PRP Records

Probable Primes Top 10000

(288949 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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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 ?
8751(2^287172+658)/286448Stefano Morozzi01/2020
8752(2^287146+2542)/286440Stefano Morozzi01/2020
8753(2^287136+1726)/286437Stefano Morozzi01/2020
8754(2^287128+958)/286434Stefano Morozzi01/2020
875587^44563-86^4456386431Robert Price05/2015
87566^111057+6186420Lelio R Paula12/2015
87572^287057-10990986413Enzo Doria04/2014
87585^123608+2286399Lelio R Paula10/2015
8759(2^286970+618)/286387Stefano Morozzi01/2020
8760(2^286916+2646)/286371Stefano Morozzi01/2020
8761(2^286907+3690)/286368Stefano Morozzi01/2020
8762(31*10^86364-121)/986365Robert Price06/2016
8763(2^286868+2686)/286356Stefano Morozzi01/2020
87642^286859+7166386354Enzo Doria04/2016
8765(2^286845+1866)/286349Stefano Morozzi01/2020
87662^286740+2983586318Lelio R Paula10/2013
87672*10^86310+9^8631086311Mike Oakes05/2011
876811^82878-186086309Enzo Doria12/2012
87692223^25780+25780^222386285Norbert Schneider12/2019
87702^286547+1609586260Lelio R Paula10/2013
8771(58*10^86242+329)/986243Robert Price11/2017
87722^286455-11042786232Enzo Doria05/2014
8773(37*10^86230+53)/986231Robert Price05/2015
87748*3^180700+586217Lelio R Paula08/2014
87753^180697-4086215Lelio R Paula12/2015
8776(2^286383+3386)/286210Stefano Morozzi01/2020
8777(13*2^286318-1)/1325786188Lelio R Paula02/2014
8778(2^286295+1934)/286184Stefano Morozzi01/2020
8779(2^286251+3974)/286170Stefano Morozzi01/2020
87802^286165+7786145Lelio R Paula08/2012
87819*2^286140+786138Lelio R Paula08/2014
8782(2^286128+1762)/286133Stefano Morozzi01/2020
8783(118*10^86131+71)/986133Robert Price11/2021
8784(29*2^286108-1)/200236786123Lelio R Paula02/2014
8785(2^286077+1122)/286118Stefano Morozzi01/2020
878610^86110+16111386111Patrick De Geest07/2013
878710^86110-6986110Robert Price05/2011
87882^286036-86968810586106Lelio R Paula07/2016
8789(2^285946+2358)/286079Stefano Morozzi01/2020
87905*10^86076-2186077Robert Price12/2021
8792(77*10^86072+31)/986073Robert Price10/2015
8791(2^285926+3382)/286073Stefano Morozzi01/2020
87932^285923+34586072Lelio R Paula09/2013
879413^77266-9086070Lelio R Paula11/2015
87952^285910-45890386068Enzo Doria04/2015
87962^285904-12586066Lelio R Paula08/2012
8797(2^285882+2830)/286059Stefano Morozzi01/2020
87982^285836+6583586046Lelio R Paula09/2013
879921587^9670+9670^2158786034Hans Havermann08/2020
8800(2^285766+78557)/386024Lelio R Paula01/2013
8801(2^285732+2682)/286014Stefano Morozzi01/2020
8802(5*10^86011-107)/386012Robert Price01/2017
88036^110522+16386003Lelio R Paula12/2015
880441^53323-40^5332385999Robert Price07/2012
88052^285678-10961785998Enzo Doria04/2014
88066^110506-1667385991Enzo Doria02/2013
88072^285569-74185965Lelio R Paula09/2013
8808(32*10^85964+31)/985965Robert Price05/2015
8809133^40466+13285944Norbert Schneider02/2019
881023378^4743+4743^2337885939Hans Havermann08/2020
88116*10^85910-785911Dmitry Domanov11/2010
8812(412*10^85897-7)/985899Robert Price10/2017
88134*10^85881+6385882Robert Price06/2016
8814(2^285257+1514)/285871Stefano Morozzi01/2020
8815(2^285248+3738)/285868Stefano Morozzi01/2020
8816(10^85864+53)/985864Robert Price01/2015
88172^285230+34585863Lelio R Paula09/2013
881821774^8777+8777^2177485863Hans Havermann08/2020
8819(5*10^85855-473)/985855Robert Price12/2017
88202^285199+7568385854Enzo Doria04/2016
8821(76*10^85847-211)/985848Robert Price10/2017
8822p(17832)#/2+51285845Robert Price05/2017
8823(16*10^85839+167)/385840Robert Price10/2017
882411^82426-123085838Enzo Doria11/2012
8825(14727^20593-1)/1472685830Serge Batalov08/2020
88262^285113-10988185828Enzo Doria04/2014
8827(2^285033+1670)/285804Stefano Morozzi01/2020
8828(2^285033+3854)/285804Stefano Morozzi01/2020
8829(2^285035+3194)/285804Stefano Morozzi01/2020
88305^122746-9285796Lelio R Paula10/2015
88312^285001-11346185794Enzo Doria08/2014
8832(11*10^85782-131)/385783Robert Price02/2017
8833(2^284963+2778)/285783Stefano Morozzi01/2020
8834(2^284960+3570)/285782Stefano Morozzi01/2020
8835(2^284937+1706)/285775Stefano Morozzi01/2020
88372^284913-11049185768Enzo Doria05/2014
88366^110220+4785768Lelio R Paula12/2015
8838(1966^26041-1)/196585765Serge Batalov08/2020
883920698^13909+13909^2069885758Hans Havermann07/2020
88403*6^110202-585755Lelio R Paula10/2014
88419*10^85746+3785747Robert Price12/2020
8842(157^39047-1)/15685742Alexander Zhirkov06/2016
8843(3^179705+7)/25085739Lelio R Paula12/2012
8844(9127^21649-1)/912685734Serge Batalov08/2020
88452^284734-655585714Lelio R Paula09/2013
8846(10^85712+53)/985712Robert Price01/2015
88473*10^85703+1185704Robert Price11/2017
8848(6883*2^284668-1)/385697Lelio R Paula04/2015
884920728^13621+13621^2072885694Hans Havermann07/2020
885022126^7459+7459^2212685687Hans Havermann07/2020
8851(9311^21589-1)/931085683Serge Batalov08/2020
885220^65855+8385680Lelio R Paula01/2016
88536^110105+5385679Lelio R Paula12/2015
88543*10^85672-7385673Robert Price02/2021
8855(10^85666-97)/385666Robert Kinser10/2017
88572^284567-760585664Lelio R Paula09/2013
88569*5^122555-285664Lelio R Paula10/2014
88585^122554-1485662Lelio R Paula10/2015
88599*5^122543+485655Lelio R Paula10/2014
8860(7*10^85647+173)/985647Robert Price01/2022
88623^179489-2^(179489-1)85639Robert Price01/2016
8861(2^284487+1970)/285639Stefano Morozzi01/2020
8863(2^284477+1614)/285636Stefano Morozzi01/2020
886423693^4114+4114^2369385633Hans Havermann07/2020
886519690^19941+19941^1969085632Norbert Schneider03/2020
88662^284429+17785622Lelio R Paula08/2012
88672*3^179452+585621Lelio R Paula07/2014
886821036^11711+11711^2103685587Hans Havermann07/2020
8870(19^66919+3^66919)/2285572Robert Price07/2013
8869(2^284265+602)/285572Stefano Morozzi01/2020
887166^47023-6585561Norbert Schneider11/2014
8872(2^284226+3802)/285561Stefano Morozzi01/2020
8873(2^284228+2170)/285561Stefano Morozzi01/2020
88746^109943+1385553Lelio R Paula12/2015
88752^284183-474785548Yves Minet05/2019
8876(5637^22807-1)/563685547Serge Batalov08/2020
887720782^13071+13071^2078285546Hans Havermann08/2020
8878(2^284167-509203)/3456477585536Lelio R Paula01/2013
8879(2^284136+2262)/285534Stefano Morozzi01/2020
88802^284133-385533M. Frind & P. Underwood07/2002
88812^284113+31585527Lelio R Paula09/2013
8882(2^284098+3082)/285522Stefano Morozzi01/2020
8883(2^284070+1482)/285514Stefano Morozzi01/2020
8884(2^284068+2866)/285513Stefano Morozzi01/2020
8885(8721^21701-1)/872085511Serge Batalov08/2020
888622085^7438+7438^2208585502Hans Havermann07/2020
8887(28*10^85500+149)/385501Robert Price10/2017
8888(16*10^85495-19)/385496Robert Price03/2016
88892^284004+17785494Lelio R Paula08/2012
8890(16*10^85473-91)/385474Robert Price06/2016
889166*10^85468+785470Robert Price07/2020
88923^179120+2285462Robert Price12/2013
88932^283872-279224985454Enzo Doria03/2016
8894(4703^23269-1)/470285449Serge Batalov08/2020
8895(29*10^85438+259)/985439Robert Price04/2017
88962^283817+8287585438Lelio R Paula09/2013
8897(2^283815-5)/20185435Lelio R Paula01/2013
88982^283796-12585432Lelio R Paula08/2012
8899(10174^21319-1)/1017385432Serge Batalov08/2020
8900(29*2^283784-1)/1385428Lelio R Paula02/2014
890115^72592-2885375Lelio R Paula11/2015
89022^283604-5869585374Lelio R Paula09/2013
890321863^8034+8034^2186385374Hans Havermann08/2020
8905(44*10^85370-503)/985371Robert Price10/2017
8904(2^283597+1854)/285371Stefano Morozzi01/2020
8906496^31671+31671^49685369Norbert Schneider07/2017
8907(2^283578+478)/285366Stefano Morozzi01/2020
8908(15*2^283583-1)/10305185364Lelio R Paula02/2014
890915^72572+9285352Lelio R Paula11/2015
89102^283473-161585334Lelio R Paula09/2013
8911(2^283469+2934)/285333Stefano Morozzi01/2020
89122^283466-1585332Lelio R Paula08/2012
8913(2^283437+3446)/285323Stefano Morozzi01/2020
891419966^18761+18761^1996685320Hans Havermann07/2020
8915(2^283411+3894)/285315Stefano Morozzi01/2020
891611^81916-702085307Enzo Doria02/2013
89176^109626-785306Lelio R Paula11/2014
89182^283374-11032785305Enzo Doria05/2014
891933*10^85297+785299Robert Price07/2016
8920(6010^22573-1)/600985297Serge Batalov08/2020
89211137^27908+27908^113785281Norbert Schneider04/2020
892218^67933+4185275Lelio R Paula11/2015
89232^283271-10934185274Enzo Doria04/2014
8924(2^283266+3678)/285272Stefano Morozzi01/2020
892519688^19855-19855^1968885262Norbert Schneider03/2020
8926(2^283216+1926)/285257Stefano Morozzi01/2020
8927(5*10^85254-191)/385255Robert Price05/2021
8928(25*10^85249-73)/385250Robert Price09/2016
89292*5^121959+385246Lelio R Paula10/2014
893019834^19834+894785235Henri Lifchitz11/2004
89312^283140+191585234Lelio R Paula09/2013
89323*10^85227-9785228Robert Price08/2017
8933(16*10^85221-31)/385222Robert Price03/2016
8934(2^283096+3186)/285221Stefano Morozzi01/2020
89352^283083+186938385217Enzo Doria05/2016
8936(24737*2^283051+1)/1785211Lelio R Paula06/2014
8937(2^283032+78557)/385201Lelio R Paula01/2013
89382^283026-10989385200Enzo Doria04/2014
8939(2^283012+78557)/12985193Lelio R Paula01/2013
8940(10^(2*42589+1)+72*10^42589-1)/985179Robert Price09/2017
89412^282860-10972785150Enzo Doria04/2014
8942(2^282847+13)/385145Stefano Morozzi03/2020
89432^282819+186941385138Enzo Doria05/2016
89443^178428+285132Ray Chandler07/2011
894519985^18162+18162^1998585120Hans Havermann07/2020
8946(22699*2^282742+1)/7385117Lelio R Paula06/2014
8947(16^70687+5^70687)/2185115Robert Price07/2013
8948(2^282732+738)/285111Stefano Morozzi01/2020
8949(2^282720+1590)/285107Stefano Morozzi01/2020
8950(3^178352-2)/785095Lelio R Paula12/2012
895122150^6939+6939^2215085085Hans Havermann07/2020
895211^81699-279085081Enzo Doria12/2012
89532^282612-9585075Lelio R Paula08/2012
89542^282609-406985074Yves Minet02/2018
895575^45366-285065Lelio R Paula08/2013
8956(2^282550+1918)/285056Stefano Morozzi01/2020
8957(2^282515+3786)/285046Stefano Morozzi01/2020
89582^282511+6985045Lelio R Paula08/2012
895969^46249+285045Lelio R Paula06/2013
8960(2^282488+2382)/285038Stefano Morozzi01/2020
8961(2^282489+1862)/285038Stefano Morozzi01/2020
89623^178226+1085036Robert Price10/2013
8963(2^282475+1050)/285034Stefano Morozzi01/2020
8964(182*10^85017+43)/985019Robert Price11/2017
8965(14*10^85010+73)/385011Robert Price04/2016
89669*2^282338-784994Lelio R Paula08/2014
8967(9913*2^282330-1)/157800384988Lelio R Paula04/2015
89685*10^84985-3184986Robert Price12/2021
896920025^17504+17504^2002584969Hans Havermann07/2020
89702^282203+584952Lelio R Paula08/2012
89712^282184+1384946Lelio R Paula08/2012
897211^81568-240084945Enzo Doria12/2012
897311^81562-234084939Enzo Doria12/2012
8974(41*10^84927+31)/984928Robert Price05/2015
8975(3923^23629-1)/392284911Serge Batalov08/2020
8976(2^282053+1406)/284907Stefano Morozzi01/2020
8977(2*10^84904-17)/384904Robert Price08/2014
8978(4^141017+23)/384901Robert Price02/2017
89796^109100-1865384897Enzo Doria03/2013
89802^281973+102584883Lelio R Paula09/2013
89812^281951-10965184876Enzo Doria04/2014
898221618^8431+8431^2161884870Hans Havermann07/2020
898311^81491-543084865Enzo Doria01/2013
898410^84863+14105784864Patrick De Geest02/2021
898510^84863-4000184863Robert Price01/2021
8986((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
8987(2^281827+650)/284839Stefano Morozzi01/2020
89882^281825-186148384838Enzo Doria03/2016
89892^281809-9730584833Lelio R Paula09/2013
89902^281780-11489384825Enzo Doria05/2015
8991(7654^21841-1)/765384825Serge Batalov08/2020
89923^177719+6484794Lelio R Paula12/2015
89942^281675-19984793Lelio R Paula08/2012
89932^281673-11122384793Enzo Doria05/2014
8995(4*10^84779+149)/984779Robert Price03/2017
8997129^40167-12884777Norbert Schneider01/2019
8996(2^281622+3970)/284777Stefano Morozzi01/2020
89989*10^84775-4784776Robert Price11/2021
8999(72*10^84772-27)/984773Ray Chandler01/2011
900011^81398-63084768Enzo Doria11/2012


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 19 2022 17:15 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!