
655997411!4-2110913Robert Price07/2017
6560(301*10^110903+23)/9110905Robert Price06/2021
6561(9179*2^368330-1)/35110881Lelio R Paula05/2015
656225830^19619+19619^25830110880Hans Havermann10/2020
6563(34*10^110882-7)/9/13/29/1019374319110871Makoto Morimoto05/2016
656426022^18191+18191^26022110850Hans Havermann10/2020
6565(2^368211+2250)/2110843Stefano Morozzi01/2021
6566(37*10^110813+251)/9110814Robert Price09/2021
65672^368050-64875110795Lelio R Paula05/2017
65682^368048+25110794Lelio R Paula02/2013
6569(2^368017+2262)/2110784Stefano Morozzi02/2021
657069^60239-2110771Lelio R Paula10/2013
6571(23*2^367952+1)/15717110762Lelio R Paula03/2014
65722^367924-69110757Lelio R Paula02/2013
6573(23*10^110738+61)/3110739Robert Price01/2022
6574(2^367779+3750)/2110713Stefano Morozzi01/2021
65752^367709-109723110692Enzo Doria04/2014
65762^367687+213413110685Enzo Doria09/2023
6577(3*2^367644-1)/107110671Lelio R Paula03/2014
6578(2^367626+3514)/2110667Stefano Morozzi09/2020
6579(1288676*34^72242-455)/33110642Eric Chen03/2023
6580379*10^110616+9110619Jason Yuen01/2025
6581(23*2^367398+1)/57963110595Lelio R Paula03/2014
6582140^51515-139110558Norbert Schneider04/2019
65832^367215+1879223110543Enzo Doria09/2016
658425782^19375+19375^25782110534Hans Havermann10/2020
658526117^17058+17058^26117110526Hans Havermann10/2020
65862^367141+41110521Lelio R Paula02/2013
65872^367126+29835110516Lelio R Paula05/2017
6588(10^110503-1)/9+2*(10^59183-1)/9*10^25660110503Makoto Morimoto09/2020
6589(10^110503-1)/9+2*(10^65511-1)/9*10^22496110503Makoto Morimoto09/2020
6590(10^110503-1)/9+2*10^108327+2*10^2175110503Makoto Morimoto09/2020
6591(10^110503-1)/9+2*10^66251+2*10^44251110503Makoto Morimoto09/2020
6592(10^110503-1)/9+3*(10^28813-1)/9*10^40845110503Makoto Morimoto09/2020
6593(10^110503-1)/9+3*(10^82573-1)/9*10^13965110503Makoto Morimoto09/2020
6594(10^110503-1)/9+4*(10^43305-1)/9*10^33599110503Makoto Morimoto09/2020
6595(10^110503-1)/9+5*10^70327+5*10^40175110503Makoto Morimoto09/2020
6596(10^110503-1)/9+5*10^99423+5*10^11079110503Makoto Morimoto09/2020
6597(10^110503-1)/9+7*(10^23617-1)/9*10^43443110503Makoto Morimoto09/2020
6598(10^110503-1)/9+8*(10^30251-1)/9*10^40126110503Makoto Morimoto09/2020
65993*(10^110503-1)/9+1*10^106036+1*10^4466110503Makoto Morimoto09/2020
66003*(10^110503-1)/9+1*10^58962+1*10^51540110503Makoto Morimoto09/2020
66013*(10^110503-1)/9+1*10^78213+1*10^32289110503Makoto Morimoto09/2020
66023*(10^110503-1)/9+2*10^76898+2*10^33604110503Makoto Morimoto09/2020
66033*(10^110503-1)/9-1*10^100802-1*10^9700110503Makoto Morimoto09/2020
66043*(10^110503-1)/9-1*10^76355-1*10^34147110503Makoto Morimoto09/2020
66053*(10^110503-1)/9-2*10^105704-2*10^4798110503Makoto Morimoto09/2020
66067*(10^110503-1)/9+1*(10^27685-1)/9*10^41409110503Makoto Morimoto09/2020
66077*(10^110503-1)/9+1*(10^91035-1)/9*10^9734110503Makoto Morimoto09/2020
66087*(10^110503-1)/9-1*(10^23717-1)/9*10^43393110503Makoto Morimoto09/2020
66097*(10^110503-1)/9-1*10^57906-1*10^52596110503Makoto Morimoto09/2020
66107*(10^110503-1)/9-1*10^72287-1*10^38215110503Makoto Morimoto09/2020
66117*(10^110503-1)/9-2*(10^53823-1)/9*10^28340110503Makoto Morimoto09/2020
66127*(10^110503-1)/9-2*(10^88659-1)/9*10^10922110503Makoto Morimoto09/2020
66137*(10^110503-1)/9-3*(10^79921-1)/9*10^15291110503Makoto Morimoto09/2020
66147*(10^110503-1)/9-3*10^60024-3*10^50478110503Makoto Morimoto09/2020
66157*(10^110503-1)/9-4*(10^103091-1)/9*10^3706110503Makoto Morimoto09/2020
66167*(10^110503-1)/9-4*10^103658-4*10^6844110503Makoto Morimoto09/2020
66177*(10^110503-1)/9-4*10^78188-4*10^32314110503Makoto Morimoto09/2020
66187*(10^110503-1)/9-5*(10^35035-1)/9*10^37734110503Makoto Morimoto09/2020
66197*(10^110503-1)/9-6*(10^67347-1)/9*10^21578110503Makoto Morimoto09/2020
66207*(10^110503-1)/9-6*10^60391-6*10^50111110503Makoto Morimoto09/2020
6621(10^110503-1)-4*(10^96247-1)/9*10^7128110503Makoto Morimoto09/2020
6622(10^110503-1)-4*10^74037-4*10^36465110503Makoto Morimoto09/2020
6623(10^110503-1)-4*10^77787-4*10^32715110503Makoto Morimoto09/2020
6624(10^110503-1)-4*10^91179-4*10^19323110503Makoto Morimoto09/2020
6625(10^110503-1)-5*(10^99143-1)/9*10^5680110503Makoto Morimoto09/2020
6626(10^110503-1)-7*(10^85075-1)/9*10^12714110503Makoto Morimoto09/2020
6627(10^110503-1)-7*10^100712-7*10^9790110503Makoto Morimoto09/2020
6628(10^110503-1)-7*10^76427-7*10^34075110503Makoto Morimoto09/2020
6629(10^110503-1)-7*10^90451-7*10^20051110503Makoto Morimoto09/2020
6630(10^110503-1)-8*10^106252-8*10^4250110503Makoto Morimoto09/2020
6631(11*10^110496+49)/3110497Robert Price07/2018
663225447^21958+21958^25447110481Hans Havermann11/2020
6633(31*2^366976+1)/7110472Lelio R Paula03/2014
66347*10^110468-23110469Robert Price07/2019
66355*3^231464-2^231464110438Jon Grantham08/2023
66362^366853+5711110434Lelio R Paula05/2017
6637(21181*2^366833+1)/3110432Lelio R Paula07/2014
66382^366816+315110423Lelio R Paula05/2017
66392^366775-2787037110411Enzo Doria03/2016
6640(112*10^110405-1)/3110407Serge Batalov12/2014
66412^366751+2797553110404Enzo Doria03/2016
664225276^23331+23331^25276110404Hans Havermann10/2020
66432^366748+255110403Lelio R Paula05/2017
66442^366738-2985110400Yves Minet09/2014
6645(23*2^366739+1)/74575110396Lelio R Paula03/2014
6646(2^366722+1314)/2110395Stefano Morozzi02/2021
66472^366716+1871791110393Enzo Doria05/2016
6648(239*23^81066-349)/22110391Eric Chen08/2023
66492^366695+1334025110387Henri Lifchitz10/2024
66502^366649+1871687110373Enzo Doria05/2016
66512^366629-351205110367Enzo Doria06/2015
6652(31*10^110363+257)/9110364Robert Price12/2021
6653(17*19^86292-215)/18110347Eric Chen01/2023
66552^366558+1874479110345Enzo Doria06/2016
665425132^24581+24581^25132110345Hans Havermann10/2020
6656(2^366539+770)/2110339Stefano Morozzi09/2020
665726368^15285+15285^26368110331Hans Havermann10/2020
6658(23*10^110290+19)/3110291Robert Price07/2019
665918^87853-4409110280Enzo Doria03/2013
666028490^7419+7419^28490110267Hans Havermann11/2020
66612^366218-23110243Lelio R Paula02/2013
6662(21*2^366193-1)/197110235Lelio R Paula03/2014
66632^366178-343991110231Enzo Doria07/2015
666412^102123-11110210Riley Fisher09/2023
666525777^18798+18798^25777110174Hans Havermann10/2020
66662^365944+1871341110161Enzo Doria05/2016
66672^365838-461267110129Enzo Doria07/2015
666830152^4491+4491^30152110126Hans Havermann11/2020
66692^365802+23359110118Enzo Doria10/2023
667010^110111+464019110112Patrick De Geest05/2021
667110^110111-40001110111Robert Price01/2021
66722^365763-6555110106Lelio R Paula04/2017
6673(2^365689+2^182845+1)/511008311/2006
66742^365666-459161110077Enzo Doria05/2015
66753*10^110076-7110077Robert Price08/2015
667613^98785-72110041Lelio R Paula03/2017
6678(25^78707+1)/26110027Robert Price06/2013
6677(7*10^110027-277)/9110027Robert Price02/2022
6679(16*10^110014-73)/3110015Robert Price07/2020
6680(7*10^110006-151)/9110006Robert Price02/2018
66816^141361-7110001Lelio R Paula11/2014
668210^110000+8029681110001Hayden Chesnut11/2024
668310^110000+2044477110001Hayden Chesnut11/2024
668410^110000+76407110001Hayden Chesnut11/2024
668510^110000+167311110001Hayden Chesnut11/2024
668620^84536+81109984Lelio R Paula03/2017
66875*2^365347-9109982Lelio R Paula09/2014
66889*6^141303+7109957Lelio R Paula11/2014
668927635^9522+9522^27635109953Hans Havermann11/2020
669078^58099+77109929Norbert Schneider02/2015
66912*10^109928-7109929Robert Price10/2015
669230580^3933+3933^30580109927Hans Havermann11/2020
669326380^14689+14689^26380109926Hans Havermann11/2020
6694(2^365161+1130)/2109925Stefano Morozzi09/2020
6695(27*2^365137-1)/2021109916Lelio R Paula03/2014
669629^75157-30109910Anonymous09/2024
6697(4441*29^75152-24)/7109905Curtis Bright05/2015
6698(2^365087+7)/6015109899Lelio R Paula01/2014
6699(2^365069+3774)/2109897Stefano Morozzi02/2021
670029652^5083+5083^29652109894Mark Rodenkirch10/2020
6701(2^365049+722)/2109891Stefano Morozzi09/2020
6702(35*10^109888-89)/9109889Robert Price02/2022
670318^87533-11109878Lelio R Paula04/2017
67042^364982-5109871Henri Lifchitz04/2006
67053*10^109861+59109862Robert Price08/2018
67065*10^109860-69109861Robert Price02/2021
67072^364936-1867979109857Enzo Doria04/2016
670827013^11652+11652^27013109846Hans Havermann10/2020
67092^364867-112087109836Enzo Doria06/2014
67104^182415-85061109825Mike Oakes06/2011
6711(2^364809+1034)/2109819Stefano Morozzi09/2020
671224972^24972-8323^8323109814Henri Lifchitz10/2024
6713(53*10^109809-287)/9109810Robert Price02/2022
6714(52*10^109807-133)/9109808Robert Price09/2021
671525708^18675+18675^25708109806Hans Havermann10/2020
6716(17^89227+16^89227)/33109788Robert Price08/2013
67172^364687-187109782Lelio R Paula01/2012
67182^364644+67109769Lelio R Paula01/2012
6719(9787*2^364625-1)/24947109763Lelio R Paula05/2015
6720(2^364616+5)/9109760Lelio R Paula01/2014
6721(55*10^109759+89)/9109760Robert Price03/2019
6722(14*32^72921+4171)/31109757Eric Chen04/2023
672312^101694+73109747Lelio R Paula03/2017
672413^98518-66109744Lelio R Paula03/2017
6725(35^71069+2^71069)/37109734Robert Price01/2025
6726(8*10^109721-269)/9109721Robert Price09/2021
67272^364478-113261109719Enzo Doria07/2014
6728(2^364513+1)/(3*44290516579)109719Gord Palameta08/2018
6729(24737*2^364454+1)/3109716Lelio R Paula07/2014
673027814^8777+8777^27814109681Hans Havermann10/2020
6731(62*10^109673+1)/9109674Serge Batalov11/2010
67323^229824+340109654Lelio R Paula03/2017
6733(16623*33^72206-8095)/16109649Eric Chen05/2023
6734(2*10^109645-71)/3109645Robert Price12/2017
6735V(786978)109644Serge Batalov07/2024
67362^364169-112813109626Enzo Doria06/2014
673728822^6359+6359^28822109622Hans Havermann11/2020
673810^109615+21109616Lelio R Paula03/2017
673910^109615-456267109615Patrick De Geest03/2017
6740522^40331-40331^522109607Norman Luhn09/2024
67412^364094-113109604Lelio R Paula01/2012
674225251^21898+21898^25251109600Hans Havermann11/2020
6743(4^182026+11)/3109591Robert Price02/2017
67442^364041-6883109588Lelio R Paula09/2011
674512^101545+11109586Lelio R Paula03/2017
674626536^13475+13475^26536109582Hans Havermann11/2020
67472^363842-2787101109528Enzo Doria03/2016
6748(2^363812+3570)/2109519Stefano Morozzi09/2020
6749(996^36527+1)/997109515Jinyuan Wang12/2024
6750(22699*2^363782+1)/763109511Lelio R Paula07/2014


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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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