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 ?
47512^271064-279020981599Enzo Doria03/2016
4752(13*2^271053-1)/309581593Lelio R Paula02/2014
47532^271040-5781592Lelio R Paula06/2012
4754(14*10^81585+73)/381586Robert Price04/2016
4755127^38779+12681584Norbert Schneider02/2015
475618^64966-4381551Lelio R Paula11/2015
4757(2^270840+47)/59181529Lelio R Paula12/2012
475820^62654+8781515Lelio R Paula01/2016
4759(19*10^81488+191)/381489Robert Price01/2017
47608*10^81487+2181488Robert Price02/2017
4761(73*10^81485+107)/981486Robert Price08/2016
4762536^29847+29847^53681458Norbert Schneider03/2017
47638*7^96378+981450Lelio R Paula10/2014
47642^270546-11034581443Enzo Doria05/2014
476513^73105-6081435Lelio R Paula11/2015
476644^49524+4381391Norbert Schneider06/2014
4767(3*2^270368-1)/1381389Lelio R Paula02/2014
4768(10^81363+719)/981363Serge Batalov12/2014
4769(10^81353+449)/981353Serge Batalov12/2014
477014^70978-8981350Lelio R Paula11/2015
477111^78108-204081342Enzo Doria12/2012
47723^170400-5881302Lelio R Paula12/2015
477310^81297+3699181298Patrick De Geest06/2013
477410^81297-5781297Robert Price05/2011
47752^270055-11304781295Enzo Doria07/2014
477618^64759-5581291Lelio R Paula11/2015
4777(2^269987+1)/381274H.&R. Lifchitz10/2000
4778(31^54493-1)/3081268Alexander Zhirkov10/2010
4779(2^270059-1)/540119/6481417/712497615775672596781265Dario Alpern09/2014
4780(2^269816+7)/42490181218Lelio R Paula12/2012
4781(23*10^81214+1)/381215Serge Batalov06/2009
4782(17*2^269720+1)/30381193Lelio R Paula07/2012
478356^46441-55^4644181188Robert Price10/2013
47852^269664+17781177Lelio R Paula06/2012
4784(13*2^269665-1)/18581177Lelio R Paula02/2014
47862^269539-11224981140Enzo Doria06/2014
4787((2*170026-3)*3^(170026-1)+1)/481128Robert Price01/2015
4788(2^269495-5)/981126Lelio R Paula12/2012
47892^269490-362381125Yves Minet10/2009
4790(55459*2^269444+1)/3581114Lelio R Paula06/2014
4791(2^269417+78557)/525781099Lelio R Paula12/2012
47924*5^116011-781089Lelio R Paula10/2014
47937*10^81058+7981059Robert Price02/2017
47942^269236-10990781049Enzo Doria04/2014
4795(8*10^81029-11)/381030Erik Branger03/2014
47963*10^81021+781022Erik Branger11/2013
47976^104115+10381018Lelio R Paula12/2015
47982^269120+186915181014Enzo Doria05/2016
47995^115901+1281012Lelio R Paula10/2015
4800(2^269083-9)/32036980997Lelio R Paula12/2012
480117^65810-2080976Lelio R Paula11/2015
480220^62236-2380971Lelio R Paula01/2016
48032^268974-11218180970Enzo Doria06/2014
4805L(387433)80969Renaud Lifchitz11/2003
4804V(387433)80969Serge Batalov03/2015
4806(2^268955-509203)/580963Lelio R Paula12/2012
4807(87398^16384+1)/6553780957Lelio R Paula11/2011
4808329^32160+32160^32980954Norbert Schneider11/2014
48092^268859-15980935Lelio R Paula05/2012
4810(2^268841-lucasV(1,2,268841)+1)/280929Mike Oakes11/2016
48112^268827+577580925Lelio R Paula07/2013
48122^268824-11025580925Enzo Doria05/2014
48132^268798-186832180917Enzo Doria04/2016
48142^268753-11462180903Enzo Doria05/2015
48152^268743+160580900Lelio R Paula07/2013
48166^103954-13980892Lelio R Paula12/2015
481710^80883+4980884Robert Price03/2011
481810^80883-8032780883Patrick De Geest07/2013
48196^103937+12180879Lelio R Paula12/2015
4820(26*10^80875-119)/380876Robert Price07/2016
4821(22699*2^268657+1)/635180875Lelio R Paula06/2014
48222^268581-86968810580851Lelio R Paula05/2016
4823(11*2^268521-1)/380834Lelio R Paula02/2014
48242^268516-24980832Yves Minet02/2012
48252^268500+1609580827Lelio R Paula07/2013
48263^169402+10080826Lelio R Paula12/2015
48279^84698+8^(84698-1)80823Robert Price03/2016
48282^268472-10973980819Enzo Doria04/2014
4829(9*2^268454+1)/3780813Lelio R Paula12/2012
4830(3*2^268502+1)/37790218843535364780811Lelio R Paula12/2012
4831134^37987-133^3798780803Jean-Louis Charton12/2005
483215^68702-7680800Lelio R Paula11/2015
48332^268408+780799Lelio R Paula05/2012
48342^268375+14180789Lelio R Paula05/2012
483512^74856-4780784Lelio R Paula11/2015
48366^103770-10780749Lelio R Paula12/2015
48373^169224-6280741Lelio R Paula12/2015
4838p(16866)#/2+6480741Robert Price03/2017
48395^115502-7280733Lelio R Paula10/2015
48402^268079-192780700Yves Minet10/2009
48412^268028+11780685Lelio R Paula05/2012
4842121^38738+12080683Norbert Schneider01/2015
4843(3^169097-8)/83580677Lelio R Paula12/2012
48442^267918+6780652Lelio R Paula05/2012
4845(302*10^80638+13)/980640Robert Price01/2017
48463^169004+266080636Lelio R Paula12/2015
48472^267860-11285980634Enzo Doria06/2014
48482^267828-11070580625Enzo Doria05/2014
48492^267743+1270580599Lelio R Paula07/2013
4850(22*10^80595+23)/980596Robert Price03/2015
48512^267674-5180578Lelio R Paula05/2012
4852(86*10^80571-41)/980572Robert Price11/2015
48532^267612-196580560Lelio R Paula07/2013
48542^267553+409780542Lelio R Paula07/2013
48557^95276-880518Robert Price01/2014
4856(15185*2^267457-1)/4782980513Lelio R Paula04/2015
48576^103467+16380513Lelio R Paula12/2015
4858(7*10^80490+143)/380491Robert Price04/2016
485986^41597-85^4159780470Robert Price04/2015
486013^72237+3080468Lelio R Paula11/2015
486117^65389+1480458Lelio R Paula11/2015
4862423^30634+30634^42380456Norbert Schneider05/2017
48632^267232+10580445Lelio R Paula05/2012
486411^77237-307200080435Enzo Doria01/2013
48652^267116-45995980410Enzo Doria06/2015
486638715!2+880406Robert Price01/2015
4867(2^267017+1)/380380H.&R. Lifchitz09/2000
48682^266968-4580366Lelio R Paula05/2012
486920^61768-6380363Lelio R Paula01/2016
48702^266920-11296780351Enzo Doria06/2014
487112^74428-1380322Lelio R Paula11/2015
48722^266680+2780279Lelio R Paula05/2012
48732^266630-13180264Lelio R Paula05/2012
48742^266598+7681980254Enzo Doria05/2016
48752^266587+188063380251Enzo Doria10/2016
48762^266541-11004980237Enzo Doria04/2014
487738635!2-880222Robert Price06/2015
48783^168111+168111^3-180210Robert Price04/2014
48792^266443+51380208Lelio R Paula07/2013
4880(26*10^80200+61)/380201Robert Price06/2017
48812^266412-10991380199Enzo Doria04/2014
4882(10223*2^266417+1)/4509180199Lelio R Paula06/2014
488313^71988+6680191Lelio R Paula11/2015
488411^77002-432080190Enzo Doria01/2013
488518^63879-1380186Lelio R Paula11/2015
48862^266368-11229580185Enzo Doria06/2014
4887(3^168050+5)/102145480175Lelio R Paula10/2012
4888(22*10^80167+41)/980168Robert Price02/2015
4889(34*10^80162-43)/980163Ray Chandler12/2010
4890(38*10^80150-11)/980151Robert Price05/2015
4891(598*10^80149-31)/980151Robert Price02/2017
489219^62678-8080150Lelio R Paula12/2015
489310^80139+3234380140Patrick De Geest02/2011
489410^80139-980139Alexander Gramolin01/2011
48953^167955-10680135Lelio R Paula12/2015
48962^265998+7555980074Enzo Doria04/2016
48972^265969-10980180065Enzo Doria04/2014
48982^265888-11275780041Enzo Doria06/2014
48992^265809+170180017Lelio R Paula07/2013
4900gcd(V(957175),5*F(191435)*(F(191435)+1)+1)80014Serge Batalov04/2015
49013^167687-10480008Lelio R Paula02/2015
490211^76826-579080007Enzo Doria01/2013
490310^80000+8573180001Patrick De Geest10/2009
490410^80000-716980000Patrick De Geest09/2009
490510^79999+2239980000Patrick De Geest09/2009
490610^79999-7487379999Patrick De Geest09/2009
49073^167668+5879998Lelio R Paula02/2015
49082^265612+425779958Lelio R Paula07/2013
49095*3^167577+479956Lelio R Paula06/2014
4910(9179*2^265593-1)/979955Lelio R Paula04/2015
49116^102723-4379935Lelio R Paula04/2015
491211^76748-336079925Enzo Doria12/2012
4913(13*2^265498-1)/18711979919Lelio R Paula02/2014
49142^265399-10985579894Enzo Doria04/2014
4915(20^61403-1)/1979886Paul Bourdelais03/2010
491618^63635+5979880Lelio R Paula02/2015
4917(11*10^79867-107)/379868Robert Price11/2016
49183^167375+8079859Lelio R Paula02/2015
49195^114240-1448679851Enzo Doria02/2013
492049^47238+4879842Norbert Schneider07/2014
49212^265212-377979837Yves Minet04/2017
492291^40746+40746^9179824Norbert Schneider12/2014
4923(68*10^79813-257)/979814Robert Price06/2017
4924(5*2^265118-1)/6179808Lelio R Paula02/2014
49252^265074+2842579796Lelio R Paula07/2013
49262^265072+118579795Lelio R Paula07/2013
4927p(16682)#/2-12879771Robert Price05/2017
49283^167167-3479759Robert Price11/2013
492912^73906+2979758Lelio R Paula02/2015
49302^264934+25579754Lelio R Paula07/2013
49314*10^79729-8779730Robert Price03/2017
49322^264846-11170179727Enzo Doria05/2014
49332^264831-11204179723Enzo Doria06/2014
49342^264816-45579718Yves Minet03/2012
4935(55*10^79711+89)/979712Robert Price09/2017
493647^47667-4679704Theodore Burton02/2007
493713^71547+9679700Lelio R Paula03/2015
49382^264752-11288379699Enzo Doria06/2014
49392^264732+13379693Lelio R Paula05/2012
49408*3^167010+779685Lelio R Paula06/2014
494142^49087-4179681Norbert Schneider06/2014
4942(26*10^79678-119)/379679Robert Price07/2016
49432^264683-2179678Lelio R Paula05/2012
49447^94279+1879675Lelio R Paula02/2015
49452^264655-12779670Lelio R Paula02/2012
49462^264597-45904379652Enzo Doria05/2015
4947(21*2^264566+1)/579643Lelio R Paula10/2012
49482^264536+187002179634Enzo Doria05/2016
4949(17*2^264512-1)/35979625Lelio R Paula02/2014
49502^264477-10978379616Enzo Doria04/2014
495118^63419-133379609Enzo Doria03/2013
495213^71451-3679593Lelio R Paula03/2015
4953(2^264410-5)/12800260912179585Lelio R Paula10/2012
495419^62234+9079582Lelio R Paula03/2015
495512^73714+4979551Lelio R Paula02/2015
4956(3*2^264184-1)/143333979522Lelio R Paula02/2014
49572^264103-11253179503Enzo Doria06/2014
495819^62170+7879501Lelio R Paula03/2015
495911^76340-258079500Enzo Doria12/2012
4960(23*10^79492-11)/379493Robert Price10/2015
4961((2^132049+13650)^2+(2^132049+13650)+41)/2003/2384147379491Makoto Morimoto05/2016
49622^264060-11213379490Enzo Doria06/2014
4963((2^132049+4641)^2+(2^132049+4641)+41)/487/8537/1042614779488Makoto Morimoto05/2016
49649^83298+6^83298-2^8329879487Mike Oakes08/2010
496518^63319+3579483Lelio R Paula02/2015
496638303!2+25679461Robert Price01/2015
4967(29*10^79445+61)/979446Robert Price04/2015
49682^263902-19579443Lelio R Paula05/2012
49693^166499-11269679441Enzo Doria06/2014
497011^76279-276079437Enzo Doria12/2012
49716^102077-2579432Lelio R Paula03/2015
49722^263852-101779428Lelio R Paula07/2013
49732^263842-3379425Lelio R Paula05/2012
497412^73584-5579411Lelio R Paula02/2015
49752^263772-18579404Lelio R Paula05/2012
4976(15^67489+1)/1679373Paul Bourdelais03/2010
49772^263664+1501579371Lelio R Paula07/2013
497810^79362+3^7936379363Mike Oakes06/2010
4979Phi(163244,10)/2448661/685624979331Maksym Voznyy11/2015
49803^166262+4479328Lelio R Paula02/2015
49814*10^79327-6379328Robert Price12/2016
49822^263486+51379318Lelio R Paula07/2013
49832^263448-51950979306Paul Bourdelais03/2013
498421^59971-20^5997179295Robert Price05/2012
49852^263372+12379283Lelio R Paula05/2012
498617^64429+8479277Lelio R Paula03/2015
498711^76124-1143079275Enzo Doria12/2012
4988(206*10^79268-17)/979270Robert Price03/2017
498913^71157+1879265Lelio R Paula03/2015
49902^263297+6583579261Lelio R Paula07/2013
499119^61980-1879258Theodore Burton12/2005
49922*10^79242+9379243Robert Price07/2016
4993(88^40751-1)/8779238Paul Bourdelais08/2017
4994(103*29^54179-39)/479233Curtis Bright05/2015
49959^83024-83024^979226Norbert Schneider08/2017
499617^64382-2679219Lelio R Paula03/2015
49977^93733-7479214Lelio R Paula02/2015
499815^67352+3879213Lelio R Paula02/2015
49992^263135-11023579212Enzo Doria05/2014
50002^263044+425779185Lelio R Paula07/2013


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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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