PRP Records

Probable Primes Top 10000

(271067 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 ?
925118567^7892+7892^1856772360Hans Havermann11/2019
9252(2^240381+3)/5165572358Lelio R Paula05/2012
92536^92974-5572348Lelio R Paula01/2015
92542^240295+1172337Lelio R Paula02/2012
9255(2^240294+1342)/272336Stefano Morozzi01/2020
9256(14*10^72326-53)/372327Robert Price12/2016
925715^61493-4672322Lelio R Paula01/2015
9258(2^240245+2094)/272321Stefano Morozzi01/2020
9259(2^240237+1554)/272319Stefano Morozzi01/2020
9260lucasU(46,1,43497)-lucasU(46,1,43496)72315Mike Oakes04/2009
9261(2^240211+1514)/272311Stefano Morozzi01/2020
92635*10^72302+972303Dmitry Domanov11/2010
9262(9787*2^240179-1)/26572303Lelio R Paula04/2015
9264(2^240171+3246)/272299Stefano Morozzi01/2020
926511^69419-312072293Enzo Doria12/2012
926618069^10016+10016^1806972289Hans Havermann11/2019
9267(25883^16381-1)/2588272286Serge Batalov08/2020
9268(2^240095+594)/272276Stefano Morozzi01/2020
9269(25848^16381-1)/2584772276Serge Batalov08/2020
92704*10^72274-8372275Robert Price10/2017
9271(2^240075+2790)/272270Stefano Morozzi01/2020
927210^72267+3372268Robert Price01/2011
927310^72267-55394772267Patrick De Geest05/2013
9274(2^240066+1030)/272267Stefano Morozzi01/2020
927611^69389-138072262Enzo Doria12/2012
9277(16^60013-5^60013)/1172262Robert Price07/2013
92757^85507-3072262Lelio R Paula08/2014
9278(19*2^240026-1)/1572256Lelio R Paula02/2014
9279(3^151426-2)/66133772243Lelio R Paula06/2012
9280(2^239940+3850)/272229Stefano Morozzi01/2020
9281gcd(V(1296375),5*F(259275)*(F(259275)-1)+1)72227Serge Batalov04/2015
9282(2789^20959-1)/278872210Serge Batalov08/2020
92832^239863-11226772206Enzo Doria06/2014
92842^239853-11485372203Enzo Doria05/2015
9285(14068^17401-1)/1406772180Serge Batalov08/2020
9286(5669^19231-1)/566872180Serge Batalov08/2020
9287(4*10^72174+149)/972174Robert Price03/2017
9289(2^239671+9)/29613172143Lelio R Paula05/2012
92882^239651-11066572143Enzo Doria05/2014
9290(29*2^239650-1)/330572140Lelio R Paula01/2014
9291(17099^17041-1)/1709872130Serge Batalov08/2020
9293241^30280+30280^24172128Norbert Schneider11/2014
9292(2^239603+950)/272128Stefano Morozzi01/2020
9294(2^239594+3058)/272125Stefano Morozzi01/2020
9295(68*10^72120-23)/972121Robert Price10/2015
9296(9^75571+8^75571)/1772112Robert Price12/2012
9297(15661^17191-1)/1566072109Serge Batalov08/2020
9298(3508^20341-1)/350772107Serge Batalov08/2020
9299(15*2^239530-1)/17372105Lelio R Paula01/2014
9300(2^239523+2378)/272104Stefano Morozzi01/2020
93012^239513-11251972101Enzo Doria06/2014
9302(10^72097+149)/372097Serge Batalov12/2014
93032^239442-655572080Lelio R Paula05/2012
93042*5^103106+372069Lelio R Paula10/2014
93052^239402-19772068Lelio R Paula02/2012
93062^239356-11187572054Enzo Doria05/2014
9307(38*10^72050-119)/972051Robert Price11/2016
93082^239339+1501572049Lelio R Paula01/2013
9309159^32728+272048Lelio R Paula05/2013
931015^61259-3872047Lelio R Paula01/2015
931192^36683-91^3668372038Robert Price08/2015
93122^239280+5461572031Lelio R Paula05/2012
9313(47*2^239267+1)/7772027Lelio R Paula04/2015
9314(85*10^72025-1)/372027Robert Price07/2017
9315(2^239269+1730)/272027Stefano Morozzi01/2020
93162^239236-9730572018Lelio R Paula05/2012
9318144^33361-14372006Norbert Schneider11/2018
9317(2^239198+1422)/272006Stefano Morozzi01/2020
93192^239169+5971998Lelio R Paula02/2012
9320lucasU(2010,1,21796)-lucasU(2010,1,21795)71994Mike Oakes05/2009
9321(15*2^239171-1)/10630171994Lelio R Paula01/2014
9322(2^239121+1926)/271983Stefano Morozzi01/2020
9324(29^49211-1)/2871965Robert Price04/2012
9323(299*10^71963+1)/371965Robert Price11/2017
9325L(344293)71953Renaud Lifchitz09/2003
9326V(344293)71953Serge Batalov03/2015
93276*10^71951+771952Dmitry Domanov11/2010
93283^150798+4071949Lelio R Paula01/2015
93292^238961+9571935Lelio R Paula02/2012
933012511^17556+17556^1251171933Norbert Schneider09/2019
93312^238936-40771927Yves Minet02/2012
9332(2^238930+2982)/271925Stefano Morozzi01/2020
93332^238923-2863571923Lelio R Paula05/2012
9334(8116^18397-1)/811571917Serge Batalov08/2020
933510^71910+2511971911Patrick De Geest05/2016
933610^71910-80171910Robert Price04/2016
9337(2^238862+1230)/271905Stefano Morozzi01/2020
9338(2^238864+3198)/271905Stefano Morozzi01/2020
93392^238845-11265171900Enzo Doria06/2014
93402^238792-11124571884Enzo Doria05/2014
93416*7^85059+571884Lelio R Paula10/2014
934219312^5273+5273^1931271881Hans Havermann11/2019
934319176^5603+5603^1917671880Hans Havermann11/2019
93442^238752-11058971872Enzo Doria05/2014
9345(2^238739+2738)/271868Stefano Morozzi01/2020
934612^66581+771853Lelio R Paula07/2014
9347(7*2^238691+1)/4122971850Lelio R Paula06/2012
93484*3^150568-571840Lelio R Paula04/2014
93496^92301+6771825Lelio R Paula01/2015
93502^238568+9876533171817Jason Earls01/2009
93512^238541-11272371808Enzo Doria06/2014
93522^238529-1594971805Enzo Doria04/2013
93539*5^102721-871800Lelio R Paula10/2014
93542^238494-16571794Lelio R Paula02/2012
935518035^9562+9562^1803571790Hans Havermann10/2019
935618390^7993+7993^1839071771Hans Havermann11/2019
93572^238389-11090571763Enzo Doria05/2014
9358(145*10^71760-1)/971762Serge Batalov12/2014
93597^84913+506271760Mike Oakes02/2010
936021218^2409+2409^2121871756Hans Havermann10/2019
9361(F(11446)^31-F(11445)^31)/F(11444)71753Wayne Halsdorf03/2012
9362(1227^23227-1)/122671742Serge Batalov08/2020
93632^238268-9730571726Lelio R Paula05/2012
9364gcd(V(1330365),5*F(266073)*(F(266073)-1)+1)71724Serge Batalov04/2015
9365(2^238249+3770)/271720Stefano Morozzi01/2020
93662^238235-11324771716Enzo Doria07/2014
93672*12^66450-5^6645071712Mike Oakes11/2010
9368(2^238213+lucasV(1,2,238213)+1)/471709Mike Oakes11/2016
93692^238199-11181771706Enzo Doria05/2014
9370lucasU(46,1,43125)+lucasU(46,1,43124)71696Mike Oakes04/2009
93712^238144+9876533171689Jason Earls01/2009
9372(2^238137+2810)/271687Stefano Morozzi01/2020
937318^57102-426571679Enzo Doria03/2013
9374(73*10^71670-1)/971671Robert Price01/2015
93752^238081+1155*23808171670Henri Lifchitz02/2005
93762^238067-11192571666Enzo Doria05/2014
9377(2^238024+3690)/271653Stefano Morozzi01/2020
9378(7388^18523-1)/738771653Serge Batalov08/2020
937919143^5528+5528^1914371644Hans Havermann10/2019
938065401!4+12871638Robert Price09/2019
938136^46030+3571637Norbert Schneider04/2014
9382(74*10^71621+313)/971622Robert Price11/2017
93832^237905-9171617Lelio R Paula02/2012
9384(31*2^237902-1)/12371616Lelio R Paula01/2014
9385(15185*2^237866-1)/4396771605Lelio R Paula04/2015
938616696^16957+16957^1669671603Norbert Schneider09/2019
9387(24737*2^237841+1)/2571601Lelio R Paula06/2014
93882^237846+129971599Lelio R Paula05/2012
93896^92004+19980171594Mike Oakes02/2011
9390159^32516+271581Lelio R Paula05/2013
93912^237781+85571580Lelio R Paula05/2012
9392(2^237754+814)/271571Stefano Morozzi01/2020
93932^237720-407971561Yves Minet06/2011
93942^237698-11094571555Enzo Doria05/2014
93952^237695-11323971554Enzo Doria07/2014
93968*5^102362-971549Lelio R Paula10/2014
9397(4*10^71546-31)/971546Erik Branger05/2011
93982^237650+3771540Lelio R Paula02/2012
939918^56977-439171522Enzo Doria03/2013
9401(22699*2^237565+1)/413663771512Lelio R Paula06/2014
9400((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
9402(26*10^71503+7)/371504Erik Branger11/2013
9403(4*10^71498+173)/371499Robert Price01/2017
94043^149848+11071496Lelio R Paula11/2014
94052^237498+51371495Lelio R Paula05/2012
94062^237485+10771491Lelio R Paula02/2012
9407(2^237465+9)/241971481Lelio R Paula05/2012
94082^237439-11223771477Enzo Doria06/2014
9409(2^237427+2510)/271473Stefano Morozzi01/2020
94102^237407-978771467Lelio R Paula11/2009
94112^237383+7295371460Enzo Doria04/2016
941219768^4119+4119^1976871458Hans Havermann11/2019
941382^37337-81^3733771457Robert Price01/2015
9414(1017*2^237313-1)/1971441Lelio R Paula04/2015
94152^237311+19171438Lelio R Paula02/2012
941611699^17560+17560^1169971437Norbert Schneider09/2019
9417(25188^16231-1)/2518771432Serge Batalov08/2020
94182^237280-5971429Lelio R Paula02/2012
9419(2^237275+1038)/271427Stefano Morozzi01/2020
9420(2^237265+2774)/271424Stefano Morozzi01/2020
942111^68564-9871403Lelio R Paula01/2015
94222^237173+7480171397Enzo Doria04/2016
9423(2^237150+1458)/271389Stefano Morozzi01/2020
942415^60697+5671386Lelio R Paula01/2015
94252^237118+17771380Lelio R Paula02/2012
94262^237110+6971378Lelio R Paula02/2012
942715^60690-5871377Lelio R Paula01/2015
9428(5*2^237125-1)/59985119171374Lelio R Paula01/2014
942920311^3262+3262^2031171363Hans Havermann11/2019
9430(3^149567+2)/53971359Lelio R Paula06/2012
9431(5*10^71357-143)/371358Robert Price04/2016
94322^237039-11462171356Enzo Doria05/2015
9433(2^237037+3462)/271355Stefano Morozzi01/2020
943412^66116-3771352Lelio R Paula02/2015
9435(3^149497+2^149497)/571328Jean-Louis Charton10/2010
94362^236941-6694571327Lelio R Paula05/2012
94372^236911-114771318Yves Minet10/2009
943865^39337+4271315Lelio R Paula01/2016
9439(13319^17291-1)/1331871313Serge Batalov08/2020
9440(2^236863+3234)/271303Stefano Morozzi01/2020
94416*10^71299+771300Dmitry Domanov11/2010
9442(25*2^236843+1)/375371295Lelio R Paula06/2012
944310^71291+1518771292Patrick De Geest03/2016
944510^71291-558730911971291Robert Price03/2015
944410^71291-27358171291Patrick De Geest03/2016
9446-numer(bernoulli(22808)/22808)71290T. D. Noe09/2005
9447(2^236781+1514)/271278Stefano Morozzi01/2020
9448(2^236775+2886)/271277Stefano Morozzi01/2020
944915105^17054+17054^1510571271Norbert Schneider08/2018
9450(2^236738+9)/1371265Lelio R Paula05/2012
94515^101949+4271260Lelio R Paula07/2014
9452(9811^17851-1)/981071253Serge Batalov08/2020
94537*10^71238-3971239Robert Price07/2020
94545*10^71237+971238Dmitry Domanov11/2010
94552^236634-1602571234Enzo Doria04/2013
945671^38478+7071233Norbert Schneider12/2014
94579*7^84280+871226Lelio R Paula10/2014
9458(2^236603+2378)/271225Stefano Morozzi01/2020
9459(10^71223+59)/371223Serge Batalov12/2014
946023260^1153+1153^2326071219Hans Havermann10/2019
9461(15185*2^236569-1)/45371216Lelio R Paula04/2015
946251829#+(216091#)/(51829#)71208Makoto Morimoto03/2016
94632^236528-17371203Lelio R Paula02/2012
94643*2^236511-571198Lelio R Paula04/2014
94652^236477-9971187Lelio R Paula02/2012
946611^68356-213071186Enzo Doria12/2012
946715128^17031+17031^1512871186Norbert Schneider08/2018
946811^68355-312071185Enzo Doria12/2012
9469(2^236463+998)/271183Stefano Morozzi01/2020
947036^45737-35^4573771181Robert Price10/2012
9471(3^149183-lucasV(1,3,149183)+1)/371178Paul Vanderveen12/2017
94722^236432+2571174Lelio R Paula02/2012
94735^101818-1280671168Enzo Doria02/2013
9474(7*10^71166-457)/971166Robert Price09/2017
947565^39253+6271163Lelio R Paula01/2016
947639^44718+3871150Norbert Schneider05/2014
947718996^5557+5557^1899671137Hans Havermann10/2019
947864983!4-25671135Robert Price11/2019
94792^236296-40771133Yves Minet02/2012
94802^236286-11771130Lelio R Paula02/2012
9481(2^236283+1074)/271128Stefano Morozzi01/2020
94822^236257-11119371121Enzo Doria05/2014
94837^84149-3671115Lelio R Paula08/2014
9484164176#-p(164176)71108Henri Lifchitz12/2018
9485(2^236214+2934)/271108Stefano Morozzi01/2020
94862^236209-11212371106Enzo Doria06/2014
948718^56644-498571104Enzo Doria03/2013
9488(46*10^71077+521)/971078Robert Price08/2017
948921^53753+271074Ray Chandler08/2011
9490(5482^19009-1)/548171070Serge Batalov08/2020
9491(86*10^71068-311)/971069Robert Price10/2017
94922^236081-11092371068Enzo Doria05/2014
9493(293*27^49642-1736)/1371058Curtis Bright05/2015
949465^39192+2271052Lelio R Paula01/2016
9495(2^236016+1246)/271048Stefano Morozzi01/2020
9496(439#+1)^397-439#^39771038Mike Oakes11/2010
94977^84050-271031Lelio R Paula09/2013
949815813^16916+16916^1581371031Norbert Schneider09/2019
9499(2^235956+3978)/271030Stefano Morozzi01/2020
9500(3568^19993-1)/356771021Serge Batalov08/2020


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 30 2020 10:03 (Time in France)

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