PRP Records

Probable Primes Top 10000

(293510 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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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 ?
5012^1200021+149777361243Stefano Morozzi10/2022
502(64*10^360173-1)/243360173Serge Batalov09/2014
503(59^203309+1)/60360029Paul Bourdelais09/2021
504(2*10^359860-11)/9359860Rytis Slatkevicius01/2023
5052^1195093+1882577359759Enzo Doria12/2016
5063^753451+5*2^753451359488Jon Grantham08/2023
507(6^461108-11)/5358812Paul Bourdelais04/2019
5082^1191375+8543358640Phil Moore06/2008
5092^1190972+1880191358519Enzo Doria11/2016
510(45^216551-1)/44358004Paul Bourdelais08/2020
511(50^210319-1)/49357324Paul Bourdelais08/2020
512(531^131072+25^131072)/2357184Kellen Shenton03/2021
5132^1184565+21227356590Enzo Doria08/2023
5142^1179836+1885021355167Enzo Doria02/2017
515(19*10^353884-91)/9353885Alfred Reich02/2023
51620^271951+3353817Paul Bourdelais01/2021
5172^1173095+21353137Stefano Morozzi10/2022
518(63^195893-1)/62352477Paul Bourdelais08/2020
5192^1170326+7352304Stefano Morozzi10/2022
520numbpart(100000135540)352269Serge Batalov04/2017
521(10^352237-1)/9/10567111/950335427352221Maksym Voznyy01/2015
5225*3^737931-2^737931352084Jon Grantham08/2023
5232^1168554+783529351770Enzo Doria01/2017
524(2^1168183-1)/54763676838381762583351639Matthias Wurtinger01/2011
5252^1166152+1882411351047Enzo Doria12/2016
5262^1163972+20971350391Enzo Doria08/2023
52710^350071+7350072Alfred Reich05/2021
5282^1162154+1890207349844Enzo Doria08/2017
529(7*10^348724-61)/9348724Erik Branger09/2016
530(4*10^348453+41)/9348453Serge Batalov11/2022
531(127^165601-1)/126348390Alexander Zhirkov09/2015
5322^1155085+213377347716Enzo Doria09/2023
5332^1153083+1883693347113Enzo Doria04/2017
534(2^1148729+2^574365+1)/5345802Borys Jaworski03/2007
5352^1145882+80779344945Enzo Doria09/2016
5362^1136462+1887289342110Enzo Doria05/2017
537F(1636007)341905Henri Lifchitz03/2009
538(2^1135567+13)/3341840Stefano Morozzi09/2022
5392^1133678+782569341272Enzo Doria11/2016
540(11^327001+1)/12340536Paul Bourdelais09/2013
541(2^1127239+2^563620+1)/5339333Borys Jaworski11/2006
542Tau(907^20848)339132Nik Lygeros / Olivier Rozier01/2016
5432^1126380-3339075Paul Bourdelais06/2019
5442^1125446+1885099338794Enzo Doria08/2017
545(63^188147+1)/64338539Paul Bourdelais12/2020
5462^1124549+143807338523Enzo Doria10/2016
547(4*10^338476+23)/9338476Serge Batalov11/2022
5482^1121187+1886783337511Enzo Doria04/2017
549(48^200443-1)/47336992Paul Bourdelais08/2020
550(2*10^336405+43)/9336405Rytis Slatkevicius01/2023
551(94^170371-1)/93336162Paul Bourdelais09/2020
5522^1116184+1883521336005Enzo Doria02/2017
5532^1114517+1880087335504Enzo Doria10/2016
554(5*10^335480+31)/9335480Serge Batalov11/2022
5555*3^701688+2^701688334791Jon Grantham08/2023
556(101^166849+1)/102334418Paul Bourdelais12/2020
557(3^700897+1)/4334413Paul Bourdelais04/2010
5582^1104408-114539332460Enzo Doria03/2015
5592^1101921+82085331712Enzo Doria10/2016
5602^1100655+683513331331Enzo Doria01/2017
561(10^330906+71)/9330906Serge Batalov07/2015
5622^1098346+482899330636Enzo Doria11/2016
563(2^1096212+19)/5329992Stefano Morozzi09/2022
5642^1095679+1878713329833Enzo Doria09/2016
5652^1094740-1851539329550Enzo Doria08/2015
5662^1092242+19328798Stefano Morozzi10/2022
5672^1091469-379369328565Enzo Doria03/2014
568(69^178093-1)/68327485Paul Bourdelais08/2020
569(10^326884+7)/421326882Alfred Reich12/2021
5702^1085750+582349326844Enzo Doria11/2016
5712^1083596+483061326195Enzo Doria12/2016
572(2^541456-1)*10^162995+2^541455-1325990paolo galliani01/2019
5732^1082908+583561325988Enzo Doria05/2017
57430^220411-29^220411325574Jean-Louis Charton10/2018
5752^1081308+7325507Stefano Morozzi10/2022
5762^1078242+1881649324584Enzo Doria11/2016
5772^1077737+1880117324432Enzo Doria10/2016
5783^679017-5*2^679017323974Jon Grantham08/2023
5792^1075425+1880117323736Enzo Doria10/2016
580(28^223381+1)/29323267Paul Bourdelais12/2020
58110^322999+187071323000Stefano Morozzi03/2019
58210^322999-143151322999Patrick De Geest05/2020
5832^1072146+1886869322749Enzo Doria04/2017
5842^1072118-7321953322740Enzo Doria02/2015
5852^1071026+1886869322411Enzo Doria04/2017
5862^1070539+1880633322265Enzo Doria10/2016
5872^1069293-1147195321890Enzo Doria05/2015
5882^1065968+1880941320889Enzo Doria10/2016
5892^1065897-1147195320867Enzo Doria05/2015
5902^1063427+1882103320124Enzo Doria12/2016
5912^1061095-1061095319422Henri Lifchitz10/2013
5922^1060950+653119319378Enzo Doria12/2016
5932^1060363+782753319202Enzo Doria11/2016
594(71^172259-1)/70318895Paul Bourdelais08/2020
5952^1054736+483061317508Enzo Doria12/2016
5962^1053965+1879667317276Enzo Doria10/2016
597(43^194119-1)/42317086Paul Bourdelais08/2020
5982^1052186-458165316740Enzo Doria03/2015
59911^303909+2316489Paul Bourdelais08/2023
6002^1046613-114685315062Enzo Doria04/2015
6012^1045625-459373314765Enzo Doria06/2015
60210^(2*157363+1)-8*10^157363-1314727Robert Price07/2023
603(7*10^314564-61)/9314564Erik Branger09/2016
6042^1044206+7314338Stefano Morozzi10/2022
605(7^371669-1)/6314096Paul Bourdelais02/2010
606(53^181981-1)/52313784Paul Bourdelais08/2020
607(8^347437-5^347437)/3313767Jon Grantham08/2023
6082^1041944+283051313657Enzo Doria12/2016
6092^1041153-114391313419Enzo Doria02/2015
610(2^1039700+9)/5312981Stefano Morozzi09/2022
611(74^167311+1)/75312742Paul Bourdelais12/2020
6122^1038871+1866983312732Enzo Doria04/2016
6132^1038545+71657312634Enzo Doria08/2023
614(55^179573-1)/54312521Paul Bourdelais08/2020
6152^1037647+1881263312363Enzo Doria11/2016
6162^1037226+1879699312237Enzo Doria10/2016
6172^1036867+1865843312129Enzo Doria02/2016
618(76^165947+1)/77312114Paul Bourdelais01/2021
6192^1036020-114539311874Enzo Doria02/2015
620(90^159463-1)/89311628Paul Bourdelais08/2020
6212^1032240+1883431310736Enzo Doria01/2017
6222^1030352+1870021310167Enzo Doria06/2016
6232^1030046+1882843310075Enzo Doria11/2016
6243^648872+16309591Robert Price04/2020
62564221^64366+64366^64221309451Norbert Schneider06/2023
6262^1026999+20513309158Enzo Doria07/2023
6275^442281+2309142Paul Bourdelais01/2021
6282^1026204+22741308919Enzo Doria09/2023
6292^1026190+15308914Stefano Morozzi10/2022
6302^1025108+20851308589Enzo Doria08/2023
631A352736(16)306985Kellen Shenton05/2022
632(11^293831-1)/10305993Paul Bourdelais03/2010
633(67^167449-1)/66305773Paul Bourdelais08/2020
634(62^170539+1)/63305671Paul Bourdelais12/2020
6352^1015321-1015321305643Henri Lifchitz08/2013
6362^1014450+7305380Stefano Morozzi10/2022
6372^1014224-2791229305312Enzo Doria01/2016
638(10^304986+7)/673304984Alfred Reich11/2021
63965473^45250+45250^65473304818Hans Havermann02/2022
64066012^41423+41423^66012304794Hans Havermann03/2022
64165073^48202+48202^65073304742Hans Havermann04/2022
642238176^19+19^238176304569Hans Havermann03/2022
64373122^14615+14615^73122304539Hans Havermann05/2022
64464492^52639+52639^64492304487Hans Havermann03/2022
64565955^41288+41288^65955304437Hans Havermann04/2022
64671729^17530+17530^71729304403Hans Havermann03/2022
64770170^21733+21733^70170304336Hans Havermann03/2022
6482^1010751-107709304267Enzo Doria03/2014
64984473^3994+3994^84473304222Hans Havermann03/2022
650(2^1010623-1)/12602017578957977304212Tony Prest / Never Odd Or Even02/2014
65174442^12125+12125^74442303998Hans Havermann02/2022
65277842^8039+8039^77842303989Hans Havermann01/2022
65364209^54140+54140^64209303935Hans Havermann02/2022
6542^1009577+1869587303913Enzo Doria06/2016
65567389^32338+32338^67389303906Hans Havermann02/2022
6568^336419-7^336419303817Jean-Louis Charton01/2008
6572^1009168+15303790Stefano Morozzi10/2022
65880766^5771+5771^80766303782Hans Havermann01/2022
65966094^39385+39385^66094303724Hans Havermann01/2022
66069147^24574+24574^69147303589Hans Havermann02/2022
66178390^7459+7459^78390303580Hans Havermann01/2022
6622^1008301+1869377303529Enzo Doria06/2016
66365008^46615+46615^65008303492Hans Havermann02/2022
664(2^1007838+5)/3303389Serge Batalov08/2015
66565018^46293+46293^65018303343Hans Havermann01/2022
6666^389756+5303290Paul Bourdelais02/2021
66771016^18649+18649^71016303285Hans Havermann01/2022
66880160^6047+6047^80160303129Hans Havermann01/2022
66967434^31237+31237^67434303094Hans Havermann03/2022
67065537^42102+42102^65537303063Hans Havermann02/2022
67171790^16553+16553^71790302874Hans Havermann11/2021
67265208^44129+44129^65208302874Hans Havermann11/2021
67384181^3960+3960^84181302858Hans Havermann11/2021
67471956^16087+16087^71956302682Hans Havermann11/2021
6752^1005326+383059302634Enzo Doria12/2016
6762^1004929+1877567302514Enzo Doria08/2016
67769341^22978+22978^69341302418Hans Havermann12/2021
678111443^516+516^111443302306Hans Havermann12/2021
67967638^29387+29387^67638302218Hans Havermann11/2021
6802^1003494+1874899302082Enzo Doria06/2016
68175189^10400+10400^75189302037Hans Havermann12/2021
68267237^31042+31042^67237302026Hans Havermann12/2021
68364540^47791+47791^64540302005Hans Havermann11/2021
6842^1003046+60529301947Enzo Doria04/2016
68583278^4209+4209^83278301815Hans Havermann09/2021
68664431^48250+48250^64431301763Hans Havermann09/2021
68767237^30714+30714^67237301716Hans Havermann09/2021
68864641^46288+46288^64641301581Hans Havermann09/2021
68971513^16482+16482^71513301572Hans Havermann10/2021
69072017^15396+15396^72017301565Hans Havermann09/2021
69165534^39927+39927^65534301540Hans Havermann10/2021
692(23^221411-1)/22301501Paul Bourdelais08/2020
69363169^59152+59152^63169301441Hans Havermann09/2021
69475055^10348+10348^75055301336Hans Havermann09/2021
6952^1000647+1881353301225Enzo Doria11/2016
69683686^3961+3961^83686301086Hans Havermann10/2021
69768529^24742+24742^68529301078Hans Havermann09/2021
69865207^41416+41416^65207301072Hans Havermann10/2021
7002^1000000+821751301030Tony Prest / Never Odd Or Even10/2015
6992^999999+77151301030Norman Luhn09/2023
70190762^2071+2071^90762300984Hans Havermann06/2021
70263909^51142+51142^63909300934Hans Havermann08/2021
7032^999646+1874029300924Enzo Doria06/2016
70466280^34607+34607^66280300856Hans Havermann06/2021
70565534^38925+38925^65534300817Hans Havermann07/2021
70663296^56517+56517^63296300794Hans Havermann06/2021
707110610^523+523^110610300694Hans Havermann06/2021
70866428^33609+33609^66428300684Hans Havermann06/2021
70974247^11210+11210^74247300672Hans Havermann06/2021
710(59^169777-1)/58300649Paul Bourdelais08/2020
71110^300476+3300477Ed Trice10/2012
71210^300476-530913300476Patrick De Geest03/2016
71366703^31960+31960^66703300471Hans Havermann06/2021
71463722^51915+51915^63722300468Hans Havermann06/2021
7152^998053+1879667300444Enzo Doria09/2016
71677018^7959+7959^77018300437Hans Havermann07/2021
717314738^9+9^314738300337Anatoly F. Selevich02/2011
71869478^20987+20987^69478300281Hans Havermann07/2021
71964088^48393+48393^64088300239Hans Havermann07/2021
72064605^44146+44146^64605300084Hans Havermann08/2021
7217^355039-6^355039300043Jean-Louis Charton05/2011
72267594^27465+27465^67594300035Hans Havermann06/2021
72310^300000+287389300001Patrick De Geest10/2019
72410^300000-83657300000Patrick De Geest10/2019
72570599^17756+17756^70599300000Hans Havermann06/2021
726numbpart(72526161452)299999Serge Batalov04/2017
7272^996182-114431299881Enzo Doria02/2015
7283*2^996126+5299865Jon Grantham07/2023
7292^996034-17299837Stefano Morozzi07/2022
730(19*10^299640+77)/3299641Robert Price03/2023
7312^995214-2788361299590Enzo Doria12/2015
7322^994791-114319299462Enzo Doria01/2015
7332^994490-1863791299372Enzo Doria01/2016
7342^993322+1885729299020Enzo Doria03/2017
735(36395^65536+36393^65536)/2298913Kellen Shenton04/2022
7362^992711-2788807298836Enzo Doria12/2015
7372^992525-114199298780Enzo Doria12/2014
738(7^353501-3^353501)/4298743Jon Grantham08/2023
7392^992329+1884707298721Enzo Doria02/2017
7402^991968-23298613Stefano Morozzi07/2022
7412^991715-19298536Stefano Morozzi07/2022
742(10^298414+7)/191/823/56921/1334467298398Alfred Reich10/2021
7432^989562+25297888Stefano Morozzi05/2021
744(19*10^297497+77)/3297498Robert Price03/2023
745(2*10^297488-23)/3297488Robert Price10/2022
746(2^986191+1)/3296873Vincent Diepeveen06/2008
7472^985217-114553296580Enzo Doria03/2015
748(76^157649-1)/75296507Paul Bourdelais07/2019
7492^984650+21529296410Enzo Doria08/2023
7502^984131-1828009296253Enzo Doria01/2015


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 29 2023 15:19 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!