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 ?
22512^356787-109027107404Enzo Doria04/2014
2252(2^356767+78557)/5107397Lelio R Paula12/2013
22535^153622-42107378Lelio R Paula02/2017
22542^356699-97305107378Lelio R Paula03/2017
22552^356654+85107364Lelio R Paula11/2011
22562^356641-19921107360Enzo Doria06/2013
22572^356623-465107355Lelio R Paula03/2017
225819^83945-92107345Lelio R Paula02/2017
225910^107334+28149107335Patrick De Geest03/2017
226010^107334-83107334Lelio R Paula02/2017
22612^356518+885107323Lelio R Paula03/2017
2262(3*2^356506-1)/467107317Lelio R Paula03/2014
22632^356442-114713107300Enzo Doria04/2015
22642^356425+72257107295Enzo Doria04/2016
22652^356351-112237107273Enzo Doria06/2014
2266(6^137845-11)/5107264Paul Bourdelais11/2011
22672^356322+74539107264Enzo Doria04/2016
22682^356274+1874479107250Enzo Doria06/2016
226920^82422-93107234Lelio R Paula02/2017
22702^356157-20365107214Enzo Doria06/2013
22712^356129-18949107206Enzo Doria05/2013
22722^356100-109587107197Enzo Doria04/2014
2273(31*2^355970+1)/5107159Lelio R Paula03/2014
22742^355968-64875107158Lelio R Paula01/2017
22752^355952+1870321107153Enzo Doria05/2016
22762^355915-117107142Lelio R Paula11/2011
2277(19*2^355838-1)/15107119Lelio R Paula03/2014
22783^224495-8107112Lelio R Paula12/2013
22797^126691-44107067Lelio R Paula03/2017
22804^177830-8243107065Mike Oakes02/2011
22812^355524-21237107024Enzo Doria06/2013
2282(10223*2^355515+1)/4855107022Lelio R Paula07/2014
22832^355494-19901107015Enzo Doria06/2013
22842^355454-869688105107003Lelio R Paula01/2017
22852^355366+54615106976Lelio R Paula01/2017
2286(31*2^355346-1)/1563106969Lelio R Paula03/2014
22872^355275-19861106949Enzo Doria06/2013
2288(9179*2^355234-1)/1915106937Lelio R Paula05/2015
22894*10^106892-3106893Robert Price10/2015
22902^354946-3106850M. Frind & P. Underwood08/2002
22912^354873-18693106828Enzo Doria05/2013
22922^354828+4257106814Lelio R Paula01/2017
2293(21^80761+1)/22106783Paul Bourdelais03/2010
22942^354640-354640+1106758Robert Price10/2014
22952^354585+95106741Lelio R Paula10/2011
22962^354553+189106732Lelio R Paula10/2011
22972^354514-109031106720Enzo Doria04/2014
22982^354509-109465106718Enzo Doria04/2014
2299(15*2^354478-1)/26983106706Lelio R Paula03/2014
23007^126237+34106683Lelio R Paula03/2017
23012^354385-115315106681Enzo Doria06/2015
23022^354327-19305106664Enzo Doria06/2013
2303(35*10^106649+1)/9106650Serge Batalov11/2010
230410^106636+97106637Lelio R Paula02/2017
230510^106636-22923106636Patrick De Geest03/2017
23062^354220-57106631Lelio R Paula10/2011
23072^354157-17041106612Enzo Doria05/2013
230812^98778+73106600Lelio R Paula02/2017
23092^354064+1870651106584Enzo Doria05/2016
23102^353992-57106563Lelio R Paula10/2011
23112^353832-1853849106515Enzo Doria09/2015
2312(7^126037-1)/6106513Paul Bourdelais09/2008
23132^353794-18453106503Enzo Doria05/2013
23142^353728+7695106483Lelio R Paula01/2017
23152^353672-303106466Yves Minet02/2012
23166^136811+101106460Lelio R Paula02/2017
23172^353641+1871981106457Enzo Doria05/2016
23182^353553+54615106431Lelio R Paula01/2017
23192^353544-18897106428Enzo Doria05/2013
23206^136729-133106396Lelio R Paula02/2017
23212^353418+1605106390Lelio R Paula01/2017
23222^353387+65106381Lelio R Paula10/2011
23232^353372+74311106376Enzo Doria04/2016
23242^353344-3693106368Yves Minet03/2017
23252^353277-20089106347Enzo Doria06/2013
23262^353275+72173106347Enzo Doria04/2016
23272^353268-17705106345Enzo Doria05/2013
23282^353267-19857106344Enzo Doria06/2013
2329222748^3+3^222748106278Anatoly F. Selevich12/2010
2330(9179*2^353019-1)/9106273Lelio R Paula05/2015
23312^353025+72257106272Enzo Doria04/2016
23322^352932-20345106244Enzo Doria06/2013
2333(2^353011-3)/745325861246794515484535106244Lelio R Paula12/2013
23342^352883-187106229Lelio R Paula10/2011
233520^81649-19^81649106228Jean-Louis Charton03/2011
23362^352814-131106208Lelio R Paula10/2011
23372^352752+73951106189Enzo Doria04/2016
23386^136434+5106167Lelio R Paula11/2014
23397*5^151872-8106155Lelio R Paula11/2014
23402^352601-1604809106144Enzo Doria05/2015
234112^98353-43106141Lelio R Paula02/2017
23422^352585-18901106139Enzo Doria05/2013
2343(2^352554-3)/193106128Lelio R Paula12/2013
23442^352540+15015106126Lelio R Paula01/2017
23452^352524-3149106121Yves Minet10/2014
23462^352486-1858781106109Enzo Doria04/2016
23472^352444+12705106097Lelio R Paula01/2017
23482^352228-18953106032Enzo Doria05/2013
23492^352107+1872533105995Enzo Doria05/2016
23502^352066-2591105983Yves Minet07/2014
23512^352030+715105972Lelio R Paula10/2011
23529*6^136176-5105967Lelio R Paula11/2014
2353155^48377+2105962Lelio R Paula08/2013
23542^351865+1869707105922Enzo Doria05/2016
23552^351831+23105912Lelio R Paula10/2011
23569*2^351784-5105899Lelio R Paula09/2014
23572^351671-112387105864Enzo Doria06/2014
23582^351669-109501105863Enzo Doria04/2014
23592^351644+74731105856Enzo Doria04/2016
236013^95025-42105853Lelio R Paula12/2016
23612^351599+15015105842Lelio R Paula01/2017
236219^82763+90105834Lelio R Paula01/2017
2363(9179*2^351540-1)/221105826Lelio R Paula05/2015
236420^81329-51105812Lelio R Paula01/2017
23652^351483+28425105807Lelio R Paula01/2017
236615^89960+86105802Lelio R Paula02/2017
23672^351460-17289105801Enzo Doria05/2013
236819^82735+22105798Lelio R Paula01/2017
23692^351435-109077105793Enzo Doria04/2014
23702^351393+1089105780Lelio R Paula01/2017
23712^351364+72631105772Enzo Doria04/2016
23722^351305+1872467105754Enzo Doria05/2016
23733^221649+16105754Lelio R Paula11/2016
23748*3^221637-5105749Lelio R Paula09/2014
23752^351279-2780449105746Enzo Doria03/2016
237615^89903-26105735Lelio R Paula02/2017
23772^351213-73105726Lelio R Paula10/2011
23782^351192-4589105720Yves Minet07/2011
237920^81250-33105709Lelio R Paula12/2016
23802^351076-113159105685Enzo Doria07/2014
238193^53688-2105684Lelio R Paula09/2013
23822^351060-4559105680Yves Minet07/2011
238311^101473-750105674Enzo Doria11/2012
23843*5^151181-8105672Lelio R Paula11/2014
238515^89831-34105650Lelio R Paula02/2017
238711^101448-360105648Enzo Doria08/2012
23863*7^125011+4105648Lelio R Paula11/2014
23882^350943-113269105645Enzo Doria07/2014
23892^350868-19725105622Enzo Doria06/2013
23902^350858-59291105619Enzo Doria10/2015
23912^350851+135105617Lelio R Paula10/2011
23922^350841-741105614Lelio R Paula01/2017
23938*10^105571+3105572Robert Price08/2015
23942*5^151026-3105563Lelio R Paula11/2014
2395(2^350702+5)/34264674063105562Lelio R Paula12/2013
23966^135647-5^135647105554Jean-Louis Charton02/2009
23973^221211+236105545Lelio R Paula11/2016
239810^105515+33105516Lelio R Paula11/2016
239910^105515-41033105515Patrick De Geest12/2016
2400(29*2^350473-1)/267927105499Lelio R Paula03/2014
240117^85732-72105489Lelio R Paula01/2017
24022^350307-110329105453Enzo Doria05/2014
24032^350253-20365105437Enzo Doria06/2013
2404(3*29^72089-1075)/4105423Curtis Bright05/2015
24052^350139-109009105403Enzo Doria04/2014
24063*5^150763+4105380Lelio R Paula11/2014
240712^97643+91105375Lelio R Paula02/2017
24086*5^150744-7105367Lelio R Paula11/2014
24092^349996-112169105360Enzo Doria06/2014
241011^101142-1080105329Enzo Doria12/2012
2411(68*10^105320-41)/9105321Robert Price10/2013
24123^220712-9934105307Enzo Doria05/2014
24137*10^105296+9105297Robert Price09/2015
24142^349739+1873373105282Enzo Doria06/2016
24157^124574+24105278Lelio R Paula11/2016
24162^349708-20957105273Enzo Doria06/2013
24172^349649-20469105255Enzo Doria06/2013
24182^349607-20109105243Enzo Doria06/2013
24192^349594-19085105239Enzo Doria05/2013
24202^349530+1874479105220Enzo Doria06/2016
2421(3^220528+8)/8081105215Lelio R Paula12/2013
24223^220464-112852105189Enzo Doria07/2014
24232^349419-17349105186Enzo Doria05/2013
24242^349400-2579105180Yves Minet07/2014
24258*5^150471+3105176Lelio R Paula11/2014
242613^94403+94105160Lelio R Paula12/2016
24272^349301-112309105151Enzo Doria06/2014
24289*2^349220+5105127Lelio R Paula09/2014
24297*3^220317+8105119Lelio R Paula09/2014
24307^124386+88105119Lelio R Paula11/2016
24312^349171-19657105111Enzo Doria06/2013
2432(2^(6*58185+1)-5)/3105093Kevin Acres11/2013
2433(2^349111-5)/3105093Lelio R Paula12/2013
24342^348981-2797573105054Enzo Doria04/2016
24352^348869-6555105021Lelio R Paula01/2017
24365^150217+78104998Lelio R Paula11/2016
24372^348703-113005104971Enzo Doria06/2014
24392^348612-809104943Yves Minet05/2013
2438(73*10^104942-1)/9104943Robert Price01/2015
24402^348583-350407104934Enzo Doria06/2015
24412^348531-949104919Yves Minet05/2012
244220^80636-59104910Lelio R Paula12/2016
24432^348437+35104890Lelio R Paula09/2011
24442^348348+135104864Lelio R Paula09/2011
2445(2^348284+9)/25104843Lelio R Paula12/2013
244675^55914-74104843Norbert Schneider01/2015
24472^348268+255255104840Lelio R Paula01/2017
24485^149985-52104836Lelio R Paula11/2016
24492^348224-20249104826Enzo Doria06/2013
24502^348212-20105104823Enzo Doria06/2013
245120^80562+19104814Lelio R Paula12/2016
24522^348149-20053104804Enzo Doria06/2013
24532^348095-171104788Lelio R Paula09/2011
24542^348003-20377104760Enzo Doria06/2013
24552^347994-741104757Lelio R Paula12/2016
2456(13*2^347972-1)/282309104746Lelio R Paula03/2014
24572^347910-109937104732Enzo Doria04/2014
24585^149794+28104702Lelio R Paula11/2016
2459(16^86939+3^86939)/19104684Robert Price06/2013
2460(15^89009-1)/14104682Paul Bourdelais03/2010
24612^347731-18609104678Enzo Doria05/2013
24624*6^134519+7104677Lelio R Paula11/2014
24632^347612-18545104642Enzo Doria05/2013
24646^134465+95104635Lelio R Paula11/2016
24652^347517-17301104614Enzo Doria05/2013
24663^219222-310104596Lelio R Paula11/2016
2467(15*2^347399-1)/13104578Lelio R Paula03/2014
24682^347372-17853104570Enzo Doria05/2013
24692^347314+99104552Lelio R Paula09/2011
24702^347300-22233104548Enzo Doria06/2013
24712^347287-19845104544Enzo Doria06/2013
2472(31*2^347254-1)/891104533Lelio R Paula03/2014
24735*F(250091)*(F(250091)-1)+1104532Serge Batalov04/2015
24747*2^347239-3104531Lelio R Paula09/2014
2475(3^219098-8)/514147439969104525Lelio R Paula12/2013
24765*3^219047+8104513Lelio R Paula09/2014
24772^347148-109073104502Enzo Doria04/2014
24782^347129-20145104497Enzo Doria06/2013
24792^346923-19585104435Enzo Doria05/2013
2480(11*2^346864-1)/175104416Lelio R Paula03/2014
24812^346854+346854^2+1104414Robert Price06/2014
24822^346834+11715104408Lelio R Paula04/2015
248379^55009+78104387Norbert Schneider02/2015
24843^218744+58104368Lelio R Paula11/2016
24852^346649+65104352Lelio R Paula09/2011
24862^346638-17265104349Enzo Doria05/2013
24882^346527-111817104316Enzo Doria05/2014
24876^134055+101104316Lelio R Paula11/2016
24896^134013+163104283Lelio R Paula11/2016
249018^83049-89104250Lelio R Paula01/2017
249118^83021-91104214Lelio R Paula01/2017
249210^104212+128779104213Patrick De Geest05/2016
249310^104212+237447104213Patrick De Geest05/2016
249410^104212+242139104213Patrick De Geest05/2016
249510^104212+269199104213Patrick De Geest05/2016
2496(10^104212-71)/1104212Serge Batalov12/2014
24972^346078+7695104180Lelio R Paula12/2016
24982^346055-19537104173Enzo Doria05/2013
2499(3*2^346057+1)/77104173Lelio R Paula12/2013
25002^346037-20125104168Enzo Doria06/2013


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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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