PRP Records

Probable Primes Top 10000

(181746 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 ?
450121234^9067+9067^2123484033Hans Havermann05/2017
45022^279095-10971784016Enzo Doria04/2014
450314^73282-9983991Lelio R Paula11/2015
450421457^8200+8200^2145783979Hans Havermann06/2017
450589*10^83976-783978Robert Price03/2017
45062^278955+17383974Lelio R Paula06/2012
4507(7*2^278851+1)/3983942Lelio R Paula12/2012
4508(9913*2^278844-1)/4080383940Lelio R Paula04/2015
45095^120076-1484683930Enzo Doria02/2013
4510(85*10^83921-1)/383923Robert Price07/2017
4511(2^278770-3)/2383917Lelio R Paula12/2012
4512(10^83916+449)/983916Serge Batalov12/2014
45132^278715+9983902Lelio R Paula06/2012
451440235!2-2^4023583899Robert Price09/2015
45152^278698-17183897Lelio R Paula06/2012
45166^107802+2583887Lelio R Paula12/2015
45178*10^83880+3983881Robert Price01/2017
4518(58*10^83878+23)/983879Robert Price09/2015
45197^99244-9083871Lelio R Paula10/2015
45202^278554+425783854Lelio R Paula08/2013
45212^278504-10961983839Enzo Doria04/2014
45222^278499+187043383837Enzo Doria05/2016
4523105^41475+10483829Norbert Schneider11/2016
452415^71276-6883828Lelio R Paula11/2015
45252^278464-21641383827Enzo Doria04/2013
45262^278400+4075583807Lelio R Paula08/2013
4527(9*2^278381-1)/783802Lelio R Paula02/2014
45283*9^87813+6^87813+2*4^8781383796Mike Oakes12/2010
452919551^19268+19268^1955183773Hans Havermann05/2017
453020625^11522+11522^2062583770Hans Havermann05/2017
4531(87^43189+1)/8883764Paul Bourdelais08/2017
45322^278235-4983758Lelio R Paula06/2012
453323543^3610+3610^2354383755Hans Havermann05/2017
453518^66711-9183741Lelio R Paula11/2015
45344*10^83740-8983741Robert Price08/2017
4536(3*2^278172-1)/1183738Lelio R Paula02/2014
4537(15*29^57251+2561)/2883724Curtis Bright05/2015
45384*7^99059-983716Lelio R Paula10/2014
4539(2^278128-3)/12684472414983714Lelio R Paula12/2012
45402^278077+186721183710Enzo Doria03/2016
45412^278059-2783705Lelio R Paula06/2012
4542214^35917+35917^21483702Norbert Schneider12/2014
4543(23*10^83693+7)/383694Robert Price10/2015
454485^43375-283689Lelio R Paula09/2013
45455*3^175360+483669Lelio R Paula07/2014
4546(23^61441-1)/2283665Robert Price01/2012
454720091^14596+14596^2009183664Hans Havermann03/2017
45482^277907-11062983659Enzo Doria05/2014
454919522^19283+19283^1952283656Hans Havermann04/2017
45508*5^119664-383643Lelio R Paula10/2014
45518*3^175299-783640Lelio R Paula07/2014
45523^175250+2283616Robert Price12/2013
455311^80285+3083609Lelio R Paula10/2015
455426870^1293+1293^2687083609Hans Havermann03/2017
45552^277691+187442383594Enzo Doria06/2016
455613^75022-6083571Lelio R Paula11/2015
455714^72905-5183559Lelio R Paula11/2015
4558(17*2^277565-1)/54383554Lelio R Paula02/2014
45595^119532-1283550Lelio R Paula10/2015
45606^107358-1625383541Enzo Doria02/2013
45612^277478-46021183530Enzo Doria06/2015
4562(22*10^83525-7)/383526Erik Branger09/2014
4563(30^56543+1)/3183520Robert Price07/2013
45642^277417-46078383511Paul Bourdelais04/2013
4565(22699*2^277387+1)/21983504Lelio R Paula06/2014
4566(31*2^277383-1)/24783500Lelio R Paula02/2014
456721368^8085+8085^2136883500Hans Havermann04/2017
4568(9*2^277342+1)/1383489Lelio R Paula12/2012
45695^119439-6683485Lelio R Paula10/2015
4570(14*10^83471-101)/383472Robert Price04/2017
45715*6^107263+783468Lelio R Paula10/2014
4572(64*10^83461-1)/983462Serge Batalov11/2010
457317^67796-9283420Lelio R Paula11/2015
45742^277106-11005783418Enzo Doria04/2014
45756^107200-1983418Lelio R Paula12/2015
457611^80096-183083412Enzo Doria12/2012
45773^174801+5683402Lelio R Paula12/2015
45782^277033-11197383396Enzo Doria05/2014
457920519^11572+11572^2051983378Hans Havermann03/2017
458020850^9971+9971^2085083374Hans Havermann03/2017
45816^107122-1886383358Enzo Doria03/2013
45824*10^83354-8983355Robert Price08/2017
45833^174697-3483352Robert Price11/2013
4584(9787*2^276855-1)/234583343Lelio R Paula04/2015
45852^276825+7522783333Enzo Doria04/2016
45865^119214+8483328Lelio R Paula10/2015
45872^276803-15983327Lelio R Paula06/2012
4588(3*2^276753-1)/2583311Lelio R Paula02/2014
4589114^40495+40495^11483295Norbert Schneider12/2014
459039967!2+102483282Robert Price02/2015
45912^276641+5783278Lelio R Paula06/2012
459235^53934-341483278Enzo Doria03/2013
4593(2^276655+78557)/36542583276Lelio R Paula12/2012
45942^276615-403583270Lelio R Paula08/2013
45952^276588+115583262Lelio R Paula08/2013
45972^276587-93783261Yves Minet10/2009
45962^276584-11318383261Enzo Doria07/2014
4598(2^276592-1017)/1384373983256Lelio R Paula12/2012
45992^276547-10959183249Enzo Doria04/2014
460013^74733-3283249Lelio R Paula11/2015
46012^276523-258783242Yves Minet07/2014
460218^66311-4383239Lelio R Paula11/2015
460311^79919-153083228Enzo Doria12/2012
46042^276468-10974583226Enzo Doria04/2014
46052^276462+538583224Lelio R Paula08/2013
4606(9787*2^276422-1)/383215Lelio R Paula04/2015
46082^276391-1583202Lelio R Paula06/2012
4607(4*10^83201+173)/383202Robert Price01/2017
46092^276316-10965583180Enzo Doria04/2014
46102^276305-11206383177Enzo Doria06/2014
4611(10^(2*41585+1)+54*10^41585-1)/983171Robert Price04/2017
461274913!4-283161Robert Price07/2017
46132^276227-183720783153Enzo Doria05/2015
4614(2^276227+3)/783152Lelio R Paula12/2012
46152^276184-6338983140Paul Bourdelais02/2012
46162^276066-11160383105Enzo Doria05/2014
4617(2^276028-3)*6-783094Gilbert Mozzo09/2016
4618(2^275897+9)/115383051Lelio R Paula12/2012
46192^275879-10980783048Enzo Doria04/2014
4621F(397379)83047Henri Lifchitz08/2003
4620U(397379)83047Serge Batalov03/2015
46223^174040-1483039Robert Price08/2013
4623(86*10^83038-221)/983039Robert Price06/2017
46242^275841-688383037Lelio R Paula07/2011
46253^174002-14083021Lelio R Paula12/2015
46266^106681+7783014Lelio R Paula12/2015
462711^79701-315083001Enzo Doria12/2012
4628(55459*2^275657+1)/2182985Lelio R Paula06/2014
46292^275535-685582945Lelio R Paula08/2013
46313^173828-1482938Robert Price08/2013
46302^275512-10967782938Enzo Doria04/2014
46322^275446-11004582918Enzo Doria04/2014
4633(2^275473+47)/2952609744782916Lelio R Paula12/2012
46343^173755-1482903Robert Price08/2013
46352^275363-11230982893Enzo Doria06/2014
463661^46427-6082888Norbert Schneider10/2014
46373*10^82880-7^8288082881Mike Oakes02/2010
46392^275290+9019582871Lelio R Paula07/2013
4638(35*10^82870-71)/982871Robert Price05/2015
46402^275270-185962182865Enzo Doria03/2016
46412^275259+8182862Henri Lifchitz01/2007
46427^98003+98003^7+182823Robert Price05/2014
464310^82790+12604382791Patrick De Geest07/2013
464410^82790-4782790Robert Price05/2011
46452^274985-11266382779Enzo Doria06/2014
46462^274935+1501582764Lelio R Paula07/2013
4647(17*2^274922+1)/382761Lelio R Paula12/2012
4648(43*10^82752-61)/982753Robert Price06/2015
4649(3*2^274862+1)/102782740Lelio R Paula12/2012
4650(31*2^274848-1)/406582736Lelio R Paula02/2014
4651(4^137405+23)/382726Robert Price02/2017
46522^274791-11049182721Enzo Doria05/2014
4653(11*2^274776-1)/9582715Lelio R Paula02/2014
4654(47*10^82706-119)/982707Robert Price09/2017
46552^274704-11139582695Enzo Doria05/2014
46562^274686-391182689Yves Minet04/2017
4657(2^274663-1017)/4887131829227982669Lelio R Paula12/2012
4658(3^173263-5)/1449882664Lelio R Paula12/2012
46592^274511-6487582637Lelio R Paula08/2013
466012^76572-8382636Lelio R Paula11/2015
46613^173191-2^17319182634Mike Oakes02/2004
466214^72072-1582604Lelio R Paula11/2015
4663(55459*2^274339+1)/382589Lelio R Paula06/2014
46642^274351+12382588Lelio R Paula06/2012
4665(1017*2^274339-1)/351582584Lelio R Paula04/2015
46666^106086+11382551Lelio R Paula12/2015
46672^274093-5869582511Lelio R Paula07/2013
46687*10^82509-4782510Robert Price02/2017
46692^274081-655582507Lelio R Paula07/2013
46712^274074-274074+182505Robert Price10/2014
467214^71985+4782505Lelio R Paula11/2015
46705*10^82504+2182505Robert Price01/2017
46736^106014-13982495Lelio R Paula12/2015
4674(2^274046+47)/75382494Lelio R Paula12/2012
46752^274008-183809982485Enzo Doria05/2015
46762^273981-11002982477Enzo Doria04/2014
467719^64490-3082467Lelio R Paula12/2015
46792^273785+1171582418Lelio R Paula07/2013
46788*10^82417+5182418Robert Price05/2017
468011^79133-1082409Theodore Burton11/2005
468191^42063+9082404Norbert Schneider01/2016
46832^273662-6382381Lelio R Paula06/2012
46822^273661+25582381Lelio R Paula07/2013
4684(62*10^82377-17)/982378Robert Price09/2015
4685(11*10^82323+91)/382323Robert Price02/2017
468615^69984+3282308Lelio R Paula11/2015
46879*6^105746+782288Lelio R Paula10/2014
468889^42211-8882286Norbert Schneider01/2016
4689gcd(V(1476435),5*F(295287)*(F(295287)+1)+1)82281Serge Batalov04/2015
46902^273282-11024182267Enzo Doria05/2014
4691(13^73849+4^73849)/1782263Robert Price05/2013
469310^82254+9^(82254+1)82255Robert Price08/2016
469210^82254+45777382255Patrick De Geest12/2016
469410^82254-9960982254Patrick De Geest12/2016
469518^65524+1382251Lelio R Paula11/2015
46962^273206-10782244Lelio R Paula06/2012
46972^273193-45914582240Enzo Doria05/2015
46992^273126+3693782220Yves Minet06/2010
469839505!2+12882220Robert Price03/2015
47002^273053-11211182198Enzo Doria06/2014
47012^273016+118582187Lelio R Paula07/2013
4702(2^273008+3)/782183Lelio R Paula12/2012
47035^117554-1538682167Enzo Doria02/2013
47042^272907-11143982154Enzo Doria05/2014
4705(67607*2^272901+1)/5079011582149Lelio R Paula06/2014
47062^272875-6982144Lelio R Paula06/2012
47077^97197+482141Robert Price01/2014
4708(4*6^105554+1)/582137Serge Batalov10/2014
47096^105531-10982120Lelio R Paula12/2015
47102^272766-6582111Lelio R Paula06/2012
471119^64205-7882103Lelio R Paula12/2015
47122^272702+186997982092Enzo Doria05/2016
4713(29*2^272687-1)/982088Lelio R Paula02/2014
4714(5*10^82085-119)/382086Robert Price04/2016
47152^272660-11004982079Enzo Doria04/2014
47166^105474+6782075Lelio R Paula12/2015
47172^272637+8287582072Lelio R Paula07/2013
47182^272587-3182057Lelio R Paula06/2012
47198*5^117368+982038Lelio R Paula10/2014
4720(101525^16384+1)/13107482023Lelio R Paula11/2011
47214*5^117343-782020Lelio R Paula10/2014
4722(265*10^81990+17)/381992Robert Price05/2016
47233^171843+1081990Robert Price10/2013
4724(7*10^81985+107)/381986Robert Price02/2017
4725(3*2^272356+1)/17716381983Lelio R Paula12/2012
47262^272296-11114981970Enzo Doria05/2014
4727(9*2^272243-1)/781954Lelio R Paula02/2014
47282^272177-11122381934Enzo Doria05/2014
4729(151009^15817+1)/15101081912Faysal YAtim06/2017
4730(16*10^81896-19)/381897Robert Price03/2016
4731(2^271922+78557)/6381855Lelio R Paula12/2012
4732(10^81848+77)/381848Robert Price01/2017
4733(24737*2^271883+1)/375781846Lelio R Paula06/2014
473410^81778+3981779Robert Price03/2011
473510^81778-17199981778Patrick De Geest07/2013
4736(14*10^81767-11)/381768Erik Branger09/2014
47372^271541+186841781742Enzo Doria04/2016
4738(2^271549-1)/23874968248781734Jens K. Andersen02/2009
47392^271484-16781725Lelio R Paula06/2012
47402^271382+1290981695Lelio R Paula07/2013
474149^48334+4881694Norbert Schneider07/2014
47427^96668+4881694Lelio R Paula10/2015
474311^78435-141081682Enzo Doria12/2012
47445*10^81653+981654Dmitry Domanov11/2010
4745(2^271211-1)/61396149515981631Jens K. Andersen02/2009
47463^171068+5281621Lelio R Paula12/2015
47472^271115-11040781614Enzo Doria05/2014
47482^271111-11063581613Enzo Doria05/2014
47492^271098-11181609Lelio R Paula06/2012
4750(77*10^81606+13)/981607Robert Price10/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 14 2017 17:05 (Time in France)

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