PRP Records

Probable Primes Top 10000

(292102 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 ?
5012^1075425+1880117323736Enzo Doria10/2016
502(28^223381+1)/29323267Paul Bourdelais12/2020
50310^322999+187071323000Stefano Morozzi03/2019
50410^322999-143151322999Patrick De Geest05/2020
5052^1072146+1886869322749Enzo Doria04/2017
5062^1072118-7321953322740Enzo Doria02/2015
5072^1071026+1886869322411Enzo Doria04/2017
5082^1070539+1880633322265Enzo Doria10/2016
5092^1069293-1147195321890Enzo Doria05/2015
5102^1065968+1880941320889Enzo Doria10/2016
5112^1065897-1147195320867Enzo Doria05/2015
5122^1063427+1882103320124Enzo Doria12/2016
5132^1061095-1061095319422Henri Lifchitz10/2013
5142^1060950+653119319378Enzo Doria12/2016
5152^1060363+782753319202Enzo Doria11/2016
516(71^172259-1)/70318895Paul Bourdelais08/2020
5172^1054736+483061317508Enzo Doria12/2016
5182^1053965+1879667317276Enzo Doria10/2016
519(43^194119-1)/42317086Paul Bourdelais08/2020
5202^1052186-458165316740Enzo Doria03/2015
5212^1046613-114685315062Enzo Doria04/2015
5222^1045625-459373314765Enzo Doria06/2015
523(7*10^314564-61)/9314564Erik Branger09/2016
5242^1044206+7314338Stefano Morozzi10/2022
525(7^371669-1)/6314096Paul Bourdelais02/2010
526(53^181981-1)/52313784Paul Bourdelais08/2020
5272^1041944+283051313657Enzo Doria12/2016
5282^1041153-114391313419Enzo Doria02/2015
529(2^1039700+9)/5312981Stefano Morozzi09/2022
530(74^167311+1)/75312742Paul Bourdelais12/2020
5312^1038871+1866983312732Enzo Doria04/2016
532(55^179573-1)/54312521Paul Bourdelais08/2020
5332^1037647+1881263312363Enzo Doria11/2016
5342^1037226+1879699312237Enzo Doria10/2016
5352^1036867+1865843312129Enzo Doria02/2016
536(76^165947+1)/77312114Paul Bourdelais01/2021
5372^1036020-114539311874Enzo Doria02/2015
538(90^159463-1)/89311628Paul Bourdelais08/2020
5392^1032240+1883431310736Enzo Doria01/2017
5402^1030352+1870021310167Enzo Doria06/2016
5412^1030046+1882843310075Enzo Doria11/2016
5423^648872+16309591Robert Price04/2020
5435^442281+2309142Paul Bourdelais01/2021
5442^1026190+15308914Stefano Morozzi10/2022
545A352736(16)306985Kellen Shenton05/2022
546(11^293831-1)/10305993Paul Bourdelais03/2010
547(67^167449-1)/66305773Paul Bourdelais08/2020
548(62^170539+1)/63305671Paul Bourdelais12/2020
5492^1015321-1015321305643Henri Lifchitz08/2013
5502^1014450+7305380Stefano Morozzi10/2022
5512^1014224-2791229305312Enzo Doria01/2016
552(10^304986+7)/673304984Alfred Reich11/2021
55365473^45250+45250^65473304818Hans Havermann02/2022
55466012^41423+41423^66012304794Hans Havermann03/2022
55565073^48202+48202^65073304742Hans Havermann04/2022
556238176^19+19^238176304569Hans Havermann03/2022
55773122^14615+14615^73122304539Hans Havermann05/2022
55864492^52639+52639^64492304487Hans Havermann03/2022
55965955^41288+41288^65955304437Hans Havermann04/2022
56071729^17530+17530^71729304403Hans Havermann03/2022
56170170^21733+21733^70170304336Hans Havermann03/2022
5622^1010751-107709304267Enzo Doria03/2014
56384473^3994+3994^84473304222Hans Havermann03/2022
564(2^1010623-1)/12602017578957977304212Tony Prest / Never Odd Or Even02/2014
56574442^12125+12125^74442303998Hans Havermann02/2022
56677842^8039+8039^77842303989Hans Havermann01/2022
56764209^54140+54140^64209303935Hans Havermann02/2022
5682^1009577+1869587303913Enzo Doria06/2016
56967389^32338+32338^67389303906Hans Havermann02/2022
5708^336419-7^336419303817Jean-Louis Charton01/2008
5712^1009168+15303790Stefano Morozzi10/2022
57280766^5771+5771^80766303782Hans Havermann01/2022
57366094^39385+39385^66094303724Hans Havermann01/2022
57469147^24574+24574^69147303589Hans Havermann02/2022
57578390^7459+7459^78390303580Hans Havermann01/2022
5762^1008301+1869377303529Enzo Doria06/2016
57765008^46615+46615^65008303492Hans Havermann02/2022
578(2^1007838+5)/3303389Serge Batalov08/2015
57965018^46293+46293^65018303343Hans Havermann01/2022
5806^389756+5303290Paul Bourdelais02/2021
58171016^18649+18649^71016303285Hans Havermann01/2022
58280160^6047+6047^80160303129Hans Havermann01/2022
58367434^31237+31237^67434303094Hans Havermann03/2022
58465537^42102+42102^65537303063Hans Havermann02/2022
58571790^16553+16553^71790302874Hans Havermann11/2021
58665208^44129+44129^65208302874Hans Havermann11/2021
58784181^3960+3960^84181302858Hans Havermann11/2021
58871956^16087+16087^71956302682Hans Havermann11/2021
5892^1005326+383059302634Enzo Doria12/2016
5902^1004929+1877567302514Enzo Doria08/2016
59169341^22978+22978^69341302418Hans Havermann12/2021
592111443^516+516^111443302306Hans Havermann12/2021
59367638^29387+29387^67638302218Hans Havermann11/2021
5942^1003494+1874899302082Enzo Doria06/2016
59575189^10400+10400^75189302037Hans Havermann12/2021
59667237^31042+31042^67237302026Hans Havermann12/2021
59764540^47791+47791^64540302005Hans Havermann11/2021
5982^1003046+60529301947Enzo Doria04/2016
59983278^4209+4209^83278301815Hans Havermann09/2021
60064431^48250+48250^64431301763Hans Havermann09/2021
60167237^30714+30714^67237301716Hans Havermann09/2021
60264641^46288+46288^64641301581Hans Havermann09/2021
60371513^16482+16482^71513301572Hans Havermann10/2021
60472017^15396+15396^72017301565Hans Havermann09/2021
60565534^39927+39927^65534301540Hans Havermann10/2021
606(23^221411-1)/22301501Paul Bourdelais08/2020
60763169^59152+59152^63169301441Hans Havermann09/2021
60875055^10348+10348^75055301336Hans Havermann09/2021
6092^1000647+1881353301225Enzo Doria11/2016
61083686^3961+3961^83686301086Hans Havermann10/2021
61168529^24742+24742^68529301078Hans Havermann09/2021
61265207^41416+41416^65207301072Hans Havermann10/2021
6132^1000000+821751301030Tony Prest / Never Odd Or Even10/2015
61490762^2071+2071^90762300984Hans Havermann06/2021
61563909^51142+51142^63909300934Hans Havermann08/2021
6162^999646+1874029300924Enzo Doria06/2016
61766280^34607+34607^66280300856Hans Havermann06/2021
61865534^38925+38925^65534300817Hans Havermann07/2021
61963296^56517+56517^63296300794Hans Havermann06/2021
620110610^523+523^110610300694Hans Havermann06/2021
62166428^33609+33609^66428300684Hans Havermann06/2021
62274247^11210+11210^74247300672Hans Havermann06/2021
623(59^169777-1)/58300649Paul Bourdelais08/2020
62410^300476+3300477Ed Trice10/2012
62510^300476-530913300476Patrick De Geest03/2016
62666703^31960+31960^66703300471Hans Havermann06/2021
62763722^51915+51915^63722300468Hans Havermann06/2021
6282^998053+1879667300444Enzo Doria09/2016
62977018^7959+7959^77018300437Hans Havermann07/2021
630314738^9+9^314738300337Anatoly F. Selevich02/2011
63169478^20987+20987^69478300281Hans Havermann07/2021
63264088^48393+48393^64088300239Hans Havermann07/2021
63364605^44146+44146^64605300084Hans Havermann08/2021
6347^355039-6^355039300043Jean-Louis Charton05/2011
63567594^27465+27465^67594300035Hans Havermann06/2021
63610^300000+287389300001Patrick De Geest10/2019
63710^300000-83657300000Patrick De Geest10/2019
63870599^17756+17756^70599300000Hans Havermann06/2021
639numbpart(72526161452)299999Serge Batalov04/2017
6402^996182-114431299881Enzo Doria02/2015
6412^996034-17299837Stefano Morozzi07/2022
642(19*10^299640+77)/3299641Robert Price03/2023
6432^995214-2788361299590Enzo Doria12/2015
6442^994791-114319299462Enzo Doria01/2015
6452^994490-1863791299372Enzo Doria01/2016
6462^993322+1885729299020Enzo Doria03/2017
647(36395^65536+36393^65536)/2298913Kellen Shenton04/2022
6482^992711-2788807298836Enzo Doria12/2015
6492^992525-114199298780Enzo Doria12/2014
6502^992329+1884707298721Enzo Doria02/2017
6512^991968-23298613Stefano Morozzi07/2022
6522^991715-19298536Stefano Morozzi07/2022
653(10^298414+7)/191/823/56921/1334467298398Alfred Reich10/2021
6542^989562+25297888Stefano Morozzi05/2021
655(19*10^297497+77)/3297498Robert Price03/2023
656(2*10^297488-23)/3297488Robert Price10/2022
657(2^986191+1)/3296873Vincent Diepeveen06/2008
6582^985217-114553296580Enzo Doria03/2015
659(76^157649-1)/75296507Paul Bourdelais07/2019
6602^984131-1828009296253Enzo Doria01/2015
6612^983620+60451296100Phil Moore03/2008
6622^982721-2683295829Yves Minet02/2016
6632^981298-2788421295401Enzo Doria12/2015
6642^981163-2790967295360Enzo Doria12/2015
6652^981016-15295316Stefano Morozzi07/2022
6662^979594+1865839294888Enzo Doria02/2016
6672*10^294527-91294528Robert Price02/2023
66810^294475+49294476Robert Price02/2023
6692^976760+1885021294035Enzo Doria02/2017
6702^974441+1878407293336Enzo Doria08/2016
6712^974180+1876831293258Enzo Doria07/2016
6722^974170+453319293255Enzo Doria01/2017
6732^972744-114419292826Enzo Doria03/2015
67411^281143+6292781Paul Bourdelais03/2021
675(4*10^292619-91)/3292620Robert Price12/2022
676CopelandErdos(292447)292447Mark Rodenkirch12/2015
6773*10^292344-97292345Robert Price01/2023
6782^970911+1873373292274Enzo Doria07/2016
6792^970670+383059292201Enzo Doria12/2016
6802^970141-100363292042Enzo Doria02/2014
6812^969945+1874717291983Enzo Doria06/2016
6822^969384+1880701291814Enzo Doria10/2016
683(3^611333-2^611333)/(99035947*87109884549431)291659Mike Oakes02/2017
6842^962194+60139289650Enzo Doria02/2016
6852^959307-1861507288781Enzo Doria11/2015
68614^251797-3288592Paul Bourdelais12/2020
687(2*10^288371-23)/3288371Robert Price10/2022
688(31*10^288238-1)/3288240Robert Price02/2023
6892^957372+283531288198Enzo Doria02/2017
6902^957192-1864049288144Enzo Doria01/2016
6912^956446+1875199287919Enzo Doria06/2016
6927*10^287854+39287855Robert Price01/2023
693(17^233689+1)/18287542Paul Bourdelais09/2013
6942^955178+1883587287538Enzo Doria12/2016
6952^954127-954127^2287221Henri Lifchitz01/2021
6962^954001+1875257287183Enzo Doria07/2016
697(23891^65536+1)/2286932Serge Batalov03/2018
6982^952268+1878601286662Enzo Doria09/2016
6992^950801+81557286220Enzo Doria08/2016
70022845^65536+22844^65536285658Kellen Shenton03/2021
701(11*2^948635-13)/15285568Renaud Lifchitz11/2011
702(54^164839+1)/55285565Paul Bourdelais07/2019
7032^948510+782569285530Enzo Doria10/2016
7042^948374-114137285490Enzo Doria01/2015
7052^947739+1872923285298Enzo Doria06/2016
7062^944561-21284342Stefano Morozzi07/2022
707(4*10^284330-31)/9284330Serge Batalov11/2022
708(32*10^283826-23)/9283827Serge Batalov01/2023
7092^942533+82067283731Enzo Doria09/2016
710(10^283342-31)/3283342Robert Price03/2023
7112^940950+1874989283255Enzo Doria06/2016
7122^940426-2786141283097Enzo Doria11/2015
713(2*10^282948-11)/9282948Serge Batalov11/2022
7142^939881-114115282933Enzo Doria12/2014
71510^282493+632551282494Patrick De Geest02/2017
71710^282493-9^282493282493Jean-Louis Charton03/2007
71610^282493-132327282493Patrick De Geest02/2017
7183^591827-2^591827282374Mike Oakes08/2009
719Tau(509^18946)282048Nik Lygeros / Olivier Rozier05/2015
7202^936716-1835519281980Enzo Doria04/2015
7212^936588+79411281942Enzo Doria06/2016
7222^936047+1877423281779Enzo Doria08/2016
7232^935713+1869377281678Enzo Doria05/2016
7242^933082+1877059280886Enzo Doria08/2016
725(5*10^280710+1)/3280711Serge Batalov10/2014
7262^931976+25280553Stefano Morozzi05/2021
727(42^172663+1)/43280274Paul Bourdelais07/2019
728(10^279978+11)/3279978Serge Batalov07/2015
7292^929524-1864829279815Enzo Doria01/2016
7302^929152+60181279703Enzo Doria02/2016
7312^928621-2787883279543Enzo Doria11/2015
732(2^927763+lucasV(-1,2,927763)+1)/2279285Mike Oakes04/2017
7332^927429+1882277279184Enzo Doria12/2016
7342^926766-11278985Stefano Morozzi07/2022
735(71^150697-1)/70278978Paul Bourdelais07/2019
736(33^183661-1)/32278891Paul Bourdelais12/2018
737(166*10^278633-7)/3278635Robert Price02/2023
738(2^925391+lucasV(-1,2,925391)+1)/2278571Mike Oakes03/2017
7392^925330-1301278553Yves Minet06/2015
740(299*10^278546+1)/3278548Robert Price01/2023
741(21^210599+1)/22278457Paul Bourdelais08/2013
742(266*10^278325+1)/3278327Robert Price01/2023
7432^923261-69175277930Enzo Doria11/2015
744757^96487-756^96487277796Jean-Louis Charton12/2012
7452^922301+57277641Stefano Morozzi05/2021
746((((((((((((((291487327^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2277369Serge Batalov07/2016
747(5^396413-1)/4277081Paul Bourdelais06/2010
7482^920318+2792299277044Enzo Doria02/2016
7492^918596-2786939276525Enzo Doria11/2015
7502^916639+60563275936Enzo Doria04/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 20 2023 09:01 (Time in France)

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