PRP Records

Probable Primes Top 10000

(295012 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 ?
350137875^7112+7112^37875145895Hans Havermann01/2021
350232862^27473+27473^32862145872Hans Havermann01/2021
350332836^27587+27587^32836145815Hans Havermann01/2021
35042^484341+1879157145802Enzo Doria08/2016
35052*10^145784-91145785Robert Price04/2020
35062^484271-51145781Lelio R Paula11/2017
3507(188*10^145750-11)/3145752Robert Price02/2022
350870^78989-69^78989145743Robert Price01/2014
350951^85334+2145714Robert Price07/2015
35102^483886-1857101145665Enzo Doria10/2015
351133350^23307+23307^33350145656Hans Havermann01/2021
3512(19*10^145585+131)/3145586Robert Price06/2020
351331815^32332-32332^31815145580Frank Doornink01/2024
35142^483563-1863457145567Enzo Doria12/2015
35154*10^145563-69145564Robert Price01/2022
35162^483516-1861409145553Enzo Doria11/2015
35172^483384-115019145514Enzo Doria06/2015
3518(259*10^145501-1)/3145503Robert Price12/2020
3519(19*10^145499-61)/3145500Robert Price05/2019
35202^483302-3221145489Lelio R Paula12/2012
3521(23*10^145463+61)/3145464Robert Price01/2022
352235523^12434+12434^35523145453Hans Havermann01/2021
3523(29121^32761-1)/(29121^181-1)145444Ryan Propper11/2023
35242^483046+1874029145412Enzo Doria06/2016
35252^482991-2789317145395Enzo Doria12/2015
35262^482978-2789711145391Enzo Doria12/2015
35272^482966-2789711145388Enzo Doria12/2015
35282^482817-1858843145343Enzo Doria10/2015
35292^482751-113635145323Enzo Doria08/2014
35302^482705-459763145309Enzo Doria05/2015
3531(4^241306+11)/3145281Robert Price03/2017
3532(238*10^145276-1)/3145278Robert Price04/2020
3533(19*2^482534+1)/7145258Lelio R Paula09/2015
353453^84239-52^84239145252Robert Price01/2013
35352^482386+212419145213Enzo Doria08/2023
353647952^1067+1067^47952145207Hans Havermann01/2021
3537(2^482333+5)/9287145193Lelio R Paula09/2015
35382^482087+72623145123Enzo Doria04/2016
35392^482016-286565145102Enzo Doria07/2015
3540(19*10^145093+101)/3145094Robert Price09/2019
35412^481956+121145084Stefano Morozzi04/2021
35422^481840+15145049Robert Price09/2015
3543(23*10^145040+7)/3145041Robert Price05/2023
35442^481801-481801145037Henri Lifchitz03/2005
35452^481775+1869083145029Enzo Doria05/2016
354629^99167+2145022Ray Chandler08/2011
35472^481663+1875653144996Enzo Doria07/2016
35488*10^144977+27144978Robert Price09/2021
354936486^9379+9379^36486144929Hans Havermann12/2020
355031580^32209-32209^31580144922Frank Doornink01/2024
355135111^13378+13378^35111144882Hans Havermann01/2021
35522^481149-459073144841Enzo Doria05/2015
355334619^15246+15246^34619144817Hans Havermann01/2021
35542^481045-113215144809Enzo Doria07/2014
3555(64*10^144797+287)/9144798Robert Price04/2019
35562^480859-113695144753Enzo Doria09/2014
3557(106*10^144744+17)/3144746Robert Price04/2021
35587*10^144742-27144743Robert Price11/2022
35592^480766-2787191144725Enzo Doria11/2015
3560(21*27^101106-151)/26144720Curtis Bright05/2015
35612^480678+1874239144699Enzo Doria06/2016
3562(8*10^144683+1)/9144683Serge Batalov05/2010
3563L(692147)144651Henri Lifchitz10/2008
3564(76*10^144648+77)/9144649Robert Price10/2019
356532672^26721+26721^32672144635Hans Havermann01/2021
356631478^32153-32153^31478144625Frank Doornink01/2024
35672^480417+35144620Robert Price11/2015
35682^480296-59879144584Enzo Doria10/2015
356933157^22878+22878^33157144546Hans Havermann12/2020
357045494^1497+1497^45494144454Hans Havermann12/2020
35712^479844+3144448Donovan Johnson06/2006
357233442^20803+20803^33442144407Hans Havermann01/2021
3573(441*33^95095-3833)/32144405Eric Chen12/2023
357431892^32061-32061^31892144393Norbert Schneider01/2023
3575(27*2^479642+1)/733144386Lelio R Paula08/2015
3576(56*10^144380+169)/9144381Robert Price03/2022
357744917^1638+1638^44917144378Hans Havermann12/2020
3578(21*2^479605-1)/11144376Lelio R Paula09/2015
3579(56*10^144336+583)/9144337Robert Price08/2021
35805*2^479430-3144324Jon Grantham07/2023
35812^479348-2792219144299Enzo Doria02/2016
358231134^32111-32111^31134144283Frank Doornink01/2024
35833^302389-6242144277Enzo Doria05/2014
358431665^32056-32056^31665144271Frank Doornink01/2024
358533778^18641+18641^33778144248Hans Havermann01/2021
35862*10^144220-3144221Robert Price07/2015
358725313^32750-32750^25313144210Frank Doornink01/2024
35882^478904-109109144165Enzo Doria04/2014
358943698^1987+1987^43698144125Hans Havermann12/2020
359079^75948+75948144121Kellen Shenton06/2023
359136128^9723+9723^36128144072Hans Havermann01/2021
359232817^24518+24518^32817144050Hans Havermann12/2020
3593(772*10^144036-7)/9144038Robert Price06/2022
359434295^15828+15828^34295144020Hans Havermann01/2021
35952^478337-115333143994Enzo Doria07/2015
3596(7*2^478330-1)/3143993Lelio R Paula08/2015
359788^74047-87^74047143984Robert Price05/2015
359833242^21441+21441^33242143980Hans Havermann01/2021
3599(19*10^143963+467)/9143964Robert Price02/2018
3600(71^77761+1)/72143954Paul Bourdelais09/2017
360133490^19859+19859^33490143939Hans Havermann01/2021
3602(853*10^143931-7)/9143933Robert Price07/2021
36032^478088+27143919Robert Price11/2015
3604(8*10^143898-137)/3143899Robert Price03/2022
36057*10^143857-93143858Robert Price08/2020
36063*10^143844+61143845Robert Price09/2020
360741358^3005+3005^41358143837Hans Havermann01/2021
36082^477475-22071143735Enzo Doria07/2013
36092^477417-22123143717Enzo Doria07/2013
36102^477359-3577143700Yves Minet03/2017
361139435^4402+4402^39435143688Hans Havermann01/2021
3612(14*10^143662-71)/3143663Robert Price12/2018
36136^184614+5143658Paul Bourdelais01/2021
361446371^1252+1252^46371143640Hans Havermann12/2020
361534975^12748+12748^34975143588Hans Havermann01/2021
36162^476936-396765143573Enzo Doria07/2013
36172^476888-2791229143558Enzo Doria01/2016
36182^476868-1859939143552Enzo Doria11/2015
361940807^3294+3294^40807143548Hans Havermann12/2020
3620755^49878+49878^755143547Norbert Schneider04/2019
3621(19^112247-4^112247)/15143536Robert Price03/2021
362235561^10872+10872^35561143536Hans Havermann06/2021
362337637^6492+6492^37637143487Hans Havermann05/2021
362461567^214+214^61567143477Hans Havermann05/2021
362525933^32504-32504^25933143468Frank Doornink03/2024
36262^476558-113627143459Enzo Doria08/2014
36272^476478-45143435Lelio R Paula11/2017
362836380^8757+8757^36380143423Hans Havermann06/2021
362932510^25707+25707^32510143371Hans Havermann05/2021
36308*10^143361+17143362Robert Price07/2021
3631(2^475854+9)/73143245Lelio R Paula08/2015
36322^475813-113239143234Enzo Doria07/2014
3633(19*10^143212+137)/3143213Robert Price03/2022
363432218^27849+27849^32218143203Hans Havermann04/2021
3635580*33^94296+19143193Eric Chen12/2023
36362^475624-114059143178Enzo Doria11/2014
3637(11*2^475553-7)/15143156Renaud Lifchitz03/2011
36382^475480-2786129143134Enzo Doria10/2015
363933912^16621+16621^33912143131Hans Havermann05/2021
3640(19*10^143129-43)/3143130Robert Price05/2019
364131830^31373+31373^31830143126Hans Havermann05/2021
36426*10^143105-53143106Robert Price05/2021
3643(14*10^143097+73)/3143098Robert Price12/2018
36442^475299-111937143080Enzo Doria05/2014
364535488^10753+10753^35488143071Hans Havermann04/2021
36462^475160-2797859143038Enzo Doria04/2016
3647(2^475069+3)/395143008Lelio R Paula08/2015
36482^475027-461437142998Enzo Doria07/2015
3649(2^474958+78557)/3142977Lelio R Paula07/2015
3650(8*10^142932+43)/3142933Robert Price06/2018
365135055^11942+11942^35055142922Hans Havermann05/2021
365237650^6239+6239^37650142887Hans Havermann05/2021
3653(54^82471-1)/53142871Paul Bourdelais09/2017
365431205^31784-31784^31205142845Frank Doornink01/2024
3655(11*2^474432-1)/95142818Lelio R Paula09/2015
36562^474417-59923142814Enzo Doria10/2015
36574*10^142810-21142811Robert Price09/2018
365832287^26494+26494^32287142811Hans Havermann06/2021
365937162^6965+6965^37162142811Hans Havermann06/2021
3660(34*10^142805-601)/9142806Robert Price07/2022
366137456^6493+6493^37456142799Hans Havermann05/2021
366235141^11572+11572^35141142793Hans Havermann05/2021
366332231^26908+26908^32231142780Hans Havermann05/2021
3664(3*2^474166+1)/7142738Lelio R Paula08/2015
36652^474053+2897142705Lelio R Paula08/2012
3666(10^142699+359)/9142699Serge Batalov12/2014
366726073^32312-32312^26073142696Frank Doornink03/2024
3668898^48311-897^48311142676Jean-Louis Charton12/2012
36692^473740-1856639142610Enzo Doria09/2015
3670(25*10^142573-403)/9142574Robert Price12/2020
36712^473617-114223142573Enzo Doria12/2014
367236115^8856+8856^36115142555Hans Havermann05/2021
3673fibonacci(682007)+4142531Jon Grantham08/2023
36742^473257+1873217142465Enzo Doria06/2016
3675(19*2^473242+1)/11142461Lelio R Paula09/2015
367632750^22371+22371^32750142453Hans Havermann06/2021
3677(61*10^142446-1)/3142448Robert Price01/2020
3678(14*10^142440+61)/3142441Robert Price12/2018
3679(10^142425+359)/9142425Serge Batalov12/2014
36802^473101+773027142418Enzo Doria05/2016
3681(13*2^472838-1)/3142340Lelio R Paula09/2015
3682(17*2^472789-1)/187347142320Lelio R Paula09/2015
368336915^7162+7162^36915142309Hans Havermann05/2021
36842^472634-109511142278Enzo Doria04/2014
368531870^28997+28997^31870142216Hans Havermann06/2021
3686(48^84589+1)/49142213Robert Price01/2014
36877*10^142189+87142190Robert Price07/2019
36882^472258+7142164Lelio R Paula08/2015
368940135^3484+3484^40135142162Hans Havermann05/2021
36909*33^93598+26142131Eric Chen12/2023
3691(23*10^142105+91)/3142106Robert Price08/2019
3692tau(317^10330)142098Nik Lygeros / Olivier Rozier / LR team10/2013
3693(11*2^471913-1)/21142060Lelio R Paula09/2015
3694(16*10^142058+197)/3142059Robert Price04/2019
36959*10^142037+91142038Robert Price10/2020
3696(4*10^142034+17)/3142035Tyler Busby01/2023
36972^471792+1880881142024Enzo Doria11/2016
3698(509*10^142018+31)/9142020Robert Price08/2022
3699(31*2^471580-1)/135141960Lelio R Paula08/2015
3700(4*10^141926-79)/3141927Robert Price02/2018
37012^471464-111546435141925Paul Bourdelais10/2021
3702(904*19^110984-1)/3141924Curtis Bright05/2015
3703(14*10^141853+37)/3141854Robert Price12/2018
3704(41*10^141836-59)/9141837Robert Price10/2018
37054*5^202913-9141831Lelio R Paula04/2015
37062*7^167812-3141818Lelio R Paula12/2014
37072^471043+35141799Robert Price11/2015
3708(11*2^470956-1)/7945141770Lelio R Paula08/2015
370943636^1773+1773^43636141761Hans Havermann05/2021
3710(2*10^141751-17)/3141751Serge Batalov11/2022
3711(53*10^141722-611)/9141723Robert Price02/2022
3712(11*10^141718-131)/3141719Robert Price09/2018
3713(61*10^141716+47)/9141717Robert Price07/2022
371426057^32088-32088^26057141699Frank Doornink03/2024
37152^470692+76771141693Enzo Doria05/2016
371650160^667+667^50160141659Hans Havermann05/2021
371731522^31181+31181^31522141657Hans Havermann05/2021
371833076^19135+19135^33076141626Hans Havermann04/2021
3719(91*10^141610+71)/9141612Robert Price01/2022
3720(21*2^470391+1)/533141601Lelio R Paula09/2015
3721(5*10^141594-23)/9141594Serge Batalov11/2022
372231932^27155+27155^31932141582Hans Havermann05/2021
372336449^7660+7660^36449141577Hans Havermann05/2021
37242^470305-459373141576Enzo Doria05/2015
372532195^24936+24936^32195141556Hans Havermann05/2021
37262^470183+72623141540Enzo Doria04/2016
37272^470173-16465141537Enzo Doria04/2013
372837297^6234+6234^37297141534Hans Havermann05/2021
3729(509*10^141479+13)/9141481Robert Price05/2022
373044*10^141476+9141478Robert Price10/2020
37312^469974-1841141477Enzo Doria05/2014
3732(23*2^469939+1)/25141466Lelio R Paula08/2015
3733312*33^93158+23141465Eric Chen12/2023
37342*10^141448+63141449Robert Price05/2018
37352^469824+43141432Lelio R Paula09/2017
37362*10^141407-27141408Robert Price05/2018
3737(214*10^141385-1)/3141387Robert Price01/2021
37382^469630-59711141373Enzo Doria10/2015
373935277^10172+10172^35277141370Hans Havermann04/2021
374033397^17100+17100^33397141370Hans Havermann04/2021
3741(25*10^141366-331)/9141367Robert Price08/2018
374236986^6639+6639^36986141365Hans Havermann06/2021
374334572^12271+12271^34572141361Hans Havermann06/2021
374437179^6338+6338^37179141353Hans Havermann05/2021
3745(2^469564-3)/611141351Lelio R Paula08/2015
3746197^61601+2141342Lelio R Paula08/2017
374733420^16951+16951^33420141340Hans Havermann05/2021
374831623^29458+29458^31623141330Hans Havermann05/2021
374948112^865+865^48112141306Hans Havermann05/2021
37502^469372-112949141296Enzo Doria07/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 15 2024 22:24 (Time in France)

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