PRP Records

Probable Primes Top 10000

(253476 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 ?
67512^249726-11218175176Enzo Doria06/2014
67522^249721+1171575174Lelio R Paula05/2013
6753(38661^16384+1)/275158Lelio R Paula11/2011
67542^249658-4735575155Lelio R Paula05/2013
6755155^34311+275153Lelio R Paula05/2013
6756(10^87682+1)/(10^12526+1)/99009900990175145Maksym Voznyy06/2015
6757(23*2^249602+1)/9375138Lelio R Paula08/2012
67582^249522+841575114Lelio R Paula05/2013
67592^249489-11091175104Enzo Doria05/2014
6760(28*10^75078+131)/375079Robert Price02/2017
6761(206*10^75073-17)/975075Robert Price03/2017
67622^249368-11057375068Enzo Doria05/2014
6763NaturalLogarithmOf10(75067)75067Eric W. Weisstein10/2015
6764(2^249375+78557)/4505612575062Lelio R Paula07/2012
6765(26*10^75055-173)/375056Robert Price10/2017
67662^249272+19375039Lelio R Paula03/2012
676714^65468+4375035Lelio R Paula01/2015
676837^47844+3675030Norbert Schneider05/2014
6769(52*10^75027-7)/975028Robert Price12/2014
677020^57653+8975009Lelio R Paula01/2015
67712^249061-186835374975Enzo Doria04/2016
67727^88713+2*3^8871374972Mike Oakes07/2010
67732*6^96313+574947Lelio R Paula10/2014
6774(8*10^74944+49)/374945Robert Price03/2016
6775300^30247+30247^30074926Norbert Schneider11/2014
67762^248866-17174917Lelio R Paula03/2012
67776*5^107168-774908Lelio R Paula10/2014
677811^71926+7874904Lelio R Paula02/2015
67792^248824+186939174904Enzo Doria05/2016
67802^248816+111174902Lelio R Paula01/2011
6781V(388219)74890Serge Batalov03/2015
6782159^34017+15874885Norbert Schneider12/2018
67832*F(358297)-174880Henri Lifchitz12/2009
6784(22*10^74874-31)/974875Robert Price04/2015
678511^71892-7680000074868Enzo Doria01/2013
67869*5^107107-474866Lelio R Paula10/2014
67872^248678-71011174860Paul Bourdelais03/2013
6788(14*10^74858+211)/974859Robert Price11/2017
678913^67194+1274851Lelio R Paula01/2015
6790(7*2^248634+1)/7174846Lelio R Paula08/2012
679111^71867-309074842Enzo Doria12/2012
67922^248609+26214574839Lelio R Paula05/2013
67933^156852+5074838Lelio R Paula01/2015
679418^59607-1174824Lelio R Paula01/2015
67952^248556-11050774823Enzo Doria05/2014
67967^88531-3674818Lelio R Paula01/2015
6797p(15738)#/2+102474814Robert Price07/2017
67984*3^156740-574785Lelio R Paula05/2014
6799(32*10^74773-41)/974774Robert Price05/2015
6800(29*2^248384-1)/1374772Lelio R Paula01/2014
680119401!+19401#+174765D. Gazzoni Filho & Lucas Teixeira06/2005
68022^248357-1279741374763Enzo Doria03/2016
680342^46057+4174762Lelio R Paula07/2012
680411^71784-300074756Enzo Doria12/2012
680519^58458+1874754Lelio R Paula01/2015
680612^69265-3574750Lelio R Paula02/2015
680711^71771-4800074742Enzo Doria12/2012
6808(7*10^74741+197)/374742Robert Price07/2017
6809(2^248282-5)/5012974736Lelio R Paula06/2012
68102^248252-11010574732Enzo Doria04/2014
6811(7*10^74729+71)/374730Robert Price03/2016
68123^156614-5074724Lelio R Paula01/2015
6813(7*2^248213+1)/13574719Lelio R Paula07/2012
6814(2^248173+78557)/76774705Lelio R Paula07/2012
6815125^35622+12474697Norbert Schneider02/2015
6816(19*2^248099-1)/2974686Lelio R Paula01/2014
6817(86*10^74676-41)/974677Robert Price11/2015
6818(p(15711)#-4)/274672Robert Price09/2017
681910^74670+3174671Robert Price01/2011
682010^74670-12246374670Patrick De Geest05/2013
68212^248036-6974667Lelio R Paula03/2012
682211^71698-600074666Enzo Doria12/2012
682358*(10^(3*24887)-1)/111-174661Robert Price10/2014
682414^65139-4574658Lelio R Paula01/2015
68256^95921-13374642Lelio R Paula01/2015
682611^71675+7874642Lelio R Paula02/2015
682718^59449-9174625Lelio R Paula01/2015
68286^95864-1604374597Enzo Doria02/2013
68295*7^88261+674590Lelio R Paula10/2014
68309*5^106710+474589Lelio R Paula10/2014
6831(777*2^247788+1)/(11*754121)74588Jens K. Andersen09/2007
6832(265*10^74579+17)/374581Robert Price05/2016
6833(2^247759-1017)/331831171774574Lelio R Paula07/2012
68345^106682-2474568Lelio R Paula08/2014
6835474^27863+27863^47474556Norbert Schneider01/2017
6836(14*10^74540+79)/374541Robert Price11/2017
6837(35365^16384+1)/274524Lelio R Paula11/2011
68383^156161+266074508Lelio R Paula01/2015
68392^247474-5869574498Lelio R Paula05/2013
684011^71519-9074480Enzo Doria07/2012
6841(19*2^247419-1)/2320298374475Lelio R Paula01/2014
6843(2^247394-7)/374473Lelio R Paula06/2012
684218^59328+1774473Lelio R Paula01/2015
68442^247379-18174469Lelio R Paula03/2012
6845(15*2^247370-1)/47974465Lelio R Paula01/2014
68462^247344+204774458Lelio R Paula05/2013
68472^247311-101774449Lelio R Paula05/2013
68482^247280+774439Lelio R Paula03/2012
6849(68*10^74434+13)/974435Ray Chandler11/2010
68503^156004-6274433Lelio R Paula01/2015
685136095!2-6474416Robert Price06/2015
68522^247165-374405M. Frind & P. Underwood07/2002
68532^247150+3276974400Lelio R Paula05/2013
685412^68911+7374368Lelio R Paula01/2015
68552^246999+7490374355Enzo Doria04/2016
68562^246989-11064374352Enzo Doria05/2014
685710^74350+27943974351Patrick De Geest07/2017
6860(10^74350+11)/374350Robert Price11/2014
685810^74350-40000000174350Robert Price07/2017
685910^74350-71624174350Patrick De Geest07/2017
686110^74335+1365974336Patrick De Geest05/2013
686210^74335-5374335Robert Price05/2011
68632^246906-121574327Lelio R Paula05/2013
68642^246848+11174309Lelio R Paula03/2012
68656^95490-1844374306Enzo Doria03/2013
686618^59188-236974298Enzo Doria03/2013
6867(1363*2^246767+1)/(3*5*7*13^2*743)74281Jens K. Andersen09/2007
68682^246744+4075574278Lelio R Paula05/2013
6869(29*10^74276+91)/374277Robert Price03/2016
68706^95441+16374268Lelio R Paula01/2015
6871V(390863)74258Serge Batalov03/2015
687210^74254+9174255Robert Price03/2011
6874(19*10^74253-1)/974254Ray Chandler02/2012
687310^74254-13056974254Patrick De Geest05/2013
6875771^25718+25718^77174250Norbert Schneider10/2016
68762^246618+42774240Henri Lifchitz02/2005
687788*10^74234+374236Robert Price11/2016
68788*10^74234-4974235Robert Price04/2016
68792^246578+1228574228Lelio R Paula05/2013
6880(3^155569-5)/274225Lelio R Paula06/2012
688113^66628+4674220Lelio R Paula01/2015
68822^246476-1729574197Lelio R Paula05/2013
6883(61*10^74189-1)/374191Robert Price11/2017
6884(15185*2^246432-1)/1374187Lelio R Paula04/2015
68855*2^246413-374179Lelio R Paula05/2014
68862^246386-2863574170Lelio R Paula05/2013
68872^246334-11124574154Enzo Doria05/2014
68883*9^77708+7^77708-2*4^77708-374153Mike Oakes12/2010
688915^63045+8274147Lelio R Paula01/2015
689019255!+19255#+174140D. Gazzoni Filho & Lucas Teixeira06/2005
68912^246268-11050774135Enzo Doria05/2014
68923^155328+266074111Lelio R Paula01/2015
68932^246148-278624974098Enzo Doria03/2016
6894(16*10^74092-19)/374093Robert Price03/2016
68952^246115-11076774088Enzo Doria05/2014
68967^87666-6874087Lelio R Paula08/2014
689710^74079+114514191974080Marisa Kirisame03/2015
689810^74079+621974080Patrick De Geest03/2016
689910^74079-28270774079Patrick De Geest03/2016
6900129^35098+274078Lelio R Paula05/2013
69012^246025-11212374061Enzo Doria06/2014
6902(67*10^74045+17)/374047Robert Price02/2017
69032^245823+6683174001Marek Hubal02/2017
69045^105869+4274000Lelio R Paula08/2014
6905(21*2^245806+1)/63455573991Lelio R Paula08/2012
6906(22699*2^245762+1)/11973985Lelio R Paula06/2014
6907(3^155048-7)/26273975Lelio R Paula06/2012
69089998*2^245696+373966Donovan Johnson10/2004
690913^66400-8073966Lelio R Paula01/2015
6910(2^245704+9)/2573963Lelio R Paula07/2012
691211^71023-717073963Enzo Doria01/2013
69113*10^73962+1373963Robert Price08/2017
6913(31*2^245660-1)/11419573948Lelio R Paula01/2014
69142^245629-279781373942Eric Chen03/2016
69152^245557-15373921Lelio R Paula03/2012
6916(77*10^73917-59)/973918Robert Price11/2017
69172^245525+186988173911Enzo Doria06/2016
69182^245522+15973910Lelio R Paula03/2012
6919(13*10^73891-43)/373892Robert Price08/2017
692019^57783-5673891Lelio R Paula01/2015
69217*10^73888+7973889Robert Price02/2017
69226^94948+17428173884Mike Oakes02/2011
692311^70939-486073876Enzo Doria01/2013
69242^245372+5461573865Lelio R Paula05/2013
69252^245362-14373862Lelio R Paula03/2012
69267^87396+6^(87396-1)73859Robert Price03/2016
6927(22*10^73853-37)/373854Robert Price05/2017
69285^105646-1424673844Enzo Doria02/2013
69302^245290-4173840Lelio R Paula03/2012
69292^245290-9439573840Lelio R Paula05/2013
69318*5^105600-773813Lelio R Paula10/2014
69327*5^105573-473794Lelio R Paula10/2014
693318^58742-480573738Enzo Doria03/2013
693413^66179+6673720Lelio R Paula01/2015
6935(82*10^73714-1)/973715Robert Price12/2014
6936(29*2^244856-1)/18612173706Lelio R Paula01/2014
6937(13*2^244840-1)/279973702Lelio R Paula01/2014
6938(13*10^73701+17)/373702Robert Price06/2015
6939(2^244787-1017)/2841173684Lelio R Paula07/2012
6940(3^154421-4)/2373677Lelio R Paula06/2012
69418*7^87170+573669Lelio R Paula10/2014
6942(29*10^73659-113)/373660Robert Price11/2017
6943Phi(40100,-40100)73651Henri Lifchitz06/2013
6944(4*10^73647-19)/373648Robert Price06/2017
69452^244618-229773638Yves Minet10/2009
69463*5^105344+873633Lelio R Paula10/2014
69475^105334-1409673626Enzo Doria02/2013
6948(2^244584-7)/1323707424303373614Lelio R Paula07/2012
69492^244465-11018573592Enzo Doria05/2014
69502^244443+4075573585Lelio R Paula05/2013
69512^244404+384173573Yves Minet03/2011
69522^244372-11062773564Enzo Doria05/2014
6953(3*2^244255+1)/24573527Lelio R Paula08/2012
6954(11*2^244245+1)/2373525Lelio R Paula08/2012
6955(15185*2^244187-1)/611173509Lelio R Paula04/2015
695617063^17362+17362^1706373477Norbert Schneider04/2019
6957(91^37507+1)/9273476Paul Bourdelais08/2017
695818^58521+6573460Lelio R Paula01/2015
695913^65940+3673454Lelio R Paula01/2015
6960(625^26267+1)/62673437Richard Fischer12/2017
69615^105050-1473427Lelio R Paula08/2014
6962(((((((((((((30201^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-273401Serge Batalov07/2016
696315^62410-4673400Lelio R Paula01/2015
69642^243733+186970773371Enzo Doria05/2016
696511^70439-543073355Enzo Doria01/2013
69662^243676-8773354Lelio R Paula03/2012
6967(101*10^73346-17)/373348Robert Price08/2016
69682^243621-11318573338Enzo Doria07/2014
6969(5*2^243610-1)/166973332Lelio R Paula01/2014
69702*5^104888-773314Lelio R Paula10/2014
6971(58695*2^243516-1)/98373308Lelio R Paula04/2015
6972(3^153648-2)/3342313809773299Lelio R Paula06/2012
697318^58376-525573278Enzo Doria03/2013
697411^70363+3273276Lelio R Paula02/2015
69752^243413+425773275Lelio R Paula05/2013
6976104824^5+5^10482473269Andrey Kulsha07/2010
69777^86689-6^8668973261Predrag Minovic09/2004
69782^243296+9019573240Lelio R Paula05/2013
69792^243281-484373235Yves Minet05/2019
6981p(15433)#/2-473218Robert Price12/2016
6980(59*10^73217-77)/973218Robert Price11/2017
69822^243127+7135573189Lelio R Paula05/2013
69832^243116-24941973186Paul Bourdelais03/2013
6984(58695*2^243085-1)/1173180Lelio R Paula04/2015
698511^70262-9873171Lelio R Paula02/2015
6986(2^243034+47)/72270330373152Lelio R Paula07/2012
6987(2^242966+47)/4688773136Lelio R Paula07/2012
6988(43^44773-1)/4273134Robert Price04/2014
69896^93980-15835973131Mike Oakes02/2011
69906^93915+5373081Lelio R Paula01/2015
6991(5*10^73079+211)/973079Robert Price12/2017
6992(74*10^73076+43)/973077Robert Price10/2015
6993(3^153125+2)/114495573054Lelio R Paula06/2012
69942^242632-11219973040Enzo Doria06/2014
6995V(351646)73029Serge Batalov03/2015
699618^58175-8573026Lelio R Paula01/2015
6997p(15395)#/2-473019Robert Price12/2016
6998(4^121271+3^121271)/773012Jean-Louis Charton03/2011
69998*6^93825-573011Lelio R Paula10/2014
7000(73^39181+1)/7473005Paul Bourdelais08/2017


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 25 2019 15:53 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!