PRP Records

Probable Primes Top 10000

(252538 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 (> 50000) Who ? When ?
27512^360706-458903108584Enzo Doria04/2015
27522^360641-113185108564Enzo Doria07/2014
27532^360618+75019108557Enzo Doria04/2016
2754(14*10^108545-221)/9108546Robert Price04/2018
2755(44*10^108544-233)/9108545Robert Price01/2019
27563*5^155286+2108541Lelio R Paula11/2014
27577^128422+4108530Lelio R Paula11/2014
27587^128421-80108529Lelio R Paula03/2017
27592^360497+53807108521Yves Minet07/2010
27602^360366+1459108481Lelio R Paula09/2011
27612^360364-1499108481Yves Minet05/2013
276214^94642-23108472Lelio R Paula05/2017
27634*10^108412+9108413Robert Price05/2015
27642^360093-351103108399Enzo Doria06/2015
27652^360042+723108384Lelio R Paula01/2012
276685^56164-2108364Lelio R Paula10/2013
27672^359937-29323108352Enzo Doria07/2015
27682^359898-19997108341Enzo Doria06/2013
27692*5^154948-7108305Lelio R Paula11/2014
277010^108303+13108304Lelio R Paula02/2017
277110^108303-207959108303Patrick De Geest03/2017
27722^359730+753108290Lelio R Paula12/2011
2773(8*10^108273+13)/3108274Robert Price06/2018
27742^359650-19797108266Enzo Doria06/2013
277591^55259-90^55259108255Robert Price07/2015
27764*10^108238-71108239Robert Price12/2018
27773^226845+68108233Lelio R Paula03/2017
27785^154822-12866108216Enzo Doria05/2014
2779(9*2^359480+1)/5108215Lelio R Paula03/2014
27802^359454-177108207Lelio R Paula12/2011
27816^139022-59108181Lelio R Paula02/2017
27822^359352-179108176Lelio R Paula12/2011
27832^359338-1858781108172Enzo Doria04/2016
278412^100230-97108167Lelio R Paula03/2017
2785(25*2^359297-1)/137108159Lelio R Paula03/2014
2786(2^359262-509203)/9108148Lelio R Paula12/2013
2787(3^226648-8)/352715633108131Lelio R Paula12/2013
27886^138956-59108129Lelio R Paula02/2017
27892^359184+30285108126Lelio R Paula04/2017
279013^97059+10108119Lelio R Paula03/2017
27912^359137-81108112Lelio R Paula12/2011
2793(15185*2^359105-1)/567108103Lelio R Paula05/2015
27922^359110-11655108103Lelio R Paula04/2017
27948*6^138875+5108067Lelio R Paula11/2014
27952^358987-216919108066Enzo Doria05/2014
279639^67918-67918^39108062Norbert Schneider02/2017
27972^358785-16933108006Enzo Doria05/2013
2798(2^358783+5)/33383108000Lelio R Paula12/2013
27996^138770-77107985Lelio R Paula02/2017
2800(2^358727-1017)/94178479107980Lelio R Paula12/2013
280110^107976+19107977Lelio R Paula02/2017
280210^107976-202103107976Patrick De Geest03/2017
28032^358684+75781107975Enzo Doria04/2016
280499^54094+2107952Lelio R Paula06/2013
2805(2^358583-9)/391107942Lelio R Paula12/2013
28062^358538+55107931Lelio R Paula12/2011
28072^358517-109009107925Enzo Doria03/2014
28083^226159+104107906Lelio R Paula03/2017
28092^358310-11655107863Lelio R Paula03/2017
28102^358275-112987107852Enzo Doria07/2014
28112^358233-20005107839Enzo Doria06/2013
28122^358194+175107828Lelio R Paula12/2011
2813107^53125-106107812Norbert Schneider12/2016
28143^225922-2107793Lelio R Paula10/2013
281512^99874-95107783Lelio R Paula03/2017
28162^358030-171107778Lelio R Paula12/2011
281711^103488-4170107772Enzo Doria12/2012
28182^357911-20089107742Enzo Doria06/2013
28192^357885+12857107735Yves Minet07/2010
28207^127473+40107728Lelio R Paula03/2017
28215*2^357850+9107725Lelio R Paula09/2014
28222^357786-291191107705Enzo Doria06/2015
282318^85798-23107700Lelio R Paula04/2017
2824(14*10^107694-83)/3107695Robert Price12/2018
28252^357688-1854269107675Enzo Doria09/2015
28262^357671-112225107670Enzo Doria06/2014
28272^357618-21005107654Enzo Doria06/2013
28282^357615-17505107653Enzo Doria05/2013
2829(30^72871-1)/29107638Robert Price12/2011
28302^357521+1870217107625Enzo Doria05/2016
28312^357477-1203107612Lelio R Paula03/2017
28325^153894-18107568Lelio R Paula02/2017
28332^357324-69059107566Enzo Doria11/2015
28342^357283-869688105107553Lelio R Paula01/2017
28352^357280-16805107552Enzo Doria05/2013
283610^107547+481719107548Patrick De Geest03/2017
283710^107547-47107547Lelio R Paula02/2017
283817^87396-32107537Lelio R Paula04/2017
28392^357081+107107493Lelio R Paula12/2011
28402^357058-3911107486Yves Minet04/2017
28413^225274+64107484Lelio R Paula03/2017
284218^85619-95107476Lelio R Paula04/2017
28433^225248-130107471Lelio R Paula03/2017
2844(5*2^356961+1)/143107455Lelio R Paula03/2014
28452^356935-18085107449Enzo Doria05/2013
284610^107409+37107410Lelio R Paula02/2017
284710^107409-329633107409Patrick De Geest03/2017
28482^356787-109027107404Enzo Doria04/2014
2849(2^356767+78557)/5107397Lelio R Paula12/2013
28503*10^107389+77107390Robert Price09/2018
28515^153622-42107378Lelio R Paula02/2017
28522^356699-97305107378Lelio R Paula03/2017
28532^356654+85107364Lelio R Paula11/2011
28542^356641-19921107360Enzo Doria06/2013
28552^356623-465107355Lelio R Paula03/2017
285619^83945-92107345Lelio R Paula02/2017
285710^107334+28149107335Patrick De Geest03/2017
285810^107334-83107334Lelio R Paula02/2017
28592^356518+885107323Lelio R Paula03/2017
2860(3*2^356506-1)/467107317Lelio R Paula03/2014
28612^356442-114713107300Enzo Doria04/2015
28622^356425+72257107295Enzo Doria04/2016
28632^356351-112237107273Enzo Doria06/2014
2865(6^137845-11)/5107264Paul Bourdelais11/2011
28642^356322+74539107264Enzo Doria04/2016
28662^356274+1874479107250Enzo Doria06/2016
286720^82422-93107234Lelio R Paula02/2017
28682^356157-20365107214Enzo Doria06/2013
28692^356129-18949107206Enzo Doria05/2013
28702^356100-109587107197Enzo Doria04/2014
2871(31*2^355970+1)/5107159Lelio R Paula03/2014
28722^355968-64875107158Lelio R Paula01/2017
28732^355952+1870321107153Enzo Doria05/2016
28742^355915-117107142Lelio R Paula11/2011
2875(19*2^355838-1)/15107119Lelio R Paula03/2014
28763^224495-8107112Lelio R Paula12/2013
28777^126691-44107067Lelio R Paula03/2017
28784^177830-8243107065Mike Oakes02/2011
28792^355524-21237107024Enzo Doria06/2013
2880(10223*2^355515+1)/4855107022Lelio R Paula07/2014
28812^355494-19901107015Enzo Doria06/2013
28822^355454-869688105107003Lelio R Paula01/2017
28832^355366+54615106976Lelio R Paula01/2017
2884(31*2^355346-1)/1563106969Lelio R Paula03/2014
28852^355275-19861106949Enzo Doria06/2013
2886(9179*2^355234-1)/1915106937Lelio R Paula05/2015
28874*10^106892-3106893Robert Price10/2015
2888(66^58741+1)/67106881Paul Bourdelais08/2017
28892^354946-3106850M. Frind & P. Underwood08/2002
28902^354873-18693106828Enzo Doria05/2013
28912^354828+4257106814Lelio R Paula01/2017
2892(21^80761+1)/22106783Paul Bourdelais03/2010
28932^354640-354640+1106758Robert Price10/2014
28942^354585+95106741Lelio R Paula10/2011
28952^354553+189106732Lelio R Paula10/2011
28962^354514-109031106720Enzo Doria04/2014
28972^354509-109465106718Enzo Doria04/2014
2898(15*2^354478-1)/26983106706Lelio R Paula03/2014
289915^90710+28106684Lelio R Paula04/2017
29007^126237+34106683Lelio R Paula03/2017
29012^354385-115315106681Enzo Doria06/2015
29022^354327-19305106664Enzo Doria06/2013
2903(35*10^106649+1)/9106650Serge Batalov11/2010
290410^106636+97106637Lelio R Paula02/2017
290510^106636-22923106636Patrick De Geest03/2017
29062^354220-57106631Lelio R Paula10/2011
29072^354157-17041106612Enzo Doria05/2013
290812^98778+73106600Lelio R Paula02/2017
29092^354064+1870651106584Enzo Doria05/2016
29102^353992-57106563Lelio R Paula10/2011
2911NSW(139160)106535Robert Price12/2018
2912(7*10^106516+113)/3106517Robert Price02/2018
29132^353832-1853849106515Enzo Doria09/2015
2914(7^126037-1)/6106513Paul Bourdelais09/2008
29152^353794-18453106503Enzo Doria05/2013
29162^353728+7695106483Lelio R Paula01/2017
29172^353672-303106466Yves Minet02/2012
29186^136811+101106460Lelio R Paula02/2017
29192^353641+1871981106457Enzo Doria05/2016
2920(8*10^106454-29)/3106455Robert Price07/2018
29212^353553+54615106431Lelio R Paula01/2017
29222^353544-18897106428Enzo Doria05/2013
29236^136729-133106396Lelio R Paula02/2017
29242^353418+1605106390Lelio R Paula01/2017
29252^353387+65106381Lelio R Paula10/2011
29262^353372+74311106376Enzo Doria04/2016
29272^353344-3693106368Yves Minet03/2017
29282^353277-20089106347Enzo Doria06/2013
29292^353275+72173106347Enzo Doria04/2016
29302^353268-17705106345Enzo Doria05/2013
29312^353267-19857106344Enzo Doria06/2013
2932(46*10^106343+143)/9106344Robert Price01/2019
2933222748^3+3^222748106278Anatoly F. Selevich12/2010
2934(9179*2^353019-1)/9106273Lelio R Paula05/2015
29352^353025+72257106272Enzo Doria04/2016
29372^352932-20345106244Enzo Doria06/2013
2936(2^353011-3)/745325861246794515484535106244Lelio R Paula12/2013
29382^352883-187106229Lelio R Paula10/2011
293920^81649-19^81649106228Jean-Louis Charton03/2011
29402^352814-131106208Lelio R Paula10/2011
29412^352752+73951106189Enzo Doria04/2016
29426^136434+5106167Lelio R Paula11/2014
29437*5^151872-8106155Lelio R Paula11/2014
2944105^52520-2106153Lelio R Paula10/2017
29452^352601-1604809106144Enzo Doria05/2015
294612^98353-43106141Lelio R Paula02/2017
29472^352585-18901106139Enzo Doria05/2013
2948(2^352554-3)/193106128Lelio R Paula12/2013
29492^352540+15015106126Lelio R Paula01/2017
29502^352524-3149106121Yves Minet10/2014
29512^352486-1858781106109Enzo Doria04/2016
29522^352444+12705106097Lelio R Paula01/2017
29532^352228-18953106032Enzo Doria05/2013
29542^352107+1872533105995Enzo Doria05/2016
29552^352066-2591105983Yves Minet07/2014
29562^352030+715105972Lelio R Paula10/2011
29579*6^136176-5105967Lelio R Paula11/2014
295817099*2^351991+58329105965Paul Vanderveen12/2017
2959155^48377+2105962Lelio R Paula08/2013
29602^351865+1869707105922Enzo Doria05/2016
29612^351831+23105912Lelio R Paula10/2011
29629*2^351784-5105899Lelio R Paula09/2014
29632^351671-112387105864Enzo Doria06/2014
29642^351669-109501105863Enzo Doria04/2014
29652^351644+74731105856Enzo Doria04/2016
296613^95025-42105853Lelio R Paula12/2016
29672^351599+15015105842Lelio R Paula01/2017
296819^82763+90105834Lelio R Paula01/2017
2969(9179*2^351540-1)/221105826Lelio R Paula05/2015
297020^81329-51105812Lelio R Paula01/2017
2971(5*10^105811+211)/9105811Robert Price02/2018
29722^351483+28425105807Lelio R Paula01/2017
297315^89960+86105802Lelio R Paula02/2017
29742^351460-17289105801Enzo Doria05/2013
297519^82735+22105798Lelio R Paula01/2017
29762^351435-109077105793Enzo Doria04/2014
29772^351393+1089105780Lelio R Paula01/2017
29782^351364+72631105772Enzo Doria04/2016
29792^351305+1872467105754Enzo Doria05/2016
29803^221649+16105754Lelio R Paula11/2016
29818*3^221637-5105749Lelio R Paula09/2014
29822^351279-2780449105746Enzo Doria03/2016
298315^89903-26105735Lelio R Paula02/2017
29842^351213-73105726Lelio R Paula10/2011
29852^351192-4589105720Yves Minet07/2011
298620^81250-33105709Lelio R Paula12/2016
29872^351076-113159105685Enzo Doria07/2014
298893^53688-2105684Lelio R Paula09/2013
29892^351060-4559105680Yves Minet07/2011
299011^101473-750105674Enzo Doria11/2012
29913*5^151181-8105672Lelio R Paula11/2014
299215^89831-34105650Lelio R Paula02/2017
299411^101448-360105648Enzo Doria08/2012
29933*7^125011+4105648Lelio R Paula11/2014
29952^350943-113269105645Enzo Doria07/2014
29962^350868-19725105622Enzo Doria06/2013
29972^350858-59291105619Enzo Doria10/2015
29982^350851+135105617Lelio R Paula10/2011
29992^350841-741105614Lelio R Paula01/2017
30003*10^105582+77105583Robert Price09/2018


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: February, 14 2019 10:37 (Time in France)

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