PRP Records

Probable Primes Top 10000

(177649 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 ?
425111^82426-123085838Enzo Doria11/2012
42522^285113-10988185828Enzo Doria04/2014
42535^122746-9285796Lelio R Paula10/2015
42542^285001-11346185794Enzo Doria08/2014
4255(11*10^85782-131)/385783Robert Price02/2017
42562^284913-11049185768Enzo Doria05/2014
42576^110220+4785768Lelio R Paula12/2015
42583*6^110202-585755Lelio R Paula10/2014
4259(157^39047-1)/15685742Alexander Zhirkov06/2016
4260(3^179705+7)/25085739Lelio R Paula12/2012
42612^284734-655585714Lelio R Paula09/2013
4262(10^85712+53)/985712Robert Price01/2015
4263(6883*2^284668-1)/385697Lelio R Paula04/2015
426420^65855+8385680Lelio R Paula01/2016
42656^110105+5385679Lelio R Paula12/2015
42672^284567-760585664Lelio R Paula09/2013
42669*5^122555-285664Lelio R Paula10/2014
42685^122554-1485662Lelio R Paula10/2015
42699*5^122543+485655Lelio R Paula10/2014
42703^179489-2^(179489-1)85639Robert Price01/2016
42712^284429+17785622Lelio R Paula08/2012
42722*3^179452+585621Lelio R Paula07/2014
4273(19^66919+3^66919)/2285572Robert Price07/2013
427466^47023-6585561Norbert Schneider11/2014
42756^109943+1385553Lelio R Paula12/2015
4276(2^284167-509203)/3456477585536Lelio R Paula01/2013
42772^284133-385533M. Frind & P. Underwood07/2002
42782^284113+31585527Lelio R Paula09/2013
4279(16*10^85495-19)/385496Robert Price03/2016
42802^284004+17785494Lelio R Paula08/2012
4281(16*10^85473-91)/385474Robert Price06/2016
42823^179120+2285462Robert Price12/2013
42832^283872-279224985454Enzo Doria03/2016
4284(29*10^85438+259)/985439Robert Price04/2017
42852^283817+8287585438Lelio R Paula09/2013
4286(2^283815-5)/20185435Lelio R Paula01/2013
42872^283796-12585432Lelio R Paula08/2012
4288(29*2^283784-1)/1385428Lelio R Paula02/2014
428915^72592-2885375Lelio R Paula11/2015
42902^283604-5869585374Lelio R Paula09/2013
4291(15*2^283583-1)/10305185364Lelio R Paula02/2014
429215^72572+9285352Lelio R Paula11/2015
42932^283473-161585334Lelio R Paula09/2013
42942^283466-1585332Lelio R Paula08/2012
429511^81916-702085307Enzo Doria02/2013
42966^109626-785306Lelio R Paula11/2014
42972^283374-11032785305Enzo Doria05/2014
429833*10^85297+785299Robert Price07/2016
429918^67933+4185275Lelio R Paula11/2015
43002^283271-10934185274Enzo Doria04/2014
4301(25*10^85249-73)/385250Robert Price09/2016
43022*5^121959+385246Lelio R Paula10/2014
430319834^19834+894785235Henri Lifchitz11/2004
43042^283140+191585234Lelio R Paula09/2013
4305(16*10^85221-31)/385222Robert Price03/2016
43062^283083+186938385217Enzo Doria05/2016
4307(24737*2^283051+1)/1785211Lelio R Paula06/2014
4308(2^283032+78557)/385201Lelio R Paula01/2013
43092^283026-10989385200Enzo Doria04/2014
4310(2^283012+78557)/12985193Lelio R Paula01/2013
43112^282860-10972785150Enzo Doria04/2014
43122^282819+186941385138Enzo Doria05/2016
43133^178428+285132Ray Chandler07/2011
4314(22699*2^282742+1)/7385117Lelio R Paula06/2014
4315(16^70687+5^70687)/2185115Robert Price07/2013
4316(3^178352-2)/785095Lelio R Paula12/2012
431711^81699-279085081Enzo Doria12/2012
43182^282612-9585075Lelio R Paula08/2012
431975^45366-285065Lelio R Paula08/2013
43202^282511+6985045Lelio R Paula08/2012
432169^46249+285045Lelio R Paula06/2013
43223^178226+1085036Robert Price10/2013
4323(14*10^85010+73)/385011Robert Price04/2016
43249*2^282338-784994Lelio R Paula08/2014
4325(9913*2^282330-1)/157800384988Lelio R Paula04/2015
43262^282203+584952Lelio R Paula08/2012
43272^282184+1384946Lelio R Paula08/2012
432811^81568-240084945Enzo Doria12/2012
432911^81562-234084939Enzo Doria12/2012
4330(41*10^84927+31)/984928Robert Price05/2015
4331(2*10^84904-17)/384904Robert Price08/2014
4332(4^141017+23)/384901Robert Price02/2017
43336^109100-1865384897Enzo Doria03/2013
43342^281973+102584883Lelio R Paula09/2013
43352^281951-10965184876Enzo Doria04/2014
433611^81491-543084865Enzo Doria01/2013
4337((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
43382^281825-186148384838Enzo Doria03/2016
43392^281809-9730584833Lelio R Paula09/2013
43402^281780-11489384825Enzo Doria05/2015
43413^177719+6484794Lelio R Paula12/2015
43432^281675-19984793Lelio R Paula08/2012
43422^281673-11122384793Enzo Doria05/2014
4344(4*10^84779+149)/984779Robert Price03/2017
4345(72*10^84772-27)/984773Ray Chandler01/2011
434611^81398-63084768Enzo Doria11/2012
4347(25*2^281577-1)/2384764Lelio R Paula02/2014
43482^281500-45584740Yves Minet03/2012
434910^84725+114514191984726Marisa Kirisame03/2015
435010^84725+14204184726Patrick De Geest10/2015
435110^84725-13867784725Patrick De Geest02/2016
435276^45044+7584720Norbert Schneider02/2015
435354^48897-5384709Norbert Schneider08/2014
4354(9913*2^281377-1)/6584706Lelio R Paula04/2015
4355Phi(171124,10)/29946701/7761329021/5856034404184700Maksym Voznyy11/2015
43562^281337-11122384691Enzo Doria05/2014
43572^281308+5461584683Lelio R Paula09/2013
43587*5^121144-684677Lelio R Paula10/2014
4359(2^281252+47)/384665Lelio R Paula01/2013
436011^81297-315084663Enzo Doria12/2012
43612^281208-30384653Yves Minet02/2012
4362(21*2^281187+1)/248384644Lelio R Paula01/2013
436311^81247-8484611Lelio R Paula10/2015
436417^68747-6484590Lelio R Paula11/2015
43655^121018-1559684588Enzo Doria02/2013
43666^108702+784587Lelio R Paula11/2014
436710^84582+10067784583Patrick De Geest05/2016
436810^84582-800184582Robert Price03/2016
43693*5^121004-884579Lelio R Paula10/2014
43705^120996-8484573Lelio R Paula10/2015
4371(10223*2^280881+1)/6841984553Lelio R Paula06/2014
43722^280852+9768184545Yves Minet08/2004
43732^280848-120384544Lelio R Paula09/2013
43745^120946-2484538Lelio R Paula10/2015
43752^280810-211184533Yves Minet08/2013
437611^81161-516084521Enzo Doria01/2013
43772^280737-9384511Lelio R Paula08/2012
43782^280698+31584499Lelio R Paula09/2013
43793^177099-34084498Lelio R Paula12/2015
4380(5*10^84469-107)/384470Robert Price01/2017
4381(3^177002+7)/669602227216174484436Lelio R Paula12/2012
4382(2^280500-1017)/82384436Lelio R Paula01/2013
438314^73660-584424Lelio R Paula11/2015
4384(19*10^84409-61)/384410Robert Price04/2017
43852^280388+11784406Lelio R Paula08/2012
43862^280389-56653384406Paul Bourdelais03/2013
4387(141584^16384+1)/6553784390Syoichiro Yamada06/2008
43882^280240-17384361Lelio R Paula08/2012
4389(184*10^84348-1)/384350Robert Price02/2017
43904*10^84346+9384347Robert Price01/2017
43917*2^280156-584337Lelio R Paula08/2014
43928*7^99782-384327Lelio R Paula10/2014
43932^280116+13384324Lelio R Paula08/2012
43942^280118+5461584324Lelio R Paula09/2013
4395(509203*2^280090-1)/384321Lelio R Paula04/2015
43966^108354+4784316Lelio R Paula12/2015
439710^84305+14196384306Patrick De Geest07/2013
439810^84305-5784305Robert Price05/2011
43999^88339+3*8^88339-2*4^88339-3*2^8833984297Mike Oakes01/2011
44003^176648-11280484283Enzo Doria06/2014
44016^108310+11584282Lelio R Paula12/2015
4402(11*2^279968-1)/584280Lelio R Paula02/2014
44036^108288-1664384265Enzo Doria02/2013
44042^279917-5869584264Lelio R Paula08/2013
440565^46477+3684259Lelio R Paula01/2016
44062^279866-190784249Yves Minet05/2013
4407(3^176580-5)/2807684246Lelio R Paula12/2012
4408(2*10^84239+1)/384239Serge Batalov07/2009
441018^67103-4184233Lelio R Paula11/2015
440920^64743-4384233Lelio R Paula01/2016
4411143^39070+39070^14384209Serge Batalov05/2014
441211^80857-540084204Enzo Doria01/2013
4413(13*10^84179+161)/384180Robert Price04/2017
44142^279634-11040584179Enzo Doria05/2014
44152^279582-101784163Lelio R Paula08/2013
4416(22*10^84159-19)/384160Robert Price02/2017
4417p(17513)#/2+51284156Robert Price05/2017
4418(9*2^279507-1)/13784139Lelio R Paula02/2014
441911^80792-81084137Enzo Doria11/2012
4420(97*10^84134-1)/384136Serge Batalov12/2014
4421p(17507)#/2+3284125Robert Price12/2016
442221485^8224+8224^2148584116Hans Havermann04/2017
44233^176294-34084114Lelio R Paula12/2015
4424(3^176287+4)/219184107Lelio R Paula12/2012
44252^279388-71984105Yves Minet05/2012
4426(22699*2^279378+1)/22184104Lelio R Paula06/2014
44272^279332-11044784088Enzo Doria05/2014
44282^279320+784084Lelio R Paula06/2012
4429(11*2^279240-1)/9584059Lelio R Paula02/2014
44302^279218-11134784053Enzo Doria05/2014
443135^54435+284052Lelio R Paula05/2013
4432(31*2^279191-1)/1251152384040Lelio R Paula02/2014
443320996^10059+10059^2099684038Hans Havermann05/2017
443497*10^84033-384035Robert Price01/2017
443521234^9067+9067^2123484033Hans Havermann05/2017
44362^279095-10971784016Enzo Doria04/2014
443714^73282-9983991Lelio R Paula11/2015
443821457^8200+8200^2145783979Hans Havermann06/2017
443989*10^83976-783978Robert Price03/2017
44402^278955+17383974Lelio R Paula06/2012
4441(7*2^278851+1)/3983942Lelio R Paula12/2012
4442(9913*2^278844-1)/4080383940Lelio R Paula04/2015
44435^120076-1484683930Enzo Doria02/2013
4444(85*10^83921-1)/383923Robert Price07/2017
4445(2^278770-3)/2383917Lelio R Paula12/2012
4446(10^83916+449)/983916Serge Batalov12/2014
44472^278715+9983902Lelio R Paula06/2012
444840235!2-2^4023583899Robert Price09/2015
44492^278698-17183897Lelio R Paula06/2012
44506^107802+2583887Lelio R Paula12/2015
44518*10^83880+3983881Robert Price01/2017
4452(58*10^83878+23)/983879Robert Price09/2015
44537^99244-9083871Lelio R Paula10/2015
44542^278554+425783854Lelio R Paula08/2013
44552^278504-10961983839Enzo Doria04/2014
44562^278499+187043383837Enzo Doria05/2016
4457105^41475+10483829Norbert Schneider11/2016
445815^71276-6883828Lelio R Paula11/2015
44592^278464-21641383827Enzo Doria04/2013
44602^278400+4075583807Lelio R Paula08/2013
4461(9*2^278381-1)/783802Lelio R Paula02/2014
44623*9^87813+6^87813+2*4^8781383796Mike Oakes12/2010
446319551^19268+19268^1955183773Hans Havermann05/2017
446420625^11522+11522^2062583770Hans Havermann05/2017
44652^278235-4983758Lelio R Paula06/2012
446623543^3610+3610^2354383755Hans Havermann05/2017
446718^66711-9183741Lelio R Paula11/2015
4468(3*2^278172-1)/1183738Lelio R Paula02/2014
4469(15*29^57251+2561)/2883724Curtis Bright05/2015
44704*7^99059-983716Lelio R Paula10/2014
4471(2^278128-3)/12684472414983714Lelio R Paula12/2012
44722^278077+186721183710Enzo Doria03/2016
44732^278059-2783705Lelio R Paula06/2012
4474214^35917+35917^21483702Norbert Schneider12/2014
4475(23*10^83693+7)/383694Robert Price10/2015
447685^43375-283689Lelio R Paula09/2013
44775*3^175360+483669Lelio R Paula07/2014
4478(23^61441-1)/2283665Robert Price01/2012
447920091^14596+14596^2009183664Hans Havermann03/2017
44802^277907-11062983659Enzo Doria05/2014
448119522^19283+19283^1952283656Hans Havermann04/2017
44828*5^119664-383643Lelio R Paula10/2014
44838*3^175299-783640Lelio R Paula07/2014
44843^175250+2283616Robert Price12/2013
448511^80285+3083609Lelio R Paula10/2015
448626870^1293+1293^2687083609Hans Havermann03/2017
44872^277691+187442383594Enzo Doria06/2016
448813^75022-6083571Lelio R Paula11/2015
448914^72905-5183559Lelio R Paula11/2015
4490(17*2^277565-1)/54383554Lelio R Paula02/2014
44915^119532-1283550Lelio R Paula10/2015
44926^107358-1625383541Enzo Doria02/2013
44932^277478-46021183530Enzo Doria06/2015
4494(22*10^83525-7)/383526Erik Branger09/2014
4495(30^56543+1)/3183520Robert Price07/2013
44962^277417-46078383511Paul Bourdelais04/2013
4497(22699*2^277387+1)/21983504Lelio R Paula06/2014
4498(31*2^277383-1)/24783500Lelio R Paula02/2014
449921368^8085+8085^2136883500Hans Havermann04/2017
4500(9*2^277342+1)/1383489Lelio R Paula12/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 27 2017 08:43 (Time in France)

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