PRP Records

Probable Primes Top 10000

(172213 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 ?
5501(25*2^241048+1)/8972563Lelio R Paula08/2012
5502(22*10^72560+17)/372561Robert Price09/2015
55032^241032-2372558Lelio R Paula02/2012
550434485*10^72550+2^241004-372555Gilbert Mozzo12/2012
55052^241004-372550M. Frind & P. Underwood07/2002
550697*10^72522-372524Robert Price01/2017
5507(68*10^72516+7)/372518Robert Price03/2016
5508(78557*2^240844+1)/6372505Lelio R Paula06/2014
550967^39701-6672497Norbert Schneider11/2014
5510(185*10^72484+7)/372486Robert Price02/2017
5512(293*27^50631-1736)/1372473Curtis Bright05/2015
5511103^36005-10272473Norbert Schneider10/2016
551315^61616+8872467Lelio R Paula01/2015
551445^43831+272462Lelio R Paula05/2013
55152^240692-49238972456Paul Bourdelais03/2013
5516(646*10^72446-7)/972448Robert Price07/2016
55179*6^93083+772434Lelio R Paula10/2014
55182^240617-364572433Lelio R Paula05/2013
551911^69531-2400072410Enzo Doria12/2012
5520(22699*2^240396+1)/5572370Lelio R Paula06/2014
55216^92995+1372365Lelio R Paula01/2015
5522(11*10^72362-149)/372363Robert Price01/2017
5523(2^240381+3)/5165572358Lelio R Paula05/2012
55246^92974-5572348Lelio R Paula01/2015
55252^240295+1172337Lelio R Paula02/2012
5526(14*10^72326-53)/372327Robert Price12/2016
552715^61493-4672322Lelio R Paula01/2015
5528lucasU(46,1,43497)-lucasU(46,1,43496)72315Mike Oakes04/2009
55295*10^72302+972303Dmitry Domanov11/2010
5530(9787*2^240179-1)/26572303Lelio R Paula04/2015
553111^69419-312072293Enzo Doria12/2012
553210^72267+3372268Robert Price01/2011
553310^72267-55394772267Patrick De Geest05/2013
553411^69389-138072262Enzo Doria12/2012
5535(16^60013-5^60013)/1172262Robert Price07/2013
55367^85507-3072262Lelio R Paula08/2014
5537(19*2^240026-1)/1572256Lelio R Paula02/2014
5538(3^151426-2)/66133772243Lelio R Paula06/2012
5539gcd(V(1296375),5*F(259275)*(F(259275)-1)+1)72227Serge Batalov04/2015
55402^239863-11226772206Enzo Doria06/2014
55412^239853-11485372203Enzo Doria05/2015
5543(2^239671+9)/29613172143Lelio R Paula05/2012
55422^239651-11066572143Enzo Doria05/2014
5544(29*2^239650-1)/330572140Lelio R Paula01/2014
5545241^30280+30280^24172128Norbert Schneider11/2014
5546(68*10^72120-23)/972121Robert Price10/2015
5547(9^75571+8^75571)/1772112Robert Price12/2012
5548(15*2^239530-1)/17372105Lelio R Paula01/2014
55492^239513-11251972101Enzo Doria06/2014
5550(10^72097+149)/372097Serge Batalov12/2014
55512^239442-655572080Lelio R Paula05/2012
55522*5^103106+372069Lelio R Paula10/2014
55532^239402-19772068Lelio R Paula02/2012
55542^239356-11187572054Enzo Doria05/2014
5555(38*10^72050-119)/972051Robert Price11/2016
55562^239339+1501572049Lelio R Paula01/2013
5557159^32728+272048Lelio R Paula05/2013
555815^61259-3872047Lelio R Paula01/2015
555992^36683-91^3668372038Robert Price08/2015
55602^239280+5461572031Lelio R Paula05/2012
5561(47*2^239267+1)/7772027Lelio R Paula04/2015
55622^239236-9730572018Lelio R Paula05/2012
55632^239169+5971998Lelio R Paula02/2012
5565lucasU(2010,1,21796)-lucasU(2010,1,21795)71994Mike Oakes05/2009
5564(15*2^239171-1)/10630171994Lelio R Paula01/2014
5566(29^49211-1)/2871965Robert Price04/2012
5568L(344293)71953Renaud Lifchitz09/2003
5567V(344293)71953Serge Batalov03/2015
55696*10^71951+771952Dmitry Domanov11/2010
55703^150798+4071949Lelio R Paula01/2015
55712^238961+9571935Lelio R Paula02/2012
55722^238936-40771927Yves Minet02/2012
55732^238923-2863571923Lelio R Paula05/2012
557410^71910+2511971911Patrick De Geest05/2016
557510^71910-80171910Robert Price04/2016
55762^238845-11265171900Enzo Doria06/2014
55772^238792-11124571884Enzo Doria05/2014
55786*7^85059+571884Lelio R Paula10/2014
55792^238752-11058971872Enzo Doria05/2014
558012^66581+771853Lelio R Paula07/2014
5581(7*2^238691+1)/4122971850Lelio R Paula06/2012
55824*3^150568-571840Lelio R Paula04/2014
55836^92301+6771825Lelio R Paula01/2015
55842^238568+9876533171817Jason Earls01/2009
55852^238541-11272371808Enzo Doria06/2014
55862^238529-1594971805Enzo Doria04/2013
55879*5^102721-871800Lelio R Paula10/2014
55882^238494-16571794Lelio R Paula02/2012
55892^238389-11090571763Enzo Doria05/2014
5590(145*10^71760-1)/971762Serge Batalov12/2014
55917^84913+506271760Mike Oakes02/2010
5592(F(11446)^31-F(11445)^31)/F(11444)71753Wayne Halsdorf03/2012
55932^238268-9730571726Lelio R Paula05/2012
5594gcd(V(1330365),5*F(266073)*(F(266073)-1)+1)71724Serge Batalov04/2015
55952^238235-11324771716Enzo Doria07/2014
55962*12^66450-5^6645071712Mike Oakes11/2010
5597(2^238213+lucasV(1,2,238213)+1)/471709Mike Oakes11/2016
55982^238199-11181771706Enzo Doria05/2014
5599lucasU(46,1,43125)+lucasU(46,1,43124)71696Mike Oakes04/2009
56002^238144+9876533171689Jason Earls01/2009
560118^57102-426571679Enzo Doria03/2013
5602(73*10^71670-1)/971671Robert Price01/2015
56032^238081+1155*23808171670Henri Lifchitz02/2005
56042^238067-11192571666Enzo Doria05/2014
560536^46030+3571637Norbert Schneider04/2014
56062^237905-9171617Lelio R Paula02/2012
5607(31*2^237902-1)/12371616Lelio R Paula01/2014
5608(15185*2^237866-1)/4396771605Lelio R Paula04/2015
5609(24737*2^237841+1)/2571601Lelio R Paula06/2014
56102^237846+129971599Lelio R Paula05/2012
56116^92004+19980171594Mike Oakes02/2011
5612159^32516+271581Lelio R Paula05/2013
56132^237781+85571580Lelio R Paula05/2012
56142^237720-407971561Yves Minet06/2011
56152^237698-11094571555Enzo Doria05/2014
56162^237695-11323971554Enzo Doria07/2014
56178*5^102362-971549Lelio R Paula10/2014
5618(4*10^71546-31)/971546Erik Branger05/2011
56192^237650+3771540Lelio R Paula02/2012
562018^56977-439171522Enzo Doria03/2013
5622(22699*2^237565+1)/413663771512Lelio R Paula06/2014
5621((1+sqrt(7)+sqrt(6))^48479-1)*((1+sqrt(7)-sqrt(6))^48479-1)*((1-sqrt(7)+sqrt(6))^48479-1)*((1-sqrt(771512Mike Oakes05/2009
5623(26*10^71503+7)/371504Erik Branger11/2013
5624(4*10^71498+173)/371499Robert Price01/2017
56253^149848+11071496Lelio R Paula11/2014
56262^237498+51371495Lelio R Paula05/2012
56272^237485+10771491Lelio R Paula02/2012
5628(2^237465+9)/241971481Lelio R Paula05/2012
56292^237439-11223771477Enzo Doria06/2014
56302^237407-978771467Lelio R Paula11/2009
56312^237383+7295371460Enzo Doria04/2016
563282^37337-81^3733771457Robert Price01/2015
5633(1017*2^237313-1)/1971441Lelio R Paula04/2015
56342^237311+19171438Lelio R Paula02/2012
56352^237280-5971429Lelio R Paula02/2012
563611^68564-9871403Lelio R Paula01/2015
56372^237173+7480171397Enzo Doria04/2016
563815^60697+5671386Lelio R Paula01/2015
56392^237118+17771380Lelio R Paula02/2012
56402^237110+6971378Lelio R Paula02/2012
564115^60690-5871377Lelio R Paula01/2015
5642(5*2^237125-1)/59985119171374Lelio R Paula01/2014
5643(3^149567+2)/53971359Lelio R Paula06/2012
5644(5*10^71357-143)/371358Robert Price04/2016
56452^237039-11462171356Enzo Doria05/2015
564612^66116-3771352Lelio R Paula02/2015
5647(3^149497+2^149497)/571328Jean-Louis Charton10/2010
56482^236941-6694571327Lelio R Paula05/2012
56492^236911-114771318Yves Minet10/2009
565065^39337+4271315Lelio R Paula01/2016
56516*10^71299+771300Dmitry Domanov11/2010
5652(25*2^236843+1)/375371295Lelio R Paula06/2012
565310^71291+1518771292Patrick De Geest03/2016
565510^71291-558730911971291Robert Price03/2015
565410^71291-27358171291Patrick De Geest03/2016
5656-numer(bernoulli(22808)/22808)71290T. D. Noe09/2005
5657(2^236738+9)/1371265Lelio R Paula05/2012
56585^101949+4271260Lelio R Paula07/2014
56595*10^71237+971238Dmitry Domanov11/2010
56602^236634-1602571234Enzo Doria04/2013
566171^38478+7071233Norbert Schneider12/2014
56629*7^84280+871226Lelio R Paula10/2014
5663(10^71223+59)/371223Serge Batalov12/2014
5664(15185*2^236569-1)/45371216Lelio R Paula04/2015
566551829#+(216091#)/(51829#)71208Makoto Morimoto03/2016
56662^236528-17371203Lelio R Paula02/2012
56673*2^236511-571198Lelio R Paula04/2014
56682^236477-9971187Lelio R Paula02/2012
566911^68356-213071186Enzo Doria12/2012
567011^68355-312071185Enzo Doria12/2012
567136^45737-35^4573771181Robert Price10/2012
56722^236432+2571174Lelio R Paula02/2012
56735^101818-1280671168Enzo Doria02/2013
567465^39253+6271163Lelio R Paula01/2016
567539^44718+3871150Norbert Schneider05/2014
56762^236296-40771133Yves Minet02/2012
56772^236286-11771130Lelio R Paula02/2012
56782^236257-11119371121Enzo Doria05/2014
56797^84149-3671115Lelio R Paula08/2014
56802^236209-11212371106Enzo Doria06/2014
568118^56644-498571104Enzo Doria03/2013
568221^53753+271074Ray Chandler08/2011
56832^236081-11092371068Enzo Doria05/2014
5684(293*27^49642-1736)/1371058Curtis Bright05/2015
568565^39192+2271052Lelio R Paula01/2016
5686(439#+1)^397-439#^39771038Mike Oakes11/2010
56877^84050-271031Lelio R Paula09/2013
568820^54558-2370982Lelio R Paula01/2015
56892^235793-11255570981Enzo Doria06/2014
569049936!3-3^4993670981Robert Price08/2015
56912^235787-7879570979Lelio R Paula05/2012
5692Perrin(581132)70970Eric W. Weisstein02/2011
569314^61913-9770961Lelio R Paula01/2015
56942^235720+1632170959Yves Minet03/2010
56952^235718+1609570959Lelio R Paula05/2012
5696163841#+34993370957Nicolas PALAU11/2016
56972^235710+770956Lelio R Paula02/2012
56982^235635-11208770934Enzo Doria06/2014
57002^235575-196570916Lelio R Paula05/2012
56996^91133+10170916Lelio R Paula01/2015
5701(21181*2^235505+1)/370898Lelio R Paula06/2014
57025^101425+8470894Lelio R Paula07/2014
5703177^31536+270893Lelio R Paula05/2013
570443*71^38292+470891Serge Batalov03/2016
5705(29*2^235506-1)/11202978570888Lelio R Paula01/2014
570611^68045-153070862Enzo Doria12/2012
57075*10^70858+2170859Robert Price01/2017
57092^235326+370841Donovan Johnson02/2006
570834523!2+470841Robert Price02/2015
5710(31*2^235307+1)/370836Lelio R Paula06/2012
57112^235308+13570835Lelio R Paula02/2012
5712r(35414,90)*1000+91170831Patrick De Geest07/2004
57132^235274+15970825Lelio R Paula02/2012
57143^148409+7070810Lelio R Paula11/2014
5715(19*10^70794+17)/970795Robert Price03/2015
57162^235108-23270970775Paul Bourdelais03/2013
5717(2^235099-2^117550+1)/57077211/2006
571819^55325-670748Lelio R Paula08/2014
5719257^29356+29356^25770746Norbert Schneider10/2014
57202^234956+1171570729Lelio R Paula05/2012
5721(7*10^70727-43)/970727Robert Price10/2014
57222^234890-3034170709Enzo Doria11/2012
572317^57461+1470703Lelio R Paula01/2015
5724(9179*2^234834-1)/570696Lelio R Paula04/2015
5725123^33822-12270685Norbert Schneider01/2015
5726(21*2^234772-1)/209570672Lelio R Paula01/2014
5727(29*2^234686-1)/2114570645Lelio R Paula01/2014
5728(15*2^234688-1)/527814170643Lelio R Paula01/2014
57302^234655-6770639Lelio R Paula02/2012
5729(79*10^70638-61)/970639Robert Price10/2015
57312^234652-17370638Lelio R Paula02/2012
57322^234618-364570628Lelio R Paula05/2012
5733(2^234610-5)/1970624Lelio R Paula05/2012
57344*5^101038+970624Lelio R Paula10/2014
57352^234603+7196370623Enzo Doria04/2016
57362^234600-11312970622Enzo Doria07/2014
57382^234586+970618Lelio R Paula02/2012
57373^148008+2670618Robert Price11/2013
573965^38947+3270608Lelio R Paula01/2016
5740(2^234488-3)/1170587Lelio R Paula05/2012
5741(3*2^234451+1)/3570576Lelio R Paula08/2012
5742Phi(159495,10)70560Maksym Voznyy09/2015
57432^234383-403570557Lelio R Paula05/2012
57442^234315-11124170536Enzo Doria05/2014
574514^61526+9770517Lelio R Paula01/2015
5746(3*2^234170+1)/1370492Lelio R Paula08/2012
574751^41281-50^4128170491Robert Price02/2013
57482^234141-11212370484Enzo Doria06/2014
57492^234139+1228570483Lelio R Paula04/2012
57502^234133-316370482Yves Minet04/2009


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 26 2017 17:51 (Time in France)

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