PRP Records

Probable Primes Top 10000

(173006 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 (> 30000) Who ? When ?
42512^283473-161585334Lelio R Paula09/2013
42522^283466-1585332Lelio R Paula08/2012
425311^81916-702085307Enzo Doria02/2013
42546^109626-785306Lelio R Paula11/2014
42552^283374-11032785305Enzo Doria05/2014
425633*10^85297+785299Robert Price07/2016
425718^67933+4185275Lelio R Paula11/2015
42582^283271-10934185274Enzo Doria04/2014
4259(25*10^85249-73)/385250Robert Price09/2016
42602*5^121959+385246Lelio R Paula10/2014
426119834^19834+894785235Henri Lifchitz11/2004
42622^283140+191585234Lelio R Paula09/2013
4263(16*10^85221-31)/385222Robert Price03/2016
42642^283083+186938385217Enzo Doria05/2016
4265(24737*2^283051+1)/1785211Lelio R Paula06/2014
4266(2^283032+78557)/385201Lelio R Paula01/2013
42672^283026-10989385200Enzo Doria04/2014
4268(2^283012+78557)/12985193Lelio R Paula01/2013
42692^282860-10972785150Enzo Doria04/2014
42702^282819+186941385138Enzo Doria05/2016
42713^178428+285132Ray Chandler07/2011
4272(22699*2^282742+1)/7385117Lelio R Paula06/2014
4273(16^70687+5^70687)/2185115Robert Price07/2013
4274(3^178352-2)/785095Lelio R Paula12/2012
427511^81699-279085081Enzo Doria12/2012
42762^282612-9585075Lelio R Paula08/2012
427775^45366-285065Lelio R Paula08/2013
42782^282511+6985045Lelio R Paula08/2012
427969^46249+285045Lelio R Paula06/2013
42803^178226+1085036Robert Price10/2013
4281(14*10^85010+73)/385011Robert Price04/2016
42829*2^282338-784994Lelio R Paula08/2014
4283(9913*2^282330-1)/157800384988Lelio R Paula04/2015
42842^282203+584952Lelio R Paula08/2012
42852^282184+1384946Lelio R Paula08/2012
428611^81568-240084945Enzo Doria12/2012
428711^81562-234084939Enzo Doria12/2012
4288(41*10^84927+31)/984928Robert Price05/2015
4289(2*10^84904-17)/384904Robert Price08/2014
4290(4^141017+23)/384901Robert Price02/2017
42916^109100-1865384897Enzo Doria03/2013
42922^281973+102584883Lelio R Paula09/2013
42932^281951-10965184876Enzo Doria04/2014
429411^81491-543084865Enzo Doria01/2013
4295((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
42962^281825-186148384838Enzo Doria03/2016
42972^281809-9730584833Lelio R Paula09/2013
42982^281780-11489384825Enzo Doria05/2015
42993^177719+6484794Lelio R Paula12/2015
43012^281675-19984793Lelio R Paula08/2012
43002^281673-11122384793Enzo Doria05/2014
4302(4*10^84779+149)/984779Robert Price03/2017
4303(72*10^84772-27)/984773Ray Chandler01/2011
430411^81398-63084768Enzo Doria11/2012
4305(25*2^281577-1)/2384764Lelio R Paula02/2014
43062^281500-45584740Yves Minet03/2012
430710^84725+114514191984726Marisa Kirisame03/2015
430810^84725+14204184726Patrick De Geest10/2015
430910^84725-13867784725Patrick De Geest02/2016
431076^45044+7584720Norbert Schneider02/2015
431154^48897-5384709Norbert Schneider08/2014
4312(9913*2^281377-1)/6584706Lelio R Paula04/2015
4313Phi(171124,10)/29946701/7761329021/5856034404184700Maksym Voznyy11/2015
43142^281337-11122384691Enzo Doria05/2014
43152^281308+5461584683Lelio R Paula09/2013
43167*5^121144-684677Lelio R Paula10/2014
4317(2^281252+47)/384665Lelio R Paula01/2013
431811^81297-315084663Enzo Doria12/2012
43192^281208-30384653Yves Minet02/2012
4320(21*2^281187+1)/248384644Lelio R Paula01/2013
432111^81247-8484611Lelio R Paula10/2015
432217^68747-6484590Lelio R Paula11/2015
43235^121018-1559684588Enzo Doria02/2013
43246^108702+784587Lelio R Paula11/2014
432510^84582+10067784583Patrick De Geest05/2016
432610^84582-800184582Robert Price03/2016
43273*5^121004-884579Lelio R Paula10/2014
43285^120996-8484573Lelio R Paula10/2015
4329(10223*2^280881+1)/6841984553Lelio R Paula06/2014
43302^280852+9768184545Yves Minet08/2004
43312^280848-120384544Lelio R Paula09/2013
43325^120946-2484538Lelio R Paula10/2015
43332^280810-211184533Yves Minet08/2013
433411^81161-516084521Enzo Doria01/2013
43352^280737-9384511Lelio R Paula08/2012
43362^280698+31584499Lelio R Paula09/2013
43373^177099-34084498Lelio R Paula12/2015
4338(5*10^84469-107)/384470Robert Price01/2017
4339(3^177002+7)/669602227216174484436Lelio R Paula12/2012
4340(2^280500-1017)/82384436Lelio R Paula01/2013
434114^73660-584424Lelio R Paula11/2015
4342(19*10^84409-61)/384410Robert Price04/2017
43432^280388+11784406Lelio R Paula08/2012
43442^280389-56653384406Paul Bourdelais03/2013
4345(141584^16384+1)/6553784390Syoichiro Yamada06/2008
43462^280240-17384361Lelio R Paula08/2012
4347(184*10^84348-1)/384350Robert Price02/2017
43484*10^84346+9384347Robert Price01/2017
43497*2^280156-584337Lelio R Paula08/2014
43508*7^99782-384327Lelio R Paula10/2014
43512^280116+13384324Lelio R Paula08/2012
43522^280118+5461584324Lelio R Paula09/2013
4353(509203*2^280090-1)/384321Lelio R Paula04/2015
43546^108354+4784316Lelio R Paula12/2015
435510^84305+14196384306Patrick De Geest07/2013
435610^84305-5784305Robert Price05/2011
43579^88339+3*8^88339-2*4^88339-3*2^8833984297Mike Oakes01/2011
43583^176648-11280484283Enzo Doria06/2014
43596^108310+11584282Lelio R Paula12/2015
4360(11*2^279968-1)/584280Lelio R Paula02/2014
43616^108288-1664384265Enzo Doria02/2013
43622^279917-5869584264Lelio R Paula08/2013
436365^46477+3684259Lelio R Paula01/2016
43642^279866-190784249Yves Minet05/2013
4365(3^176580-5)/2807684246Lelio R Paula12/2012
4366(2*10^84239+1)/384239Serge Batalov07/2009
436718^67103-4184233Lelio R Paula11/2015
436820^64743-4384233Lelio R Paula01/2016
4369143^39070+39070^14384209Serge Batalov05/2014
437011^80857-540084204Enzo Doria01/2013
4371(13*10^84179+161)/384180Robert Price04/2017
43722^279634-11040584179Enzo Doria05/2014
43732^279582-101784163Lelio R Paula08/2013
4374(22*10^84159-19)/384160Robert Price02/2017
4375p(17513)#/2+51284156Robert Price05/2017
4376(9*2^279507-1)/13784139Lelio R Paula02/2014
437711^80792-81084137Enzo Doria11/2012
4378(97*10^84134-1)/384136Serge Batalov12/2014
4379p(17507)#/2+3284125Robert Price12/2016
438021485^8224+8224^2148584116Hans Havermann04/2017
43813^176294-34084114Lelio R Paula12/2015
4382(3^176287+4)/219184107Lelio R Paula12/2012
43832^279388-71984105Yves Minet05/2012
4384(22699*2^279378+1)/22184104Lelio R Paula06/2014
43852^279332-11044784088Enzo Doria05/2014
43862^279320+784084Lelio R Paula06/2012
4387(11*2^279240-1)/9584059Lelio R Paula02/2014
43882^279218-11134784053Enzo Doria05/2014
438935^54435+284052Lelio R Paula05/2013
4390(31*2^279191-1)/1251152384040Lelio R Paula02/2014
439197*10^84033-384035Robert Price01/2017
439221234^9067+9067^2123484033Hans Havermann05/2017
43932^279095-10971784016Enzo Doria04/2014
439414^73282-9983991Lelio R Paula11/2015
439589*10^83976-783978Robert Price03/2017
43962^278955+17383974Lelio R Paula06/2012
4397(7*2^278851+1)/3983942Lelio R Paula12/2012
4398(9913*2^278844-1)/4080383940Lelio R Paula04/2015
43995^120076-1484683930Enzo Doria02/2013
4400(2^278770-3)/2383917Lelio R Paula12/2012
4401(10^83916+449)/983916Serge Batalov12/2014
44022^278715+9983902Lelio R Paula06/2012
440340235!2-2^4023583899Robert Price09/2015
44042^278698-17183897Lelio R Paula06/2012
44056^107802+2583887Lelio R Paula12/2015
44068*10^83880+3983881Robert Price01/2017
4407(58*10^83878+23)/983879Robert Price09/2015
44087^99244-9083871Lelio R Paula10/2015
44092^278554+425783854Lelio R Paula08/2013
44102^278504-10961983839Enzo Doria04/2014
44112^278499+187043383837Enzo Doria05/2016
4412105^41475+10483829Norbert Schneider11/2016
441315^71276-6883828Lelio R Paula11/2015
44142^278464-21641383827Enzo Doria04/2013
44152^278400+4075583807Lelio R Paula08/2013
4416(9*2^278381-1)/783802Lelio R Paula02/2014
44173*9^87813+6^87813+2*4^8781383796Mike Oakes12/2010
441819551^19268+19268^1955183773Hans Havermann05/2017
441920625^11522+11522^2062583770Hans Havermann05/2017
44202^278235-4983758Lelio R Paula06/2012
442118^66711-9183741Lelio R Paula11/2015
4422(3*2^278172-1)/1183738Lelio R Paula02/2014
4423(15*29^57251+2561)/2883724Curtis Bright05/2015
44244*7^99059-983716Lelio R Paula10/2014
4425(2^278128-3)/12684472414983714Lelio R Paula12/2012
44262^278077+186721183710Enzo Doria03/2016
44272^278059-2783705Lelio R Paula06/2012
4428214^35917+35917^21483702Norbert Schneider12/2014
4429(23*10^83693+7)/383694Robert Price10/2015
443085^43375-283689Lelio R Paula09/2013
44315*3^175360+483669Lelio R Paula07/2014
4432(23^61441-1)/2283665Robert Price01/2012
443320091^14596+14596^2009183664Hans Havermann03/2017
44342^277907-11062983659Enzo Doria05/2014
443519522^19283+19283^1952283656Hans Havermann04/2017
44368*5^119664-383643Lelio R Paula10/2014
44378*3^175299-783640Lelio R Paula07/2014
44383^175250+2283616Robert Price12/2013
443911^80285+3083609Lelio R Paula10/2015
444026870^1293+1293^2687083609Hans Havermann03/2017
44412^277691+187442383594Enzo Doria06/2016
444213^75022-6083571Lelio R Paula11/2015
444314^72905-5183559Lelio R Paula11/2015
4444(17*2^277565-1)/54383554Lelio R Paula02/2014
44455^119532-1283550Lelio R Paula10/2015
44466^107358-1625383541Enzo Doria02/2013
44472^277478-46021183530Enzo Doria06/2015
4448(22*10^83525-7)/383526Erik Branger09/2014
4449(30^56543+1)/3183520Robert Price07/2013
44502^277417-46078383511Paul Bourdelais04/2013
4451(22699*2^277387+1)/21983504Lelio R Paula06/2014
4452(31*2^277383-1)/24783500Lelio R Paula02/2014
445321368^8085+8085^2136883500Hans Havermann04/2017
4454(9*2^277342+1)/1383489Lelio R Paula12/2012
44555^119439-6683485Lelio R Paula10/2015
4456(14*10^83471-101)/383472Robert Price04/2017
44575*6^107263+783468Lelio R Paula10/2014
4458(64*10^83461-1)/983462Serge Batalov11/2010
445917^67796-9283420Lelio R Paula11/2015
44602^277106-11005783418Enzo Doria04/2014
44616^107200-1983418Lelio R Paula12/2015
446211^80096-183083412Enzo Doria12/2012
44633^174801+5683402Lelio R Paula12/2015
44642^277033-11197383396Enzo Doria05/2014
446520519^11572+11572^2051983378Hans Havermann03/2017
446620850^9971+9971^2085083374Hans Havermann03/2017
44676^107122-1886383358Enzo Doria03/2013
44683^174697-3483352Robert Price11/2013
4469(9787*2^276855-1)/234583343Lelio R Paula04/2015
44702^276825+7522783333Enzo Doria04/2016
44715^119214+8483328Lelio R Paula10/2015
44722^276803-15983327Lelio R Paula06/2012
4473(3*2^276753-1)/2583311Lelio R Paula02/2014
4474114^40495+40495^11483295Norbert Schneider12/2014
447539967!2+102483282Robert Price02/2015
44762^276641+5783278Lelio R Paula06/2012
447735^53934-341483278Enzo Doria03/2013
4478(2^276655+78557)/36542583276Lelio R Paula12/2012
44792^276615-403583270Lelio R Paula08/2013
44802^276588+115583262Lelio R Paula08/2013
44822^276587-93783261Yves Minet10/2009
44812^276584-11318383261Enzo Doria07/2014
4483(2^276592-1017)/1384373983256Lelio R Paula12/2012
44842^276547-10959183249Enzo Doria04/2014
448513^74733-3283249Lelio R Paula11/2015
44862^276523-258783242Yves Minet07/2014
448718^66311-4383239Lelio R Paula11/2015
448811^79919-153083228Enzo Doria12/2012
44892^276468-10974583226Enzo Doria04/2014
44902^276462+538583224Lelio R Paula08/2013
4491(9787*2^276422-1)/383215Lelio R Paula04/2015
44922^276391-1583202Lelio R Paula06/2012
4493(4*10^83201+173)/383202Robert Price01/2017
44942^276316-10965583180Enzo Doria04/2014
44952^276305-11206383177Enzo Doria06/2014
4496(10^(2*41585+1)+54*10^41585-1)/983171Robert Price04/2017
44972^276227-183720783153Enzo Doria05/2015
4498(2^276227+3)/783152Lelio R Paula12/2012
44992^276184-6338983140Paul Bourdelais02/2012
45002^276066-11160383105Enzo Doria05/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 25 2017 10:58 (Time in France)

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