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 ?
22513^229236+100109374Lelio R Paula03/2017
22522^363268-58695109355Lelio R Paula04/2017
22532^363191-112321109332Enzo Doria06/2014
22542^363120+3109311Donovan Johnson04/2006
2255(10^109297-1)/9109297Paul Bourdelais, Harvey Dubner04/2007
22562^363042-114641109287Enzo Doria04/2015
22572^363020-112793109280Enzo Doria06/2014
2258(67607*2^362695+1)/70499109183Lelio R Paula07/2014
2259(9*2^362644+1)/5109167Lelio R Paula03/2014
22605^156181+38109166Lelio R Paula02/2017
22613^228750+68109142Lelio R Paula03/2017
2262(10223*2^362376+1)/9109090Lelio R Paula07/2014
226365^60167-64^60167109078Robert Price08/2013
22647*3^228589-2109066Lelio R Paula09/2014
2265(78557*2^362188+1)/189109033Lelio R Paula07/2014
22662*7^129008+9109025Lelio R Paula11/2014
22672^361957+76367108960Enzo Doria05/2016
22682^361873-1411108935Yves Minet01/2013
2269(24737*2^361857+1)/35108933Lelio R Paula07/2014
227013^97745-24108883Lelio R Paula03/2017
227117^88475+8108864Lelio R Paula04/2017
22722^361567+51108843Lelio R Paula01/2012
22732^361563-109501108842Enzo Doria04/2014
227412^100852+83108838Lelio R Paula03/2017
22752^361497+767108822Lelio R Paula01/2012
22762^361280-112349108757Enzo Doria06/2014
22772^361271-5955108754Lelio R Paula04/2017
227812^100757+19108736Lelio R Paula03/2017
227914^94849-61108710Lelio R Paula05/2017
2280(19^85009-5^85009)/14108705Robert Price07/2013
2281(11*2^361027+1)/40463108677Lelio R Paula03/2014
22822^360973+1299108664Lelio R Paula04/2017
22832^360959-109101108660Enzo Doria04/2014
22846*5^155454+7108659Lelio R Paula11/2014
228510^108656+79108657Lelio R Paula02/2017
228610^108656-50001108656Patrick De Geest03/2017
22872^360918-35108648Lelio R Paula01/2012
2288(11*2^360886-1)/7108638Lelio R Paula03/2014
22892^360706-458903108584Enzo Doria04/2015
22902^360641-113185108564Enzo Doria07/2014
22912^360618+75019108557Enzo Doria04/2016
22923*5^155286+2108541Lelio R Paula11/2014
22937^128422+4108530Lelio R Paula11/2014
22947^128421-80108529Lelio R Paula03/2017
22952^360497+53807108521Yves Minet07/2010
22962^360366+1459108481Lelio R Paula09/2011
22972^360364-1499108481Yves Minet05/2013
229814^94642-23108472Lelio R Paula05/2017
22994*10^108412+9108413Robert Price05/2015
23002^360093-351103108399Enzo Doria06/2015
23012^360042+723108384Lelio R Paula01/2012
230285^56164-2108364Lelio R Paula10/2013
23032^359937-29323108352Enzo Doria07/2015
23042^359898-19997108341Enzo Doria06/2013
23052*5^154948-7108305Lelio R Paula11/2014
230610^108303+13108304Lelio R Paula02/2017
230710^108303-207959108303Patrick De Geest03/2017
23082^359730+753108290Lelio R Paula12/2011
23092^359650-19797108266Enzo Doria06/2013
231091^55259-90^55259108255Robert Price07/2015
23113^226845+68108233Lelio R Paula03/2017
23125^154822-12866108216Enzo Doria05/2014
2313(9*2^359480+1)/5108215Lelio R Paula03/2014
23142^359454-177108207Lelio R Paula12/2011
23156^139022-59108181Lelio R Paula02/2017
23162^359352-179108176Lelio R Paula12/2011
23172^359338-1858781108172Enzo Doria04/2016
231812^100230-97108167Lelio R Paula03/2017
2319(25*2^359297-1)/137108159Lelio R Paula03/2014
2320(2^359262-509203)/9108148Lelio R Paula12/2013
2321(3^226648-8)/352715633108131Lelio R Paula12/2013
23226^138956-59108129Lelio R Paula02/2017
23232^359184+30285108126Lelio R Paula04/2017
232413^97059+10108119Lelio R Paula03/2017
23252^359137-81108112Lelio R Paula12/2011
2326(15185*2^359105-1)/567108103Lelio R Paula05/2015
23272^359110-11655108103Lelio R Paula04/2017
23288*6^138875+5108067Lelio R Paula11/2014
23292^358987-216919108066Enzo Doria05/2014
233039^67918-67918^39108062Norbert Schneider02/2017
23312^358785-16933108006Enzo Doria05/2013
2332(2^358783+5)/33383108000Lelio R Paula12/2013
23336^138770-77107985Lelio R Paula02/2017
2334(2^358727-1017)/94178479107980Lelio R Paula12/2013
233510^107976+19107977Lelio R Paula02/2017
233610^107976-202103107976Patrick De Geest03/2017
23372^358684+75781107975Enzo Doria04/2016
233899^54094+2107952Lelio R Paula06/2013
2339(2^358583-9)/391107942Lelio R Paula12/2013
23402^358538+55107931Lelio R Paula12/2011
23412^358517-109009107925Enzo Doria03/2014
23423^226159+104107906Lelio R Paula03/2017
23432^358310-11655107863Lelio R Paula03/2017
23442^358275-112987107852Enzo Doria07/2014
23452^358233-20005107839Enzo Doria06/2013
23462^358194+175107828Lelio R Paula12/2011
2347107^53125-106107812Norbert Schneider12/2016
23483^225922-2107793Lelio R Paula10/2013
234912^99874-95107783Lelio R Paula03/2017
23502^358030-171107778Lelio R Paula12/2011
235111^103488-4170107772Enzo Doria12/2012
23522^357911-20089107742Enzo Doria06/2013
23532^357885+12857107735Yves Minet07/2010
23547^127473+40107728Lelio R Paula03/2017
23555*2^357850+9107725Lelio R Paula09/2014
23562^357786-291191107705Enzo Doria06/2015
235718^85798-23107700Lelio R Paula04/2017
23582^357688-1854269107675Enzo Doria09/2015
23592^357671-112225107670Enzo Doria06/2014
23602^357618-21005107654Enzo Doria06/2013
23612^357615-17505107653Enzo Doria05/2013
2362(30^72871-1)/29107638Robert Price12/2011
23632^357521+1870217107625Enzo Doria05/2016
23642^357477-1203107612Lelio R Paula03/2017
23655^153894-18107568Lelio R Paula02/2017
23662^357324-69059107566Enzo Doria11/2015
23672^357283-869688105107553Lelio R Paula01/2017
23682^357280-16805107552Enzo Doria05/2013
236910^107547+481719107548Patrick De Geest03/2017
237010^107547-47107547Lelio R Paula02/2017
237117^87396-32107537Lelio R Paula04/2017
23722^357081+107107493Lelio R Paula12/2011
23732^357058-3911107486Yves Minet04/2017
23743^225274+64107484Lelio R Paula03/2017
237518^85619-95107476Lelio R Paula04/2017
23763^225248-130107471Lelio R Paula03/2017
2377(5*2^356961+1)/143107455Lelio R Paula03/2014
23782^356935-18085107449Enzo Doria05/2013
237910^107409+37107410Lelio R Paula02/2017
238010^107409-329633107409Patrick De Geest03/2017
23812^356787-109027107404Enzo Doria04/2014
2382(2^356767+78557)/5107397Lelio R Paula12/2013
23835^153622-42107378Lelio R Paula02/2017
23842^356699-97305107378Lelio R Paula03/2017
23852^356654+85107364Lelio R Paula11/2011
23862^356641-19921107360Enzo Doria06/2013
23872^356623-465107355Lelio R Paula03/2017
238819^83945-92107345Lelio R Paula02/2017
238910^107334+28149107335Patrick De Geest03/2017
239010^107334-83107334Lelio R Paula02/2017
23912^356518+885107323Lelio R Paula03/2017
2392(3*2^356506-1)/467107317Lelio R Paula03/2014
23932^356442-114713107300Enzo Doria04/2015
23942^356425+72257107295Enzo Doria04/2016
23952^356351-112237107273Enzo Doria06/2014
2396(6^137845-11)/5107264Paul Bourdelais11/2011
23972^356322+74539107264Enzo Doria04/2016
23982^356274+1874479107250Enzo Doria06/2016
239920^82422-93107234Lelio R Paula02/2017
24002^356157-20365107214Enzo Doria06/2013
24012^356129-18949107206Enzo Doria05/2013
24022^356100-109587107197Enzo Doria04/2014
2403(31*2^355970+1)/5107159Lelio R Paula03/2014
24042^355968-64875107158Lelio R Paula01/2017
24052^355952+1870321107153Enzo Doria05/2016
24062^355915-117107142Lelio R Paula11/2011
2407(19*2^355838-1)/15107119Lelio R Paula03/2014
24083^224495-8107112Lelio R Paula12/2013
24097^126691-44107067Lelio R Paula03/2017
24104^177830-8243107065Mike Oakes02/2011
24112^355524-21237107024Enzo Doria06/2013
2412(10223*2^355515+1)/4855107022Lelio R Paula07/2014
24132^355494-19901107015Enzo Doria06/2013
24142^355454-869688105107003Lelio R Paula01/2017
24152^355366+54615106976Lelio R Paula01/2017
2416(31*2^355346-1)/1563106969Lelio R Paula03/2014
24172^355275-19861106949Enzo Doria06/2013
2418(9179*2^355234-1)/1915106937Lelio R Paula05/2015
24194*10^106892-3106893Robert Price10/2015
2420(66^58741+1)/67106881Paul Bourdelais08/2017
24212^354946-3106850M. Frind & P. Underwood08/2002
24222^354873-18693106828Enzo Doria05/2013
24232^354828+4257106814Lelio R Paula01/2017
2424(21^80761+1)/22106783Paul Bourdelais03/2010
24252^354640-354640+1106758Robert Price10/2014
24262^354585+95106741Lelio R Paula10/2011
24272^354553+189106732Lelio R Paula10/2011
24282^354514-109031106720Enzo Doria04/2014
24292^354509-109465106718Enzo Doria04/2014
2430(15*2^354478-1)/26983106706Lelio R Paula03/2014
243115^90710+28106684Lelio R Paula04/2017
24327^126237+34106683Lelio R Paula03/2017
24332^354385-115315106681Enzo Doria06/2015
24342^354327-19305106664Enzo Doria06/2013
2435(35*10^106649+1)/9106650Serge Batalov11/2010
243610^106636+97106637Lelio R Paula02/2017
243710^106636-22923106636Patrick De Geest03/2017
24382^354220-57106631Lelio R Paula10/2011
24392^354157-17041106612Enzo Doria05/2013
244012^98778+73106600Lelio R Paula02/2017
24412^354064+1870651106584Enzo Doria05/2016
24422^353992-57106563Lelio R Paula10/2011
24432^353832-1853849106515Enzo Doria09/2015
2444(7^126037-1)/6106513Paul Bourdelais09/2008
24452^353794-18453106503Enzo Doria05/2013
24462^353728+7695106483Lelio R Paula01/2017
24472^353672-303106466Yves Minet02/2012
24486^136811+101106460Lelio R Paula02/2017
24492^353641+1871981106457Enzo Doria05/2016
24502^353553+54615106431Lelio R Paula01/2017
24512^353544-18897106428Enzo Doria05/2013
24526^136729-133106396Lelio R Paula02/2017
24532^353418+1605106390Lelio R Paula01/2017
24542^353387+65106381Lelio R Paula10/2011
24552^353372+74311106376Enzo Doria04/2016
24562^353344-3693106368Yves Minet03/2017
24572^353277-20089106347Enzo Doria06/2013
24582^353275+72173106347Enzo Doria04/2016
24592^353268-17705106345Enzo Doria05/2013
24602^353267-19857106344Enzo Doria06/2013
2461222748^3+3^222748106278Anatoly F. Selevich12/2010
2462(9179*2^353019-1)/9106273Lelio R Paula05/2015
24632^353025+72257106272Enzo Doria04/2016
24652^352932-20345106244Enzo Doria06/2013
2464(2^353011-3)/745325861246794515484535106244Lelio R Paula12/2013
24662^352883-187106229Lelio R Paula10/2011
246720^81649-19^81649106228Jean-Louis Charton03/2011
24682^352814-131106208Lelio R Paula10/2011
24692^352752+73951106189Enzo Doria04/2016
24706^136434+5106167Lelio R Paula11/2014
24717*5^151872-8106155Lelio R Paula11/2014
24722^352601-1604809106144Enzo Doria05/2015
247312^98353-43106141Lelio R Paula02/2017
24742^352585-18901106139Enzo Doria05/2013
2475(2^352554-3)/193106128Lelio R Paula12/2013
24762^352540+15015106126Lelio R Paula01/2017
24772^352524-3149106121Yves Minet10/2014
24782^352486-1858781106109Enzo Doria04/2016
24792^352444+12705106097Lelio R Paula01/2017
24802^352228-18953106032Enzo Doria05/2013
24812^352107+1872533105995Enzo Doria05/2016
24822^352066-2591105983Yves Minet07/2014
24832^352030+715105972Lelio R Paula10/2011
24849*6^136176-5105967Lelio R Paula11/2014
2485155^48377+2105962Lelio R Paula08/2013
24862^351865+1869707105922Enzo Doria05/2016
24872^351831+23105912Lelio R Paula10/2011
24889*2^351784-5105899Lelio R Paula09/2014
24892^351671-112387105864Enzo Doria06/2014
24902^351669-109501105863Enzo Doria04/2014
24912^351644+74731105856Enzo Doria04/2016
249213^95025-42105853Lelio R Paula12/2016
24932^351599+15015105842Lelio R Paula01/2017
249419^82763+90105834Lelio R Paula01/2017
2495(9179*2^351540-1)/221105826Lelio R Paula05/2015
249620^81329-51105812Lelio R Paula01/2017
24972^351483+28425105807Lelio R Paula01/2017
249815^89960+86105802Lelio R Paula02/2017
24992^351460-17289105801Enzo Doria05/2013
250019^82735+22105798Lelio R Paula01/2017


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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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