PRP Records

Probable Primes Top 10000

(252675 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 ?
5251496^31671+31671^49685369Norbert Schneider07/2017
5252(15*2^283583-1)/10305185364Lelio R Paula02/2014
525315^72572+9285352Lelio R Paula11/2015
52542^283473-161585334Lelio R Paula09/2013
52552^283466-1585332Lelio R Paula08/2012
525611^81916-702085307Enzo Doria02/2013
52576^109626-785306Lelio R Paula11/2014
52582^283374-11032785305Enzo Doria05/2014
525933*10^85297+785299Robert Price07/2016
526018^67933+4185275Lelio R Paula11/2015
52612^283271-10934185274Enzo Doria04/2014
5262(25*10^85249-73)/385250Robert Price09/2016
52632*5^121959+385246Lelio R Paula10/2014
526419834^19834+894785235Henri Lifchitz11/2004
52652^283140+191585234Lelio R Paula09/2013
52663*10^85227-9785228Robert Price08/2017
5267(16*10^85221-31)/385222Robert Price03/2016
52682^283083+186938385217Enzo Doria05/2016
5269(24737*2^283051+1)/1785211Lelio R Paula06/2014
5270(2^283032+78557)/385201Lelio R Paula01/2013
52712^283026-10989385200Enzo Doria04/2014
5272(2^283012+78557)/12985193Lelio R Paula01/2013
5273(10^(2*42589+1)+72*10^42589-1)/985179Robert Price09/2017
52742^282860-10972785150Enzo Doria04/2014
52752^282819+186941385138Enzo Doria05/2016
52763^178428+285132Ray Chandler07/2011
5277(22699*2^282742+1)/7385117Lelio R Paula06/2014
5278(16^70687+5^70687)/2185115Robert Price07/2013
5279(3^178352-2)/785095Lelio R Paula12/2012
528011^81699-279085081Enzo Doria12/2012
52812^282612-9585075Lelio R Paula08/2012
52822^282609-406985074Yves Minet02/2018
528375^45366-285065Lelio R Paula08/2013
52842^282511+6985045Lelio R Paula08/2012
528569^46249+285045Lelio R Paula06/2013
52863^178226+1085036Robert Price10/2013
5287(182*10^85017+43)/985019Robert Price11/2017
5288(14*10^85010+73)/385011Robert Price04/2016
52899*2^282338-784994Lelio R Paula08/2014
5290(9913*2^282330-1)/157800384988Lelio R Paula04/2015
52912^282203+584952Lelio R Paula08/2012
52922^282184+1384946Lelio R Paula08/2012
529311^81568-240084945Enzo Doria12/2012
529411^81562-234084939Enzo Doria12/2012
5295(41*10^84927+31)/984928Robert Price05/2015
5296(2*10^84904-17)/384904Robert Price08/2014
5297(4^141017+23)/384901Robert Price02/2017
52986^109100-1865384897Enzo Doria03/2013
52992^281973+102584883Lelio R Paula09/2013
53002^281951-10965184876Enzo Doria04/2014
530111^81491-543084865Enzo Doria01/2013
5302((1+sqrt(3)+sqrt(2))^79357-1)*((1+sqrt(3)-sqrt(2))^79357-1)*((1-sqrt(3)+sqrt(2))^79357-1)*((1-sqrt(384849Mike Oakes04/2009
53032^281825-186148384838Enzo Doria03/2016
53042^281809-9730584833Lelio R Paula09/2013
53052^281780-11489384825Enzo Doria05/2015
53063^177719+6484794Lelio R Paula12/2015
53082^281675-19984793Lelio R Paula08/2012
53072^281673-11122384793Enzo Doria05/2014
5309(4*10^84779+149)/984779Robert Price03/2017
5310129^40167-12884777Norbert Schneider01/2019
5311(72*10^84772-27)/984773Ray Chandler01/2011
531211^81398-63084768Enzo Doria11/2012
5313(25*2^281577-1)/2384764Lelio R Paula02/2014
53142^281500-45584740Yves Minet03/2012
531510^84725+114514191984726Marisa Kirisame03/2015
531610^84725+14204184726Patrick De Geest10/2015
531710^84725-13867784725Patrick De Geest02/2016
531876^45044+7584720Norbert Schneider02/2015
531954^48897-5384709Norbert Schneider08/2014
5320(9913*2^281377-1)/6584706Lelio R Paula04/2015
5321Phi(171124,10)/29946701/7761329021/5856034404184700Maksym Voznyy11/2015
53222^281337-11122384691Enzo Doria05/2014
53232^281308+5461584683Lelio R Paula09/2013
53247*5^121144-684677Lelio R Paula10/2014
5325(2^281252+47)/384665Lelio R Paula01/2013
532611^81297-315084663Enzo Doria12/2012
53272^281208-30384653Yves Minet02/2012
5328197^36892-284648Lelio R Paula10/2017
5329(21*2^281187+1)/248384644Lelio R Paula01/2013
533011^81247-8484611Lelio R Paula10/2015
533117^68747-6484590Lelio R Paula11/2015
53325^121018-1559684588Enzo Doria02/2013
53336^108702+784587Lelio R Paula11/2014
533410^84582+10067784583Patrick De Geest05/2016
533510^84582-800184582Robert Price03/2016
53363*5^121004-884579Lelio R Paula10/2014
53375^120996-8484573Lelio R Paula10/2015
5338(10223*2^280881+1)/6841984553Lelio R Paula06/2014
53392^280852+9768184545Yves Minet08/2004
53402^280848-120384544Lelio R Paula09/2013
53415^120946-2484538Lelio R Paula10/2015
53422^280810-211184533Yves Minet08/2013
534311^81161-516084521Enzo Doria01/2013
53442^280737-9384511Lelio R Paula08/2012
53452^280698+31584499Lelio R Paula09/2013
53463^177099-34084498Lelio R Paula12/2015
5347(5*10^84469-107)/384470Robert Price01/2017
5348(3^177002+7)/669602227216174484436Lelio R Paula12/2012
5349(2^280500-1017)/82384436Lelio R Paula01/2013
535014^73660-584424Lelio R Paula11/2015
5351(19*10^84409-61)/384410Robert Price04/2017
53522^280388+11784406Lelio R Paula08/2012
53532^280389-56653384406Paul Bourdelais03/2013
5354(141584^16384+1)/6553784390Syoichiro Yamada06/2008
5355119^40652+11884376Norbert Schneider09/2018
53562^280240-17384361Lelio R Paula08/2012
5357(184*10^84348-1)/384350Robert Price02/2017
53584*10^84346+9384347Robert Price01/2017
53597*2^280156-584337Lelio R Paula08/2014
53608*7^99782-384327Lelio R Paula10/2014
53622^280116+13384324Lelio R Paula08/2012
53612^280118+5461584324Lelio R Paula09/2013
5363(509203*2^280090-1)/384321Lelio R Paula04/2015
53646^108354+4784316Lelio R Paula12/2015
536510^84305+14196384306Patrick De Geest07/2013
536610^84305-5784305Robert Price05/2011
53679^88339+3*8^88339-2*4^88339-3*2^8833984297Mike Oakes01/2011
53683^176648-11280484283Enzo Doria06/2014
53696^108310+11584282Lelio R Paula12/2015
5370(11*2^279968-1)/584280Lelio R Paula02/2014
53716^108288-1664384265Enzo Doria02/2013
53722^279917-5869584264Lelio R Paula08/2013
537365^46477+3684259Lelio R Paula01/2016
53742^279866-190784249Yves Minet05/2013
5375(3^176580-5)/2807684246Lelio R Paula12/2012
5376(p(17530)#+4)/284246Robert Price09/2017
5377(2*10^84239+1)/384239Serge Batalov07/2009
537918^67103-4184233Lelio R Paula11/2015
537820^64743-4384233Lelio R Paula01/2016
5380143^39070+39070^14384209Serge Batalov05/2014
538111^80857-540084204Enzo Doria01/2013
5382(13*10^84179+161)/384180Robert Price04/2017
53832^279634-11040584179Enzo Doria05/2014
5384(74*10^84170+313)/984171Robert Price11/2017
53852^279582-101784163Lelio R Paula08/2013
5386(22*10^84159-19)/384160Robert Price02/2017
5387p(17513)#/2+51284156Robert Price05/2017
5388(19*10^84144-43)/384145Robert Price10/2017
5389(9*2^279507-1)/13784139Lelio R Paula02/2014
539011^80792-81084137Enzo Doria11/2012
5391(97*10^84134-1)/384136Serge Batalov12/2014
5392p(17507)#/2+3284125Robert Price12/2016
539321485^8224+8224^2148584116Hans Havermann04/2017
53943^176294-34084114Lelio R Paula12/2015
5395(3^176287+4)/219184107Lelio R Paula12/2012
53962^279388-71984105Yves Minet05/2012
5397(22699*2^279378+1)/22184104Lelio R Paula06/2014
53982^279332-11044784088Enzo Doria05/2014
53992^279320+784084Lelio R Paula06/2012
5400127^39966-284081Lelio R Paula10/2017
5401(11*2^279240-1)/9584059Lelio R Paula02/2014
54022^279218-11134784053Enzo Doria05/2014
540335^54435+284052Lelio R Paula05/2013
5404(31*2^279191-1)/1251152384040Lelio R Paula02/2014
540520996^10059+10059^2099684038Hans Havermann05/2017
540697*10^84033-384035Robert Price01/2017
540721234^9067+9067^2123484033Hans Havermann05/2017
5408(134569^16384+1)/284033Richard Fischer06/2018
54092^279095-10971784016Enzo Doria04/2014
541014^73282-9983991Lelio R Paula11/2015
541121457^8200+8200^2145783979Hans Havermann06/2017
541289*10^83976-783978Robert Price03/2017
54132^278955+17383974Lelio R Paula06/2012
5414(7*2^278851+1)/3983942Lelio R Paula12/2012
5415(9913*2^278844-1)/4080383940Lelio R Paula04/2015
54165^120076-1484683930Enzo Doria02/2013
5417(85*10^83921-1)/383923Robert Price07/2017
5418(2^278770-3)/2383917Lelio R Paula12/2012
5419(10^83916+449)/983916Serge Batalov12/2014
54212^278715+9983902Lelio R Paula06/2012
5420(132109^16384+1)/283902Richard Fischer05/2018
542240235!2-2^4023583899Robert Price09/2015
54232^278698-17183897Lelio R Paula06/2012
5424(19*10^83894-43)/383895Robert Price10/2017
54256^107802+2583887Lelio R Paula12/2015
54268*10^83880+3983881Robert Price01/2017
5427(58*10^83878+23)/983879Robert Price09/2015
54287^99244-9083871Lelio R Paula10/2015
54292^278554+425783854Lelio R Paula08/2013
54302^278504-10961983839Enzo Doria04/2014
54312^278499+187043383837Enzo Doria05/2016
5432105^41475+10483829Norbert Schneider11/2016
543315^71276-6883828Lelio R Paula11/2015
54342^278464-21641383827Enzo Doria04/2013
5435(76*10^83816-211)/983817Robert Price10/2017
5436(8*10^83811-101)/383812Robert Price10/2017
54372^278400+4075583807Lelio R Paula08/2013
5438(9*2^278381-1)/783802Lelio R Paula02/2014
54393*9^87813+6^87813+2*4^8781383796Mike Oakes12/2010
544019551^19268+19268^1955183773Hans Havermann05/2017
544120625^11522+11522^2062583770Hans Havermann05/2017
5442(44*10^83768-791)/983769Robert Price10/2017
5443(87^43189+1)/8883764Paul Bourdelais08/2017
54442^278235-4983758Lelio R Paula06/2012
544523543^3610+3610^2354383755Hans Havermann05/2017
544718^66711-9183741Lelio R Paula11/2015
54464*10^83740-8983741Robert Price08/2017
5448(3*2^278172-1)/1183738Lelio R Paula02/2014
5449(15*29^57251+2561)/2883724Curtis Bright05/2015
54504*7^99059-983716Lelio R Paula10/2014
5451(2^278128-3)/12684472414983714Lelio R Paula12/2012
54522^278077+186721183710Enzo Doria03/2016
54532^278059-2783705Lelio R Paula06/2012
5454214^35917+35917^21483702Norbert Schneider12/2014
5455(23*10^83693+7)/383694Robert Price10/2015
545685^43375-283689Lelio R Paula09/2013
54575*3^175360+483669Lelio R Paula07/2014
5458(23^61441-1)/2283665Robert Price01/2012
545920091^14596+14596^2009183664Hans Havermann03/2017
54602^277907-11062983659Enzo Doria05/2014
546119522^19283+19283^1952283656Hans Havermann04/2017
54628*5^119664-383643Lelio R Paula10/2014
54638*3^175299-783640Lelio R Paula07/2014
5464(26*10^83638-413)/983639Robert Price10/2017
54653^175250+2283616Robert Price12/2013
546711^80285+3083609Lelio R Paula10/2015
546626870^1293+1293^2687083609Hans Havermann03/2017
54682^277691+187442383594Enzo Doria06/2016
546913^75022-6083571Lelio R Paula11/2015
547014^72905-5183559Lelio R Paula11/2015
5471(17*2^277565-1)/54383554Lelio R Paula02/2014
54725^119532-1283550Lelio R Paula10/2015
54736^107358-1625383541Enzo Doria02/2013
54742^277478-46021183530Enzo Doria06/2015
5475(22*10^83525-7)/383526Erik Branger09/2014
5476(30^56543+1)/3183520Robert Price07/2013
54772^277417-46078383511Paul Bourdelais04/2013
5478(22699*2^277387+1)/21983504Lelio R Paula06/2014
5479(31*2^277383-1)/24783500Lelio R Paula02/2014
548021368^8085+8085^2136883500Hans Havermann04/2017
5481(9*2^277342+1)/1383489Lelio R Paula12/2012
54825^119439-6683485Lelio R Paula10/2015
5483(14*10^83471-101)/383472Robert Price04/2017
54845*6^107263+783468Lelio R Paula10/2014
5485(64*10^83461-1)/983462Serge Batalov11/2010
54862^277244-17570983459Hans Havermann10/2018
548717^67796-9283420Lelio R Paula11/2015
54882^277106-11005783418Enzo Doria04/2014
54896^107200-1983418Lelio R Paula12/2015
549011^80096-183083412Enzo Doria12/2012
54913^174801+5683402Lelio R Paula12/2015
54922^277033-11197383396Enzo Doria05/2014
5493120^40105-11983386Norbert Schneider09/2018
549420519^11572+11572^2051983378Hans Havermann03/2017
549520850^9971+9971^2085083374Hans Havermann03/2017
54966^107122-1886383358Enzo Doria03/2013
54974*10^83354-8983355Robert Price08/2017
54983^174697-3483352Robert Price11/2013
5499(9787*2^276855-1)/234583343Lelio R Paula04/2015
55002^276825+7522783333Enzo Doria04/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 20 2019 09:21 (Time in France)

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