PRP Records

Probable Primes Top 10000

(252402 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 ?
50012^285001-11346185794Enzo Doria08/2014
5002(11*10^85782-131)/385783Robert Price02/2017
50032^284913-11049185768Enzo Doria05/2014
50046^110220+4785768Lelio R Paula12/2015
50053*6^110202-585755Lelio R Paula10/2014
5006(157^39047-1)/15685742Alexander Zhirkov06/2016
5007(3^179705+7)/25085739Lelio R Paula12/2012
50082^284734-655585714Lelio R Paula09/2013
5009(10^85712+53)/985712Robert Price01/2015
50103*10^85703+1185704Robert Price11/2017
5011(6883*2^284668-1)/385697Lelio R Paula04/2015
501220^65855+8385680Lelio R Paula01/2016
50136^110105+5385679Lelio R Paula12/2015
5014(10^85666-97)/385666Robert Kinser10/2017
50152^284567-760585664Lelio R Paula09/2013
50169*5^122555-285664Lelio R Paula10/2014
50175^122554-1485662Lelio R Paula10/2015
50189*5^122543+485655Lelio R Paula10/2014
50193^179489-2^(179489-1)85639Robert Price01/2016
50202^284429+17785622Lelio R Paula08/2012
50212*3^179452+585621Lelio R Paula07/2014
5022(19^66919+3^66919)/2285572Robert Price07/2013
502366^47023-6585561Norbert Schneider11/2014
50246^109943+1385553Lelio R Paula12/2015
5025(2^284167-509203)/3456477585536Lelio R Paula01/2013
50262^284133-385533M. Frind & P. Underwood07/2002
50272^284113+31585527Lelio R Paula09/2013
5028(28*10^85500+149)/385501Robert Price10/2017
5029(16*10^85495-19)/385496Robert Price03/2016
50302^284004+17785494Lelio R Paula08/2012
5031(16*10^85473-91)/385474Robert Price06/2016
50323^179120+2285462Robert Price12/2013
50332^283872-279224985454Enzo Doria03/2016
5034(29*10^85438+259)/985439Robert Price04/2017
50352^283817+8287585438Lelio R Paula09/2013
5036(2^283815-5)/20185435Lelio R Paula01/2013
50372^283796-12585432Lelio R Paula08/2012
5038(29*2^283784-1)/1385428Lelio R Paula02/2014
503915^72592-2885375Lelio R Paula11/2015
50402^283604-5869585374Lelio R Paula09/2013
5041(44*10^85370-503)/985371Robert Price10/2017
5042496^31671+31671^49685369Norbert Schneider07/2017
5043(15*2^283583-1)/10305185364Lelio R Paula02/2014
504415^72572+9285352Lelio R Paula11/2015
50452^283473-161585334Lelio R Paula09/2013
50462^283466-1585332Lelio R Paula08/2012
504711^81916-702085307Enzo Doria02/2013
50486^109626-785306Lelio R Paula11/2014
50492^283374-11032785305Enzo Doria05/2014
505033*10^85297+785299Robert Price07/2016
505118^67933+4185275Lelio R Paula11/2015
50522^283271-10934185274Enzo Doria04/2014
5053(25*10^85249-73)/385250Robert Price09/2016
50542*5^121959+385246Lelio R Paula10/2014
505519834^19834+894785235Henri Lifchitz11/2004
50562^283140+191585234Lelio R Paula09/2013
50573*10^85227-9785228Robert Price08/2017
5058(16*10^85221-31)/385222Robert Price03/2016
50592^283083+186938385217Enzo Doria05/2016
5060(24737*2^283051+1)/1785211Lelio R Paula06/2014
5061(2^283032+78557)/385201Lelio R Paula01/2013
50622^283026-10989385200Enzo Doria04/2014
5063(2^283012+78557)/12985193Lelio R Paula01/2013
5064(10^(2*42589+1)+72*10^42589-1)/985179Robert Price09/2017
50652^282860-10972785150Enzo Doria04/2014
50662^282819+186941385138Enzo Doria05/2016
50673^178428+285132Ray Chandler07/2011
5068(22699*2^282742+1)/7385117Lelio R Paula06/2014
5069(16^70687+5^70687)/2185115Robert Price07/2013
5070(3^178352-2)/785095Lelio R Paula12/2012
507111^81699-279085081Enzo Doria12/2012
50722^282612-9585075Lelio R Paula08/2012
50732^282609-406985074Yves Minet02/2018
507475^45366-285065Lelio R Paula08/2013
50752^282511+6985045Lelio R Paula08/2012
507669^46249+285045Lelio R Paula06/2013
50773^178226+1085036Robert Price10/2013
5078(182*10^85017+43)/985019Robert Price11/2017
5079(14*10^85010+73)/385011Robert Price04/2016
50809*2^282338-784994Lelio R Paula08/2014
5081(9913*2^282330-1)/157800384988Lelio R Paula04/2015
50822^282203+584952Lelio R Paula08/2012
50832^282184+1384946Lelio R Paula08/2012
508411^81568-240084945Enzo Doria12/2012
508511^81562-234084939Enzo Doria12/2012
5086(41*10^84927+31)/984928Robert Price05/2015
5087(2*10^84904-17)/384904Robert Price08/2014
5088(4^141017+23)/384901Robert Price02/2017
50896^109100-1865384897Enzo Doria03/2013
50902^281973+102584883Lelio R Paula09/2013
50912^281951-10965184876Enzo Doria04/2014
509211^81491-543084865Enzo Doria01/2013
5093((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
50942^281825-186148384838Enzo Doria03/2016
50952^281809-9730584833Lelio R Paula09/2013
50962^281780-11489384825Enzo Doria05/2015
50973^177719+6484794Lelio R Paula12/2015
50992^281675-19984793Lelio R Paula08/2012
50982^281673-11122384793Enzo Doria05/2014
5100(4*10^84779+149)/984779Robert Price03/2017
5101(72*10^84772-27)/984773Ray Chandler01/2011
510211^81398-63084768Enzo Doria11/2012
5103(25*2^281577-1)/2384764Lelio R Paula02/2014
51042^281500-45584740Yves Minet03/2012
510510^84725+114514191984726Marisa Kirisame03/2015
510610^84725+14204184726Patrick De Geest10/2015
510710^84725-13867784725Patrick De Geest02/2016
510876^45044+7584720Norbert Schneider02/2015
510954^48897-5384709Norbert Schneider08/2014
5110(9913*2^281377-1)/6584706Lelio R Paula04/2015
5111Phi(171124,10)/29946701/7761329021/5856034404184700Maksym Voznyy11/2015
51122^281337-11122384691Enzo Doria05/2014
51132^281308+5461584683Lelio R Paula09/2013
51147*5^121144-684677Lelio R Paula10/2014
5115(2^281252+47)/384665Lelio R Paula01/2013
511611^81297-315084663Enzo Doria12/2012
51172^281208-30384653Yves Minet02/2012
5118197^36892-284648Lelio R Paula10/2017
5119(21*2^281187+1)/248384644Lelio R Paula01/2013
512011^81247-8484611Lelio R Paula10/2015
512117^68747-6484590Lelio R Paula11/2015
51225^121018-1559684588Enzo Doria02/2013
51236^108702+784587Lelio R Paula11/2014
512410^84582+10067784583Patrick De Geest05/2016
512510^84582-800184582Robert Price03/2016
51263*5^121004-884579Lelio R Paula10/2014
51275^120996-8484573Lelio R Paula10/2015
5128(10223*2^280881+1)/6841984553Lelio R Paula06/2014
51292^280852+9768184545Yves Minet08/2004
51302^280848-120384544Lelio R Paula09/2013
51315^120946-2484538Lelio R Paula10/2015
51322^280810-211184533Yves Minet08/2013
513311^81161-516084521Enzo Doria01/2013
51342^280737-9384511Lelio R Paula08/2012
51352^280698+31584499Lelio R Paula09/2013
51363^177099-34084498Lelio R Paula12/2015
5137(5*10^84469-107)/384470Robert Price01/2017
5138(3^177002+7)/669602227216174484436Lelio R Paula12/2012
5139(2^280500-1017)/82384436Lelio R Paula01/2013
514014^73660-584424Lelio R Paula11/2015
5141(19*10^84409-61)/384410Robert Price04/2017
51422^280388+11784406Lelio R Paula08/2012
51432^280389-56653384406Paul Bourdelais03/2013
5144(141584^16384+1)/6553784390Syoichiro Yamada06/2008
5145119^40652+11884376Norbert Schneider09/2018
51462^280240-17384361Lelio R Paula08/2012
5147(184*10^84348-1)/384350Robert Price02/2017
51484*10^84346+9384347Robert Price01/2017
51497*2^280156-584337Lelio R Paula08/2014
51508*7^99782-384327Lelio R Paula10/2014
51512^280116+13384324Lelio R Paula08/2012
51522^280118+5461584324Lelio R Paula09/2013
5153(509203*2^280090-1)/384321Lelio R Paula04/2015
51546^108354+4784316Lelio R Paula12/2015
515510^84305+14196384306Patrick De Geest07/2013
515610^84305-5784305Robert Price05/2011
51579^88339+3*8^88339-2*4^88339-3*2^8833984297Mike Oakes01/2011
51583^176648-11280484283Enzo Doria06/2014
51596^108310+11584282Lelio R Paula12/2015
5160(11*2^279968-1)/584280Lelio R Paula02/2014
51616^108288-1664384265Enzo Doria02/2013
51622^279917-5869584264Lelio R Paula08/2013
516365^46477+3684259Lelio R Paula01/2016
51642^279866-190784249Yves Minet05/2013
5165(3^176580-5)/2807684246Lelio R Paula12/2012
5166(p(17530)#+4)/284246Robert Price09/2017
5167(2*10^84239+1)/384239Serge Batalov07/2009
516918^67103-4184233Lelio R Paula11/2015
516820^64743-4384233Lelio R Paula01/2016
5170143^39070+39070^14384209Serge Batalov05/2014
517111^80857-540084204Enzo Doria01/2013
5172(13*10^84179+161)/384180Robert Price04/2017
51732^279634-11040584179Enzo Doria05/2014
5174(74*10^84170+313)/984171Robert Price11/2017
51752^279582-101784163Lelio R Paula08/2013
5176(22*10^84159-19)/384160Robert Price02/2017
5177p(17513)#/2+51284156Robert Price05/2017
5178(19*10^84144-43)/384145Robert Price10/2017
5179(9*2^279507-1)/13784139Lelio R Paula02/2014
518011^80792-81084137Enzo Doria11/2012
5181(97*10^84134-1)/384136Serge Batalov12/2014
5182p(17507)#/2+3284125Robert Price12/2016
518321485^8224+8224^2148584116Hans Havermann04/2017
51843^176294-34084114Lelio R Paula12/2015
5185(3^176287+4)/219184107Lelio R Paula12/2012
51862^279388-71984105Yves Minet05/2012
5187(22699*2^279378+1)/22184104Lelio R Paula06/2014
51882^279332-11044784088Enzo Doria05/2014
51892^279320+784084Lelio R Paula06/2012
5190127^39966-284081Lelio R Paula10/2017
5191(11*2^279240-1)/9584059Lelio R Paula02/2014
51922^279218-11134784053Enzo Doria05/2014
519335^54435+284052Lelio R Paula05/2013
5194(31*2^279191-1)/1251152384040Lelio R Paula02/2014
519520996^10059+10059^2099684038Hans Havermann05/2017
519697*10^84033-384035Robert Price01/2017
519721234^9067+9067^2123484033Hans Havermann05/2017
5198(134569^16384+1)/284033Richard Fischer06/2018
51992^279095-10971784016Enzo Doria04/2014
520014^73282-9983991Lelio R Paula11/2015
520121457^8200+8200^2145783979Hans Havermann06/2017
520289*10^83976-783978Robert Price03/2017
52032^278955+17383974Lelio R Paula06/2012
5204(7*2^278851+1)/3983942Lelio R Paula12/2012
5205(9913*2^278844-1)/4080383940Lelio R Paula04/2015
52065^120076-1484683930Enzo Doria02/2013
5207(85*10^83921-1)/383923Robert Price07/2017
5208(2^278770-3)/2383917Lelio R Paula12/2012
5209(10^83916+449)/983916Serge Batalov12/2014
52102^278715+9983902Lelio R Paula06/2012
5211(132109^16384+1)/283902Richard Fischer05/2018
521240235!2-2^4023583899Robert Price09/2015
52132^278698-17183897Lelio R Paula06/2012
5214(19*10^83894-43)/383895Robert Price10/2017
52156^107802+2583887Lelio R Paula12/2015
52168*10^83880+3983881Robert Price01/2017
5217(58*10^83878+23)/983879Robert Price09/2015
52187^99244-9083871Lelio R Paula10/2015
52192^278554+425783854Lelio R Paula08/2013
52202^278504-10961983839Enzo Doria04/2014
52212^278499+187043383837Enzo Doria05/2016
5222105^41475+10483829Norbert Schneider11/2016
522315^71276-6883828Lelio R Paula11/2015
52242^278464-21641383827Enzo Doria04/2013
5225(76*10^83816-211)/983817Robert Price10/2017
5226(8*10^83811-101)/383812Robert Price10/2017
52272^278400+4075583807Lelio R Paula08/2013
5228(9*2^278381-1)/783802Lelio R Paula02/2014
52293*9^87813+6^87813+2*4^8781383796Mike Oakes12/2010
523019551^19268+19268^1955183773Hans Havermann05/2017
523120625^11522+11522^2062583770Hans Havermann05/2017
5232(44*10^83768-791)/983769Robert Price10/2017
5233(87^43189+1)/8883764Paul Bourdelais08/2017
52342^278235-4983758Lelio R Paula06/2012
523523543^3610+3610^2354383755Hans Havermann05/2017
523718^66711-9183741Lelio R Paula11/2015
52364*10^83740-8983741Robert Price08/2017
5238(3*2^278172-1)/1183738Lelio R Paula02/2014
5239(15*29^57251+2561)/2883724Curtis Bright05/2015
52404*7^99059-983716Lelio R Paula10/2014
5241(2^278128-3)/12684472414983714Lelio R Paula12/2012
52422^278077+186721183710Enzo Doria03/2016
52432^278059-2783705Lelio R Paula06/2012
5244214^35917+35917^21483702Norbert Schneider12/2014
5245(23*10^83693+7)/383694Robert Price10/2015
524685^43375-283689Lelio R Paula09/2013
52475*3^175360+483669Lelio R Paula07/2014
5248(23^61441-1)/2283665Robert Price01/2012
524920091^14596+14596^2009183664Hans Havermann03/2017
52502^277907-11062983659Enzo Doria05/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 17 2018 20:37 (Time in France)

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