PRP Records

Probable Primes Top 10000

(172213 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 ?
4501(7*10^81985+107)/381986Robert Price02/2017
4502(3*2^272356+1)/17716381983Lelio R Paula12/2012
45032^272296-11114981970Enzo Doria05/2014
4504(9*2^272243-1)/781954Lelio R Paula02/2014
45052^272177-11122381934Enzo Doria05/2014
4506(16*10^81896-19)/381897Robert Price03/2016
4507(2^271922+78557)/6381855Lelio R Paula12/2012
4508(10^81848+77)/381848Robert Price01/2017
4509(24737*2^271883+1)/375781846Lelio R Paula06/2014
451010^81778+3981779Robert Price03/2011
451110^81778-17199981778Patrick De Geest07/2013
4512(14*10^81767-11)/381768Erik Branger09/2014
45132^271541+186841781742Enzo Doria04/2016
4514(2^271549-1)/23874968248781734Jens K. Andersen02/2009
45152^271484-16781725Lelio R Paula06/2012
45162^271382+1290981695Lelio R Paula07/2013
451749^48334+4881694Norbert Schneider07/2014
45187^96668+4881694Lelio R Paula10/2015
451911^78435-141081682Enzo Doria12/2012
45205*10^81653+981654Dmitry Domanov11/2010
4521(2^271211-1)/61396149515981631Jens K. Andersen02/2009
45223^171068+5281621Lelio R Paula12/2015
45232^271115-11040781614Enzo Doria05/2014
45242^271111-11063581613Enzo Doria05/2014
45252^271098-11181609Lelio R Paula06/2012
4526(77*10^81606+13)/981607Robert Price10/2015
45272^271064-279020981599Enzo Doria03/2016
4528(13*2^271053-1)/309581593Lelio R Paula02/2014
45292^271040-5781592Lelio R Paula06/2012
4530(14*10^81585+73)/381586Robert Price04/2016
4531127^38779+12681584Norbert Schneider02/2015
453218^64966-4381551Lelio R Paula11/2015
4533(2^270840+47)/59181529Lelio R Paula12/2012
453420^62654+8781515Lelio R Paula01/2016
4535(19*10^81488+191)/381489Robert Price01/2017
45368*10^81487+2181488Robert Price02/2017
4537(73*10^81485+107)/981486Robert Price08/2016
45388*7^96378+981450Lelio R Paula10/2014
45392^270546-11034581443Enzo Doria05/2014
454013^73105-6081435Lelio R Paula11/2015
454144^49524+4381391Norbert Schneider06/2014
4542(3*2^270368-1)/1381389Lelio R Paula02/2014
4543(10^81363+719)/981363Serge Batalov12/2014
4544(10^81353+449)/981353Serge Batalov12/2014
454514^70978-8981350Lelio R Paula11/2015
454611^78108-204081342Enzo Doria12/2012
45473^170400-5881302Lelio R Paula12/2015
454810^81297+3699181298Patrick De Geest06/2013
454910^81297-5781297Robert Price05/2011
45502^270055-11304781295Enzo Doria07/2014
455118^64759-5581291Lelio R Paula11/2015
4552(2^269987+1)/381274H.&R. Lifchitz10/2000
4553(31^54493-1)/3081268Alexander Zhirkov10/2010
4554(2^270059-1)/540119/6481417/712497615775672596781265Dario Alpern09/2014
4555(2^269816+7)/42490181218Lelio R Paula12/2012
4556(23*10^81214+1)/381215Serge Batalov06/2009
4557(17*2^269720+1)/30381193Lelio R Paula07/2012
455856^46441-55^4644181188Robert Price10/2013
45602^269664+17781177Lelio R Paula06/2012
4559(13*2^269665-1)/18581177Lelio R Paula02/2014
45612^269539-11224981140Enzo Doria06/2014
4562((2*170026-3)*3^(170026-1)+1)/481128Robert Price01/2015
4563(2^269495-5)/981126Lelio R Paula12/2012
45642^269490-362381125Yves Minet10/2009
4565(55459*2^269444+1)/3581114Lelio R Paula06/2014
4566(2^269417+78557)/525781099Lelio R Paula12/2012
45674*5^116011-781089Lelio R Paula10/2014
45687*10^81058+7981059Robert Price02/2017
45692^269236-10990781049Enzo Doria04/2014
4570(8*10^81029-11)/381030Erik Branger03/2014
45713*10^81021+781022Erik Branger11/2013
45726^104115+10381018Lelio R Paula12/2015
45732^269120+186915181014Enzo Doria05/2016
45745^115901+1281012Lelio R Paula10/2015
4575(2^269083-9)/32036980997Lelio R Paula12/2012
457617^65810-2080976Lelio R Paula11/2015
457720^62236-2380971Lelio R Paula01/2016
45782^268974-11218180970Enzo Doria06/2014
4580L(387433)80969Renaud Lifchitz11/2003
4579V(387433)80969Serge Batalov03/2015
4581(2^268955-509203)/580963Lelio R Paula12/2012
4582(87398^16384+1)/6553780957Lelio R Paula11/2011
4583329^32160+32160^32980954Norbert Schneider11/2014
45842^268859-15980935Lelio R Paula05/2012
4585(2^268841-lucasV(1,2,268841)+1)/280929Mike Oakes11/2016
45862^268827+577580925Lelio R Paula07/2013
45872^268824-11025580925Enzo Doria05/2014
45882^268798-186832180917Enzo Doria04/2016
45892^268753-11462180903Enzo Doria05/2015
45902^268743+160580900Lelio R Paula07/2013
45916^103954-13980892Lelio R Paula12/2015
459210^80883+4980884Robert Price03/2011
459310^80883-8032780883Patrick De Geest07/2013
45946^103937+12180879Lelio R Paula12/2015
4595(26*10^80875-119)/380876Robert Price07/2016
4596(22699*2^268657+1)/635180875Lelio R Paula06/2014
45972^268581-86968810580851Lelio R Paula05/2016
4598(11*2^268521-1)/380834Lelio R Paula02/2014
45992^268516-24980832Yves Minet02/2012
46002^268500+1609580827Lelio R Paula07/2013
46013^169402+10080826Lelio R Paula12/2015
46029^84698+8^(84698-1)80823Robert Price03/2016
46032^268472-10973980819Enzo Doria04/2014
4604(9*2^268454+1)/3780813Lelio R Paula12/2012
4605(3*2^268502+1)/37790218843535364780811Lelio R Paula12/2012
4606134^37987-133^3798780803Jean-Louis Charton12/2005
460715^68702-7680800Lelio R Paula11/2015
46082^268408+780799Lelio R Paula05/2012
46092^268375+14180789Lelio R Paula05/2012
461012^74856-4780784Lelio R Paula11/2015
46116^103770-10780749Lelio R Paula12/2015
46123^169224-6280741Lelio R Paula12/2015
46135^115502-7280733Lelio R Paula10/2015
46142^268079-192780700Yves Minet10/2009
46152^268028+11780685Lelio R Paula05/2012
4616121^38738+12080683Norbert Schneider01/2015
4617(3^169097-8)/83580677Lelio R Paula12/2012
46182^267918+6780652Lelio R Paula05/2012
4619(302*10^80638+13)/980640Robert Price01/2017
46203^169004+266080636Lelio R Paula12/2015
46212^267860-11285980634Enzo Doria06/2014
46222^267828-11070580625Enzo Doria05/2014
46232^267743+1270580599Lelio R Paula07/2013
4624(22*10^80595+23)/980596Robert Price03/2015
46252^267674-5180578Lelio R Paula05/2012
4626(86*10^80571-41)/980572Robert Price11/2015
46272^267612-196580560Lelio R Paula07/2013
46282^267553+409780542Lelio R Paula07/2013
46297^95276-880518Robert Price01/2014
4630(15185*2^267457-1)/4782980513Lelio R Paula04/2015
46316^103467+16380513Lelio R Paula12/2015
4632(7*10^80490+143)/380491Robert Price04/2016
463386^41597-85^4159780470Robert Price04/2015
463413^72237+3080468Lelio R Paula11/2015
463517^65389+1480458Lelio R Paula11/2015
46362^267232+10580445Lelio R Paula05/2012
463711^77237-307200080435Enzo Doria01/2013
46382^267116-45995980410Enzo Doria06/2015
463938715!2+880406Robert Price01/2015
4640(2^267017+1)/380380H.&R. Lifchitz09/2000
46412^266968-4580366Lelio R Paula05/2012
464220^61768-6380363Lelio R Paula01/2016
46432^266920-11296780351Enzo Doria06/2014
464412^74428-1380322Lelio R Paula11/2015
46452^266680+2780279Lelio R Paula05/2012
46462^266630-13180264Lelio R Paula05/2012
46472^266598+7681980254Enzo Doria05/2016
46482^266587+188063380251Enzo Doria10/2016
46492^266541-11004980237Enzo Doria04/2014
465038635!2-880222Robert Price06/2015
46513^168111+168111^3-180210Robert Price04/2014
46522^266443+51380208Lelio R Paula07/2013
46532^266412-10991380199Enzo Doria04/2014
4654(10223*2^266417+1)/4509180199Lelio R Paula06/2014
465513^71988+6680191Lelio R Paula11/2015
465611^77002-432080190Enzo Doria01/2013
465718^63879-1380186Lelio R Paula11/2015
46582^266368-11229580185Enzo Doria06/2014
4659(3^168050+5)/102145480175Lelio R Paula10/2012
4660(22*10^80167+41)/980168Robert Price02/2015
4661(34*10^80162-43)/980163Ray Chandler12/2010
4662(38*10^80150-11)/980151Robert Price05/2015
4663(598*10^80149-31)/980151Robert Price02/2017
466419^62678-8080150Lelio R Paula12/2015
466510^80139+3234380140Patrick De Geest02/2011
466610^80139-980139Alexander Gramolin01/2011
46673^167955-10680135Lelio R Paula12/2015
46682^265998+7555980074Enzo Doria04/2016
46692^265969-10980180065Enzo Doria04/2014
46702^265888-11275780041Enzo Doria06/2014
46712^265809+170180017Lelio R Paula07/2013
4672gcd(V(957175),5*F(191435)*(F(191435)+1)+1)80014Serge Batalov04/2015
46733^167687-10480008Lelio R Paula02/2015
467411^76826-579080007Enzo Doria01/2013
467510^80000+8573180001Patrick De Geest10/2009
467610^80000-716980000Patrick De Geest09/2009
467710^79999+2239980000Patrick De Geest09/2009
467810^79999-7487379999Patrick De Geest09/2009
46793^167668+5879998Lelio R Paula02/2015
46802^265612+425779958Lelio R Paula07/2013
46815*3^167577+479956Lelio R Paula06/2014
4682(9179*2^265593-1)/979955Lelio R Paula04/2015
46836^102723-4379935Lelio R Paula04/2015
468411^76748-336079925Enzo Doria12/2012
4685(13*2^265498-1)/18711979919Lelio R Paula02/2014
46862^265399-10985579894Enzo Doria04/2014
4687(20^61403-1)/1979886Paul Bourdelais03/2010
468818^63635+5979880Lelio R Paula02/2015
4689(11*10^79867-107)/379868Robert Price11/2016
46903^167375+8079859Lelio R Paula02/2015
46915^114240-1448679851Enzo Doria02/2013
469249^47238+4879842Norbert Schneider07/2014
469391^40746+40746^9179824Norbert Schneider12/2014
4694(5*2^265118-1)/6179808Lelio R Paula02/2014
46952^265074+2842579796Lelio R Paula07/2013
46962^265072+118579795Lelio R Paula07/2013
46973^167167-3479759Robert Price11/2013
469812^73906+2979758Lelio R Paula02/2015
46992^264934+25579754Lelio R Paula07/2013
47004*10^79729-8779730Robert Price03/2017
47012^264846-11170179727Enzo Doria05/2014
47022^264831-11204179723Enzo Doria06/2014
47032^264816-45579718Yves Minet03/2012
470447^47667-4679704Theodore Burton02/2007
470513^71547+9679700Lelio R Paula03/2015
47062^264752-11288379699Enzo Doria06/2014
47072^264732+13379693Lelio R Paula05/2012
47088*3^167010+779685Lelio R Paula06/2014
470942^49087-4179681Norbert Schneider06/2014
4710(26*10^79678-119)/379679Robert Price07/2016
47112^264683-2179678Lelio R Paula05/2012
47127^94279+1879675Lelio R Paula02/2015
47132^264655-12779670Lelio R Paula02/2012
47142^264597-45904379652Enzo Doria05/2015
4715(21*2^264566+1)/579643Lelio R Paula10/2012
47162^264536+187002179634Enzo Doria05/2016
4717(17*2^264512-1)/35979625Lelio R Paula02/2014
47182^264477-10978379616Enzo Doria04/2014
471918^63419-133379609Enzo Doria03/2013
472013^71451-3679593Lelio R Paula03/2015
4721(2^264410-5)/12800260912179585Lelio R Paula10/2012
472219^62234+9079582Lelio R Paula03/2015
472312^73714+4979551Lelio R Paula02/2015
4724(3*2^264184-1)/143333979522Lelio R Paula02/2014
47252^264103-11253179503Enzo Doria06/2014
472619^62170+7879501Lelio R Paula03/2015
472711^76340-258079500Enzo Doria12/2012
4728(23*10^79492-11)/379493Robert Price10/2015
4729((2^132049+13650)^2+(2^132049+13650)+41)/2003/2384147379491Makoto Morimoto05/2016
47302^264060-11213379490Enzo Doria06/2014
4731((2^132049+4641)^2+(2^132049+4641)+41)/487/8537/1042614779488Makoto Morimoto05/2016
47329^83298+6^83298-2^8329879487Mike Oakes08/2010
473318^63319+3579483Lelio R Paula02/2015
473438303!2+25679461Robert Price01/2015
4735(29*10^79445+61)/979446Robert Price04/2015
47362^263902-19579443Lelio R Paula05/2012
47373^166499-11269679441Enzo Doria06/2014
473811^76279-276079437Enzo Doria12/2012
47396^102077-2579432Lelio R Paula03/2015
47402^263852-101779428Lelio R Paula07/2013
47412^263842-3379425Lelio R Paula05/2012
474212^73584-5579411Lelio R Paula02/2015
47432^263772-18579404Lelio R Paula05/2012
4744(15^67489+1)/1679373Paul Bourdelais03/2010
47452^263664+1501579371Lelio R Paula07/2013
474610^79362+3^7936379363Mike Oakes06/2010
4747Phi(163244,10)/2448661/685624979331Maksym Voznyy11/2015
47483^166262+4479328Lelio R Paula02/2015
47494*10^79327-6379328Robert Price12/2016
47502^263486+51379318Lelio R Paula07/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 26 2017 17:51 (Time in France)

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