PRP Records

Probable Primes Top 10000

(202632 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 ?
45016^110522+16386003Lelio R Paula12/2015
450241^53323-40^5332385999Robert Price07/2012
45032^285678-10961785998Enzo Doria04/2014
45046^110506-1667385991Enzo Doria02/2013
45062^285569-74185965Lelio R Paula09/2013
4505(32*10^85964+31)/985965Robert Price05/2015
45076*10^85910-785911Dmitry Domanov11/2010
4508(412*10^85897-7)/985899Robert Price10/2017
45094*10^85881+6385882Robert Price06/2016
4510(10^85864+53)/985864Robert Price01/2015
45112^285230+34585863Lelio R Paula09/2013
4512(5*10^85855-473)/985855Robert Price12/2017
45132^285199+7568385854Enzo Doria04/2016
4514(76*10^85847-211)/985848Robert Price10/2017
4515p(17832)#/2+51285845Robert Price05/2017
4516(16*10^85839+167)/385840Robert Price10/2017
451711^82426-123085838Enzo Doria11/2012
45182^285113-10988185828Enzo Doria04/2014
45195^122746-9285796Lelio R Paula10/2015
45202^285001-11346185794Enzo Doria08/2014
4521(11*10^85782-131)/385783Robert Price02/2017
45222^284913-11049185768Enzo Doria05/2014
45236^110220+4785768Lelio R Paula12/2015
45243*6^110202-585755Lelio R Paula10/2014
4525(157^39047-1)/15685742Alexander Zhirkov06/2016
4526(3^179705+7)/25085739Lelio R Paula12/2012
45272^284734-655585714Lelio R Paula09/2013
4528(10^85712+53)/985712Robert Price01/2015
45293*10^85703+1185704Robert Price11/2017
4530(6883*2^284668-1)/385697Lelio R Paula04/2015
453120^65855+8385680Lelio R Paula01/2016
45326^110105+5385679Lelio R Paula12/2015
4533(10^85666-97)/385666Robert Kinser10/2017
45342^284567-760585664Lelio R Paula09/2013
45359*5^122555-285664Lelio R Paula10/2014
45365^122554-1485662Lelio R Paula10/2015
45379*5^122543+485655Lelio R Paula10/2014
45383^179489-2^(179489-1)85639Robert Price01/2016
45392^284429+17785622Lelio R Paula08/2012
45402*3^179452+585621Lelio R Paula07/2014
4541(19^66919+3^66919)/2285572Robert Price07/2013
454266^47023-6585561Norbert Schneider11/2014
45436^109943+1385553Lelio R Paula12/2015
4544(2^284167-509203)/3456477585536Lelio R Paula01/2013
45452^284133-385533M. Frind & P. Underwood07/2002
45462^284113+31585527Lelio R Paula09/2013
4547(28*10^85500+149)/385501Robert Price10/2017
4548(16*10^85495-19)/385496Robert Price03/2016
45492^284004+17785494Lelio R Paula08/2012
4550(16*10^85473-91)/385474Robert Price06/2016
45513^179120+2285462Robert Price12/2013
45522^283872-279224985454Enzo Doria03/2016
4553(29*10^85438+259)/985439Robert Price04/2017
45542^283817+8287585438Lelio R Paula09/2013
4555(2^283815-5)/20185435Lelio R Paula01/2013
45562^283796-12585432Lelio R Paula08/2012
4557(29*2^283784-1)/1385428Lelio R Paula02/2014
455815^72592-2885375Lelio R Paula11/2015
45592^283604-5869585374Lelio R Paula09/2013
4560(44*10^85370-503)/985371Robert Price10/2017
4561496^31671+31671^49685369Norbert Schneider07/2017
4562(15*2^283583-1)/10305185364Lelio R Paula02/2014
456315^72572+9285352Lelio R Paula11/2015
45642^283473-161585334Lelio R Paula09/2013
45652^283466-1585332Lelio R Paula08/2012
456611^81916-702085307Enzo Doria02/2013
45676^109626-785306Lelio R Paula11/2014
45682^283374-11032785305Enzo Doria05/2014
456933*10^85297+785299Robert Price07/2016
457018^67933+4185275Lelio R Paula11/2015
45712^283271-10934185274Enzo Doria04/2014
4572(25*10^85249-73)/385250Robert Price09/2016
45732*5^121959+385246Lelio R Paula10/2014
457419834^19834+894785235Henri Lifchitz11/2004
45752^283140+191585234Lelio R Paula09/2013
45763*10^85227-9785228Robert Price08/2017
4577(16*10^85221-31)/385222Robert Price03/2016
45782^283083+186938385217Enzo Doria05/2016
4579(24737*2^283051+1)/1785211Lelio R Paula06/2014
4580(2^283032+78557)/385201Lelio R Paula01/2013
45812^283026-10989385200Enzo Doria04/2014
4582(2^283012+78557)/12985193Lelio R Paula01/2013
4583(10^(2*42589+1)+72*10^42589-1)/985179Robert Price09/2017
45842^282860-10972785150Enzo Doria04/2014
45852^282819+186941385138Enzo Doria05/2016
45863^178428+285132Ray Chandler07/2011
4587(22699*2^282742+1)/7385117Lelio R Paula06/2014
4588(16^70687+5^70687)/2185115Robert Price07/2013
4589(3^178352-2)/785095Lelio R Paula12/2012
459011^81699-279085081Enzo Doria12/2012
45912^282612-9585075Lelio R Paula08/2012
459275^45366-285065Lelio R Paula08/2013
45932^282511+6985045Lelio R Paula08/2012
459469^46249+285045Lelio R Paula06/2013
45953^178226+1085036Robert Price10/2013
4596(182*10^85017+43)/985019Robert Price11/2017
4597(14*10^85010+73)/385011Robert Price04/2016
45989*2^282338-784994Lelio R Paula08/2014
4599(9913*2^282330-1)/157800384988Lelio R Paula04/2015
46002^282203+584952Lelio R Paula08/2012
46012^282184+1384946Lelio R Paula08/2012
460211^81568-240084945Enzo Doria12/2012
460311^81562-234084939Enzo Doria12/2012
4604(41*10^84927+31)/984928Robert Price05/2015
4605(2*10^84904-17)/384904Robert Price08/2014
4606(4^141017+23)/384901Robert Price02/2017
46076^109100-1865384897Enzo Doria03/2013
46082^281973+102584883Lelio R Paula09/2013
46092^281951-10965184876Enzo Doria04/2014
461011^81491-543084865Enzo Doria01/2013
4611((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
46122^281825-186148384838Enzo Doria03/2016
46132^281809-9730584833Lelio R Paula09/2013
46142^281780-11489384825Enzo Doria05/2015
46153^177719+6484794Lelio R Paula12/2015
46172^281675-19984793Lelio R Paula08/2012
46162^281673-11122384793Enzo Doria05/2014
4618(4*10^84779+149)/984779Robert Price03/2017
4619(72*10^84772-27)/984773Ray Chandler01/2011
462011^81398-63084768Enzo Doria11/2012
4621(25*2^281577-1)/2384764Lelio R Paula02/2014
46222^281500-45584740Yves Minet03/2012
462310^84725+114514191984726Marisa Kirisame03/2015
462410^84725+14204184726Patrick De Geest10/2015
462510^84725-13867784725Patrick De Geest02/2016
462676^45044+7584720Norbert Schneider02/2015
462754^48897-5384709Norbert Schneider08/2014
4628(9913*2^281377-1)/6584706Lelio R Paula04/2015
4629Phi(171124,10)/29946701/7761329021/5856034404184700Maksym Voznyy11/2015
46302^281337-11122384691Enzo Doria05/2014
46312^281308+5461584683Lelio R Paula09/2013
46327*5^121144-684677Lelio R Paula10/2014
4633(2^281252+47)/384665Lelio R Paula01/2013
463411^81297-315084663Enzo Doria12/2012
46352^281208-30384653Yves Minet02/2012
4636197^36892-284648Lelio R Paula10/2017
4637(21*2^281187+1)/248384644Lelio R Paula01/2013
463811^81247-8484611Lelio R Paula10/2015
463917^68747-6484590Lelio R Paula11/2015
46405^121018-1559684588Enzo Doria02/2013
46416^108702+784587Lelio R Paula11/2014
464210^84582+10067784583Patrick De Geest05/2016
464310^84582-800184582Robert Price03/2016
46443*5^121004-884579Lelio R Paula10/2014
46455^120996-8484573Lelio R Paula10/2015
4646(10223*2^280881+1)/6841984553Lelio R Paula06/2014
46472^280852+9768184545Yves Minet08/2004
46482^280848-120384544Lelio R Paula09/2013
46495^120946-2484538Lelio R Paula10/2015
46502^280810-211184533Yves Minet08/2013
465111^81161-516084521Enzo Doria01/2013
46522^280737-9384511Lelio R Paula08/2012
46532^280698+31584499Lelio R Paula09/2013
46543^177099-34084498Lelio R Paula12/2015
4655(5*10^84469-107)/384470Robert Price01/2017
4656(3^177002+7)/669602227216174484436Lelio R Paula12/2012
4657(2^280500-1017)/82384436Lelio R Paula01/2013
465814^73660-584424Lelio R Paula11/2015
4659(19*10^84409-61)/384410Robert Price04/2017
46602^280388+11784406Lelio R Paula08/2012
46612^280389-56653384406Paul Bourdelais03/2013
4662(141584^16384+1)/6553784390Syoichiro Yamada06/2008
46632^280240-17384361Lelio R Paula08/2012
4664(184*10^84348-1)/384350Robert Price02/2017
46654*10^84346+9384347Robert Price01/2017
46667*2^280156-584337Lelio R Paula08/2014
46678*7^99782-384327Lelio R Paula10/2014
46682^280116+13384324Lelio R Paula08/2012
46692^280118+5461584324Lelio R Paula09/2013
4670(509203*2^280090-1)/384321Lelio R Paula04/2015
46716^108354+4784316Lelio R Paula12/2015
467210^84305+14196384306Patrick De Geest07/2013
467310^84305-5784305Robert Price05/2011
46749^88339+3*8^88339-2*4^88339-3*2^8833984297Mike Oakes01/2011
46753^176648-11280484283Enzo Doria06/2014
46766^108310+11584282Lelio R Paula12/2015
4677(11*2^279968-1)/584280Lelio R Paula02/2014
46786^108288-1664384265Enzo Doria02/2013
46792^279917-5869584264Lelio R Paula08/2013
468065^46477+3684259Lelio R Paula01/2016
46812^279866-190784249Yves Minet05/2013
4682(3^176580-5)/2807684246Lelio R Paula12/2012
4683(p(17530)#+4)/284246Robert Price09/2017
4684(2*10^84239+1)/384239Serge Batalov07/2009
468618^67103-4184233Lelio R Paula11/2015
468520^64743-4384233Lelio R Paula01/2016
4687143^39070+39070^14384209Serge Batalov05/2014
468811^80857-540084204Enzo Doria01/2013
4689(13*10^84179+161)/384180Robert Price04/2017
46902^279634-11040584179Enzo Doria05/2014
4691(74*10^84170+313)/984171Robert Price11/2017
46922^279582-101784163Lelio R Paula08/2013
4693(22*10^84159-19)/384160Robert Price02/2017
4694p(17513)#/2+51284156Robert Price05/2017
4695(19*10^84144-43)/384145Robert Price10/2017
4696(9*2^279507-1)/13784139Lelio R Paula02/2014
469711^80792-81084137Enzo Doria11/2012
4698(97*10^84134-1)/384136Serge Batalov12/2014
4699p(17507)#/2+3284125Robert Price12/2016
470021485^8224+8224^2148584116Hans Havermann04/2017
47013^176294-34084114Lelio R Paula12/2015
4702(3^176287+4)/219184107Lelio R Paula12/2012
47032^279388-71984105Yves Minet05/2012
4704(22699*2^279378+1)/22184104Lelio R Paula06/2014
47052^279332-11044784088Enzo Doria05/2014
47062^279320+784084Lelio R Paula06/2012
4707127^39966-284081Lelio R Paula10/2017
4708(11*2^279240-1)/9584059Lelio R Paula02/2014
47092^279218-11134784053Enzo Doria05/2014
471035^54435+284052Lelio R Paula05/2013
4711(31*2^279191-1)/1251152384040Lelio R Paula02/2014
471220996^10059+10059^2099684038Hans Havermann05/2017
471397*10^84033-384035Robert Price01/2017
471421234^9067+9067^2123484033Hans Havermann05/2017
47152^279095-10971784016Enzo Doria04/2014
471614^73282-9983991Lelio R Paula11/2015
471721457^8200+8200^2145783979Hans Havermann06/2017
471889*10^83976-783978Robert Price03/2017
47192^278955+17383974Lelio R Paula06/2012
4720(7*2^278851+1)/3983942Lelio R Paula12/2012
4721(9913*2^278844-1)/4080383940Lelio R Paula04/2015
47225^120076-1484683930Enzo Doria02/2013
4723(85*10^83921-1)/383923Robert Price07/2017
4724(2^278770-3)/2383917Lelio R Paula12/2012
4725(10^83916+449)/983916Serge Batalov12/2014
47262^278715+9983902Lelio R Paula06/2012
472740235!2-2^4023583899Robert Price09/2015
47282^278698-17183897Lelio R Paula06/2012
4729(19*10^83894-43)/383895Robert Price10/2017
47306^107802+2583887Lelio R Paula12/2015
47318*10^83880+3983881Robert Price01/2017
4732(58*10^83878+23)/983879Robert Price09/2015
47337^99244-9083871Lelio R Paula10/2015
47342^278554+425783854Lelio R Paula08/2013
47352^278504-10961983839Enzo Doria04/2014
47362^278499+187043383837Enzo Doria05/2016
4737105^41475+10483829Norbert Schneider11/2016
473815^71276-6883828Lelio R Paula11/2015
47392^278464-21641383827Enzo Doria04/2013
4740(76*10^83816-211)/983817Robert Price10/2017
4741(8*10^83811-101)/383812Robert Price10/2017
47422^278400+4075583807Lelio R Paula08/2013
4743(9*2^278381-1)/783802Lelio R Paula02/2014
47443*9^87813+6^87813+2*4^8781383796Mike Oakes12/2010
474519551^19268+19268^1955183773Hans Havermann05/2017
474620625^11522+11522^2062583770Hans Havermann05/2017
4747(44*10^83768-791)/983769Robert Price10/2017
4748(87^43189+1)/8883764Paul Bourdelais08/2017
47492^278235-4983758Lelio R Paula06/2012
475023543^3610+3610^2354383755Hans Havermann05/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 20 2018 10:36 (Time in France)

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