PRP Records

Probable Primes Top 10000

(277034 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 ?
97512^238541-11272371808Enzo Doria06/2014
97522^238529-1594971805Enzo Doria04/2013
97539*5^102721-871800Lelio R Paula10/2014
97542^238494-16571794Lelio R Paula02/2012
975518035^9562+9562^1803571790Hans Havermann10/2019
975618390^7993+7993^1839071771Hans Havermann11/2019
97572^238389-11090571763Enzo Doria05/2014
9758(145*10^71760-1)/971762Serge Batalov12/2014
97597^84913+506271760Mike Oakes02/2010
976021218^2409+2409^2121871756Hans Havermann10/2019
9761(F(11446)^31-F(11445)^31)/F(11444)71753Wayne Halsdorf03/2012
9762(1227^23227-1)/122671742Serge Batalov08/2020
97632^238268-9730571726Lelio R Paula05/2012
9764gcd(V(1330365),5*F(266073)*(F(266073)-1)+1)71724Serge Batalov04/2015
9765(2^238249+3770)/271720Stefano Morozzi01/2020
97662^238235-11324771716Enzo Doria07/2014
97672*12^66450-5^6645071712Mike Oakes11/2010
9768(2^238213+lucasV(1,2,238213)+1)/471709Mike Oakes11/2016
97692^238199-11181771706Enzo Doria05/2014
9770lucasU(46,1,43125)+lucasU(46,1,43124)71696Mike Oakes04/2009
97712^238144+9876533171689Jason Earls01/2009
9772(2^238137+2810)/271687Stefano Morozzi01/2020
977318^57102-426571679Enzo Doria03/2013
9774(73*10^71670-1)/971671Robert Price01/2015
97752^238081+1155*23808171670Henri Lifchitz02/2005
97762^238067-11192571666Enzo Doria05/2014
9777(2^238024+3690)/271653Stefano Morozzi01/2020
9778(7388^18523-1)/738771653Serge Batalov08/2020
977919143^5528+5528^1914371644Hans Havermann10/2019
978065401!4+12871638Robert Price09/2019
978136^46030+3571637Norbert Schneider04/2014
9782(74*10^71621+313)/971622Robert Price11/2017
97832^237905-9171617Lelio R Paula02/2012
9784(31*2^237902-1)/12371616Lelio R Paula01/2014
9785(15185*2^237866-1)/4396771605Lelio R Paula04/2015
978616696^16957+16957^1669671603Norbert Schneider09/2019
9787(24737*2^237841+1)/2571601Lelio R Paula06/2014
97882^237846+129971599Lelio R Paula05/2012
97896^92004+19980171594Mike Oakes02/2011
9790159^32516+271581Lelio R Paula05/2013
97912^237781+85571580Lelio R Paula05/2012
9792(2^237754+814)/271571Stefano Morozzi01/2020
97932^237720-407971561Yves Minet06/2011
97942^237698-11094571555Enzo Doria05/2014
97952^237695-11323971554Enzo Doria07/2014
97968*5^102362-971549Lelio R Paula10/2014
9797(4*10^71546-31)/971546Erik Branger05/2011
97982^237650+3771540Lelio R Paula02/2012
979918^56977-439171522Enzo Doria03/2013
9801(22699*2^237565+1)/413663771512Lelio R Paula06/2014
9800((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
9802(26*10^71503+7)/371504Erik Branger11/2013
9803(4*10^71498+173)/371499Robert Price01/2017
98043^149848+11071496Lelio R Paula11/2014
98052^237498+51371495Lelio R Paula05/2012
98062^237485+10771491Lelio R Paula02/2012
9807(2^237465+9)/241971481Lelio R Paula05/2012
98082^237439-11223771477Enzo Doria06/2014
9809(2^237427+2510)/271473Stefano Morozzi01/2020
98102^237407-978771467Lelio R Paula11/2009
98112^237383+7295371460Enzo Doria04/2016
981219768^4119+4119^1976871458Hans Havermann11/2019
981382^37337-81^3733771457Robert Price01/2015
9814(1017*2^237313-1)/1971441Lelio R Paula04/2015
98152^237311+19171438Lelio R Paula02/2012
981611699^17560+17560^1169971437Norbert Schneider09/2019
9817(25188^16231-1)/2518771432Serge Batalov08/2020
98182^237280-5971429Lelio R Paula02/2012
9819(2^237275+1038)/271427Stefano Morozzi01/2020
9820(2^237265+2774)/271424Stefano Morozzi01/2020
982111^68564-9871403Lelio R Paula01/2015
98222^237173+7480171397Enzo Doria04/2016
9823(2^237150+1458)/271389Stefano Morozzi01/2020
982415^60697+5671386Lelio R Paula01/2015
98252^237118+17771380Lelio R Paula02/2012
98262^237110+6971378Lelio R Paula02/2012
982715^60690-5871377Lelio R Paula01/2015
9828(5*2^237125-1)/59985119171374Lelio R Paula01/2014
982920311^3262+3262^2031171363Hans Havermann11/2019
9830(3^149567+2)/53971359Lelio R Paula06/2012
9831(5*10^71357-143)/371358Robert Price04/2016
98322^237039-11462171356Enzo Doria05/2015
9833(2^237037+3462)/271355Stefano Morozzi01/2020
983412^66116-3771352Lelio R Paula02/2015
9835(3^149497+2^149497)/571328Jean-Louis Charton10/2010
98362^236941-6694571327Lelio R Paula05/2012
98372^236911-114771318Yves Minet10/2009
983865^39337+4271315Lelio R Paula01/2016
9839(13319^17291-1)/1331871313Serge Batalov08/2020
9840(2^236863+3234)/271303Stefano Morozzi01/2020
98416*10^71299+771300Dmitry Domanov11/2010
9842(25*2^236843+1)/375371295Lelio R Paula06/2012
984310^71291+1518771292Patrick De Geest03/2016
984510^71291-558730911971291Robert Price03/2015
984410^71291-27358171291Patrick De Geest03/2016
9846-numer(bernoulli(22808)/22808)71290T. D. Noe09/2005
9847(2^236781+1514)/271278Stefano Morozzi01/2020
9848(2^236775+2886)/271277Stefano Morozzi01/2020
984915105^17054+17054^1510571271Norbert Schneider08/2018
9850(2^236738+9)/1371265Lelio R Paula05/2012
98515^101949+4271260Lelio R Paula07/2014
9852(9811^17851-1)/981071253Serge Batalov08/2020
98537*10^71238-3971239Robert Price07/2020
98545*10^71237+971238Dmitry Domanov11/2010
98552^236634-1602571234Enzo Doria04/2013
985671^38478+7071233Norbert Schneider12/2014
98579*7^84280+871226Lelio R Paula10/2014
9858(2^236603+2378)/271225Stefano Morozzi01/2020
9859(10^71223+59)/371223Serge Batalov12/2014
986023260^1153+1153^2326071219Hans Havermann10/2019
9861(15185*2^236569-1)/45371216Lelio R Paula04/2015
986251829#+(216091#)/(51829#)71208Makoto Morimoto03/2016
98632^236528-17371203Lelio R Paula02/2012
98643*2^236511-571198Lelio R Paula04/2014
98652^236477-9971187Lelio R Paula02/2012
986611^68356-213071186Enzo Doria12/2012
986715128^17031+17031^1512871186Norbert Schneider08/2018
986811^68355-312071185Enzo Doria12/2012
9869(2^236463+998)/271183Stefano Morozzi01/2020
987036^45737-35^4573771181Robert Price10/2012
9871(3^149183-lucasV(1,3,149183)+1)/371178Paul Vanderveen12/2017
98722^236432+2571174Lelio R Paula02/2012
98735^101818-1280671168Enzo Doria02/2013
9874(7*10^71166-457)/971166Robert Price09/2017
987565^39253+6271163Lelio R Paula01/2016
987639^44718+3871150Norbert Schneider05/2014
987718996^5557+5557^1899671137Hans Havermann10/2019
987864983!4-25671135Robert Price11/2019
98792^236296-40771133Yves Minet02/2012
98802^236286-11771130Lelio R Paula02/2012
9881(2^236283+1074)/271128Stefano Morozzi01/2020
98822^236257-11119371121Enzo Doria05/2014
98837^84149-3671115Lelio R Paula08/2014
9885164176#-p(164176)71108Henri Lifchitz12/2018
9884(2^236214+2934)/271108Stefano Morozzi01/2020
98862^236209-11212371106Enzo Doria06/2014
988718^56644-498571104Enzo Doria03/2013
9888(46*10^71077+521)/971078Robert Price08/2017
988921^53753+271074Ray Chandler08/2011
9890(5482^19009-1)/548171070Serge Batalov08/2020
9891(86*10^71068-311)/971069Robert Price10/2017
98922^236081-11092371068Enzo Doria05/2014
9893(293*27^49642-1736)/1371058Curtis Bright05/2015
989465^39192+2271052Lelio R Paula01/2016
9895(2^236016+1246)/271048Stefano Morozzi01/2020
9896(439#+1)^397-439#^39771038Mike Oakes11/2010
98977^84050-271031Lelio R Paula09/2013
989815813^16916+16916^1581371031Norbert Schneider09/2019
9899(2^235956+3978)/271030Stefano Morozzi01/2020
9900(3568^19993-1)/356771021Serge Batalov08/2020
990164877!4+12871007Robert Price09/2019
990218562^6681+6681^1856270997Hans Havermann10/2019
9903(2^235802+474)/270984Stefano Morozzi01/2020
990420^54558-2370982Lelio R Paula01/2015
99052^235793-11255570981Enzo Doria06/2014
990649936!3-3^4993670981Robert Price08/2015
99072^235787-7879570979Lelio R Paula05/2012
9908(2^235761+2930)/270971Stefano Morozzi01/2020
9909Perrin(581132)70970Eric W. Weisstein02/2011
9910(2^235748+3478)/270967Stefano Morozzi01/2020
991114^61913-9770961Lelio R Paula01/2015
99132^235720+1632170959Yves Minet03/2010
99122^235718+1609570959Lelio R Paula05/2012
9914163841#+34993370957Nicolas PALAU11/2016
99152^235710+770956Lelio R Paula02/2012
9916(175^31627+1)/17670939Eric Chen10/2017
9917(2^235644+670)/270936Stefano Morozzi01/2020
99182^235635-11208770934Enzo Doria06/2014
9919153^32467+15270931Norbert Schneider11/2018
99212^235575-196570916Lelio R Paula05/2012
99206^91133+10170916Lelio R Paula01/2015
9922(24755^16141-1)/2475470914Serge Batalov08/2020
9923(1102^23311-1)/110170914Serge Batalov08/2020
9924(21181*2^235505+1)/370898Lelio R Paula06/2014
9925(14*10^70896+211)/970897Robert Price11/2017
99265^101425+8470894Lelio R Paula07/2014
9927177^31536+270893Lelio R Paula05/2013
992843*71^38292+470891Serge Batalov03/2016
9929(29*2^235506-1)/11202978570888Lelio R Paula01/2014
993011^68045-153070862Enzo Doria12/2012
9931(6969^18439-1)/696870861Serge Batalov08/2020
99325*10^70858+2170859Robert Price01/2017
99342^235326+370841Donovan Johnson02/2006
993334523!2+470841Robert Price02/2015
9935(31*2^235307+1)/370836Lelio R Paula06/2012
9936(2^235310+1038)/270836Stefano Morozzi01/2020
99372^235308+13570835Lelio R Paula02/2012
9938r(35414,90)*1000+91170831Patrick De Geest07/2004
99392^235274+15970825Lelio R Paula02/2012
99403^148409+7070810Lelio R Paula11/2014
9941(19*10^70794+17)/970795Robert Price03/2015
9942(2^235144+1350)/270786Stefano Morozzi01/2020
99432^235108-23270970775Paul Bourdelais03/2013
994422995^1196+1196^2299570773Hans Havermann11/2019
9945(2^235099-2^117550+1)/57077211/2006
994619^55325-670748Lelio R Paula08/2014
9947257^29356+29356^25770746Norbert Schneider10/2014
994822*10^70729+370731Robert Price10/2017
99492^234956+1171570729Lelio R Paula05/2012
9950(7*10^70727-43)/970727Robert Price10/2014
9951(2^234897+3906)/270711Stefano Morozzi01/2020
99522^234890-3034170709Enzo Doria11/2012
995317^57461+1470703Lelio R Paula01/2015
995418281^7366+7366^1828170697Hans Havermann09/2019
9955(9179*2^234834-1)/570696Lelio R Paula04/2015
99562*10^70688+5170689Robert Price10/2017
9957123^33822-12270685Norbert Schneider01/2015
99587*10^70680-9970681Robert Price11/2017
9959(2^234784+3646)/270677Stefano Morozzi01/2020
9960(21*2^234772-1)/209570672Lelio R Paula01/2014
9961(2^234762+1498)/270671Stefano Morozzi01/2020
9962(24355^16111-1)/2435470668Serge Batalov08/2020
9963(2^234723+3690)/270659Stefano Morozzi01/2020
9964(2^234718+3798)/270657Stefano Morozzi01/2020
9965(2^234680+2902)/270646Stefano Morozzi01/2020
9966(29*2^234686-1)/2114570645Lelio R Paula01/2014
9967(15*2^234688-1)/527814170643Lelio R Paula01/2014
99692^234655-6770639Lelio R Paula02/2012
9968(79*10^70638-61)/970639Robert Price10/2015
99702^234652-17370638Lelio R Paula02/2012
99712^234618-364570628Lelio R Paula05/2012
9972(2^234610-5)/1970624Lelio R Paula05/2012
99734*5^101038+970624Lelio R Paula10/2014
99742^234603+7196370623Enzo Doria04/2016
99752^234600-11312970622Enzo Doria07/2014
9976(2^234601+1446)/270622Stefano Morozzi01/2020
99772^234586+970618Lelio R Paula02/2012
99783^148008+2670618Robert Price11/2013
9979(7*10^70616-151)/970616Robert Price09/2017
998065^38947+3270608Lelio R Paula01/2016
9981(2^234517+2750)/270597Stefano Morozzi01/2020
998218363^6988+6988^1836370594Hans Havermann10/2019
9983(2^234488-3)/1170587Lelio R Paula05/2012
9984(3*2^234451+1)/3570576Lelio R Paula08/2012
9985(8848^17881-1)/884770570Serge Batalov08/2020
9986Phi(159495,10)70560Maksym Voznyy09/2015
99872^234383-403570557Lelio R Paula05/2012
9988(2^234364+3618)/270551Stefano Morozzi01/2020
9989(2^234333+3482)/270541Stefano Morozzi01/2020
99902^234315-11124170536Enzo Doria05/2014
999114^61526+9770517Lelio R Paula01/2015
999214742^16915+16915^1474270512Norbert Schneider10/2019
9993(2^234203+3306)/270502Stefano Morozzi01/2020
9994(3*2^234170+1)/1370492Lelio R Paula08/2012
999551^41281-50^4128170491Robert Price02/2013
99962^234141-11212370484Enzo Doria06/2014
99972^234139+1228570483Lelio R Paula04/2012
99982^234133-316370482Yves Minet04/2009
99992^234115+8370476Lelio R Paula02/2012
100002^234114-159570476Lelio R Paula05/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 18 2021 19:57 (Time in France)

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