PRP Records

Probable Primes Top 10000

(253476 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 ?
30012^357885+12857107735Yves Minet07/2010
3002(248587#+9289)/(7*1327*111512899)107733Makoto Morimoto06/2019
30037^127473+40107728Lelio R Paula03/2017
30045*2^357850+9107725Lelio R Paula09/2014
30052^357786-291191107705Enzo Doria06/2015
300618^85798-23107700Lelio R Paula04/2017
3007(14*10^107694-83)/3107695Robert Price12/2018
30082^357688-1854269107675Enzo Doria09/2015
30092^357671-112225107670Enzo Doria06/2014
30102^357618-21005107654Enzo Doria06/2013
30112^357615-17505107653Enzo Doria05/2013
3012(30^72871-1)/29107638Robert Price12/2011
30132^357521+1870217107625Enzo Doria05/2016
30142^357477-1203107612Lelio R Paula03/2017
30155^153894-18107568Lelio R Paula02/2017
30162^357324-69059107566Enzo Doria11/2015
3017467^40296+40296^467107563Norbert Schneider03/2019
30182^357283-869688105107553Lelio R Paula01/2017
30192^357280-16805107552Enzo Doria05/2013
302010^107547+481719107548Patrick De Geest03/2017
302110^107547-47107547Lelio R Paula02/2017
302217^87396-32107537Lelio R Paula04/2017
30232^357081+107107493Lelio R Paula12/2011
30242^357058-3911107486Yves Minet04/2017
30253^225274+64107484Lelio R Paula03/2017
302618^85619-95107476Lelio R Paula04/2017
30273^225248-130107471Lelio R Paula03/2017
3028(5*2^356961+1)/143107455Lelio R Paula03/2014
30292^356935-18085107449Enzo Doria05/2013
303010^107409+37107410Lelio R Paula02/2017
303110^107409-329633107409Patrick De Geest03/2017
30322^356787-109027107404Enzo Doria04/2014
3033(2^356767+78557)/5107397Lelio R Paula12/2013
30343*10^107389+77107390Robert Price09/2018
30355^153622-42107378Lelio R Paula02/2017
30362^356699-97305107378Lelio R Paula03/2017
30372^356654+85107364Lelio R Paula11/2011
30382^356641-19921107360Enzo Doria06/2013
30395*10^107355+11107356Robert Price08/2019
30402^356623-465107355Lelio R Paula03/2017
304119^83945-92107345Lelio R Paula02/2017
304210^107334+28149107335Patrick De Geest03/2017
304310^107334-83107334Lelio R Paula02/2017
30442^356518+885107323Lelio R Paula03/2017
3045(3*2^356506-1)/467107317Lelio R Paula03/2014
30462^356442-114713107300Enzo Doria04/2015
30472^356425+72257107295Enzo Doria04/2016
30482^356351-112237107273Enzo Doria06/2014
3049(6^137845-11)/5107264Paul Bourdelais11/2011
30502^356322+74539107264Enzo Doria04/2016
30512^356274+1874479107250Enzo Doria06/2016
305220^82422-93107234Lelio R Paula02/2017
30532^356157-20365107214Enzo Doria06/2013
30542^356129-18949107206Enzo Doria05/2013
30552^356100-109587107197Enzo Doria04/2014
3056(31*2^355970+1)/5107159Lelio R Paula03/2014
30572^355968-64875107158Lelio R Paula01/2017
30582^355952+1870321107153Enzo Doria05/2016
30592^355915-117107142Lelio R Paula11/2011
3060(16*10^107140+77)/3107141Robert Price03/2019
3061(19*2^355838-1)/15107119Lelio R Paula03/2014
30623^224495-8107112Lelio R Paula12/2013
30637^126691-44107067Lelio R Paula03/2017
30644^177830-8243107065Mike Oakes02/2011
30652^355524-21237107024Enzo Doria06/2013
3066(10223*2^355515+1)/4855107022Lelio R Paula07/2014
30672^355494-19901107015Enzo Doria06/2013
30682^355454-869688105107003Lelio R Paula01/2017
30692^355366+54615106976Lelio R Paula01/2017
3070(31*2^355346-1)/1563106969Lelio R Paula03/2014
30712^355275-19861106949Enzo Doria06/2013
3072(9179*2^355234-1)/1915106937Lelio R Paula05/2015
30734*10^106892-3106893Robert Price10/2015
3074(66^58741+1)/67106881Paul Bourdelais08/2017
30752^354946-3106850M. Frind & P. Underwood08/2002
30762^354873-18693106828Enzo Doria05/2013
30772^354828+4257106814Lelio R Paula01/2017
3078436^40459+40459^436106791Norbert Schneider03/2019
3079(21^80761+1)/22106783Paul Bourdelais03/2010
30802^354640-354640+1106758Robert Price10/2014
30812^354585+95106741Lelio R Paula10/2011
30822^354553+189106732Lelio R Paula10/2011
30832^354514-109031106720Enzo Doria04/2014
30842^354509-109465106718Enzo Doria04/2014
3085(15*2^354478-1)/26983106706Lelio R Paula03/2014
3086Phi(217618,10)/899798636917106693Makoto Kamada06/2019
308715^90710+28106684Lelio R Paula04/2017
30887^126237+34106683Lelio R Paula03/2017
30892^354385-115315106681Enzo Doria06/2015
30902^354327-19305106664Enzo Doria06/2013
3091(35*10^106649+1)/9106650Serge Batalov11/2010
309210^106636+97106637Lelio R Paula02/2017
309310^106636-22923106636Patrick De Geest03/2017
30942^354220-57106631Lelio R Paula10/2011
30952^354157-17041106612Enzo Doria05/2013
309612^98778+73106600Lelio R Paula02/2017
30972^354064+1870651106584Enzo Doria05/2016
30982^353992-57106563Lelio R Paula10/2011
3099NSW(139160)106535Robert Price12/2018
3100(7*10^106516+113)/3106517Robert Price02/2018
31012^353832-1853849106515Enzo Doria09/2015
3102(7^126037-1)/6106513Paul Bourdelais09/2008
31032^353794-18453106503Enzo Doria05/2013
31042^353728+7695106483Lelio R Paula01/2017
31052^353672-303106466Yves Minet02/2012
31066^136811+101106460Lelio R Paula02/2017
31072^353641+1871981106457Enzo Doria05/2016
3108(8*10^106454-29)/3106455Robert Price07/2018
31092^353553+54615106431Lelio R Paula01/2017
31102^353544-18897106428Enzo Doria05/2013
31116^136729-133106396Lelio R Paula02/2017
31122^353418+1605106390Lelio R Paula01/2017
31132^353387+65106381Lelio R Paula10/2011
31142^353372+74311106376Enzo Doria04/2016
31152^353344-3693106368Yves Minet03/2017
31162^353277-20089106347Enzo Doria06/2013
31172^353275+72173106347Enzo Doria04/2016
31182^353268-17705106345Enzo Doria05/2013
31192^353267-19857106344Enzo Doria06/2013
3120(46*10^106343+143)/9106344Robert Price01/2019
3121222748^3+3^222748106278Anatoly F. Selevich12/2010
3122(9179*2^353019-1)/9106273Lelio R Paula05/2015
31232^353025+72257106272Enzo Doria04/2016
31242^352932-20345106244Enzo Doria06/2013
3125(2^353011-3)/745325861246794515484535106244Lelio R Paula12/2013
31262^352883-187106229Lelio R Paula10/2011
312720^81649-19^81649106228Jean-Louis Charton03/2011
3128(55*10^106222+377)/9106223Robert Price02/2019
31292^352814-131106208Lelio R Paula10/2011
31302^352752+73951106189Enzo Doria04/2016
31316^136434+5106167Lelio R Paula11/2014
31328*10^106157-13106158Robert Price08/2019
31337*5^151872-8106155Lelio R Paula11/2014
3134105^52520-2106153Lelio R Paula10/2017
31352^352601-1604809106144Enzo Doria05/2015
313612^98353-43106141Lelio R Paula02/2017
31372^352585-18901106139Enzo Doria05/2013
3138(2^352554-3)/193106128Lelio R Paula12/2013
31392^352540+15015106126Lelio R Paula01/2017
31402^352524-3149106121Yves Minet10/2014
31412^352486-1858781106109Enzo Doria04/2016
31422^352444+12705106097Lelio R Paula01/2017
31432^352228-18953106032Enzo Doria05/2013
31442^352107+1872533105995Enzo Doria05/2016
31452^352066-2591105983Yves Minet07/2014
31462^352030+715105972Lelio R Paula10/2011
31479*6^136176-5105967Lelio R Paula11/2014
314817099*2^351991+58329105965Paul Vanderveen12/2017
3149155^48377+2105962Lelio R Paula08/2013
31502^351865+1869707105922Enzo Doria05/2016
31512^351831+23105912Lelio R Paula10/2011
31529*2^351784-5105899Lelio R Paula09/2014
31532^351671-112387105864Enzo Doria06/2014
31542^351669-109501105863Enzo Doria04/2014
31552^351644+74731105856Enzo Doria04/2016
315613^95025-42105853Lelio R Paula12/2016
31572^351599+15015105842Lelio R Paula01/2017
315819^82763+90105834Lelio R Paula01/2017
3159(9179*2^351540-1)/221105826Lelio R Paula05/2015
316020^81329-51105812Lelio R Paula01/2017
3161(5*10^105811+211)/9105811Robert Price02/2018
31622^351483+28425105807Lelio R Paula01/2017
316315^89960+86105802Lelio R Paula02/2017
31642^351460-17289105801Enzo Doria05/2013
316519^82735+22105798Lelio R Paula01/2017
31662^351435-109077105793Enzo Doria04/2014
31672^351393+1089105780Lelio R Paula01/2017
31682^351364+72631105772Enzo Doria04/2016
31692^351305+1872467105754Enzo Doria05/2016
31703^221649+16105754Lelio R Paula11/2016
31718*3^221637-5105749Lelio R Paula09/2014
31722^351279-2780449105746Enzo Doria03/2016
317315^89903-26105735Lelio R Paula02/2017
31742^351213-73105726Lelio R Paula10/2011
31752^351192-4589105720Yves Minet07/2011
317620^81250-33105709Lelio R Paula12/2016
31772^351076-113159105685Enzo Doria07/2014
317893^53688-2105684Lelio R Paula09/2013
31792^351060-4559105680Yves Minet07/2011
3180((10^52836-1)*10000/9+5927)*10^52836+(10^52836-1)/9105676Hans Havermann08/2019
318111^101473-750105674Enzo Doria11/2012
31823*5^151181-8105672Lelio R Paula11/2014
318315^89831-34105650Lelio R Paula02/2017
318511^101448-360105648Enzo Doria08/2012
31843*7^125011+4105648Lelio R Paula11/2014
31862^350943-113269105645Enzo Doria07/2014
31872^350868-19725105622Enzo Doria06/2013
31882^350858-59291105619Enzo Doria10/2015
31892^350851+135105617Lelio R Paula10/2011
31902^350841-741105614Lelio R Paula01/2017
31913*10^105582+77105583Robert Price09/2018
31928*10^105571+3105572Robert Price08/2015
31932^350674-78557105564Jorge Menendez03/2018
31942*5^151026-3105563Lelio R Paula11/2014
3195(2^350702+5)/34264674063105562Lelio R Paula12/2013
31966^135647-5^135647105554Jean-Louis Charton02/2009
31973^221211+236105545Lelio R Paula11/2016
3198(32*10^105530-77)/9105531Robert Price06/2018
319910^105515+33105516Lelio R Paula11/2016
320010^105515-41033105515Patrick De Geest12/2016
3201(29*2^350473-1)/267927105499Lelio R Paula03/2014
320217^85732-72105489Lelio R Paula01/2017
32032^350307-110329105453Enzo Doria05/2014
32042^350253-20365105437Enzo Doria06/2013
3205(3*29^72089-1075)/4105423Curtis Bright05/2015
32062^350139-109009105403Enzo Doria04/2014
32073*5^150763+4105380Lelio R Paula11/2014
320812^97643+91105375Lelio R Paula02/2017
32096*5^150744-7105367Lelio R Paula11/2014
32102^349996-112169105360Enzo Doria06/2014
321111^101142-1080105329Enzo Doria12/2012
3212(68*10^105320-41)/9105321Robert Price10/2013
32133^220712-9934105307Enzo Doria05/2014
32147*10^105296+9105297Robert Price09/2015
32152^349739+1873373105282Enzo Doria06/2016
32167^124574+24105278Lelio R Paula11/2016
32172^349708-20957105273Enzo Doria06/2013
32182^349649-20469105255Enzo Doria06/2013
32192^349607-20109105243Enzo Doria06/2013
32202^349594-19085105239Enzo Doria05/2013
32212^349530+1874479105220Enzo Doria06/2016
3222(3^220528+8)/8081105215Lelio R Paula12/2013
32233^220464-112852105189Enzo Doria07/2014
32242^349419-17349105186Enzo Doria05/2013
32252^349400-2579105180Yves Minet07/2014
32268*5^150471+3105176Lelio R Paula11/2014
3227655^37342+37342^655105165Norbert Schneider08/2018
322813^94403+94105160Lelio R Paula12/2016
32292^349301-112309105151Enzo Doria06/2014
32309*2^349220+5105127Lelio R Paula09/2014
32317*3^220317+8105119Lelio R Paula09/2014
32327^124386+88105119Lelio R Paula11/2016
32332^349171-19657105111Enzo Doria06/2013
3234(2^(6*58185+1)-5)/3105093Kevin Acres11/2013
3235(2^349111-5)/3105093Lelio R Paula12/2013
3236675^37142+37142^675105087Norbert Schneider08/2018
32372^348981-2797573105054Enzo Doria04/2016
32382^348869-6555105021Lelio R Paula01/2017
32395^150217+78104998Lelio R Paula11/2016
32402^348703-113005104971Enzo Doria06/2014
32422^348612-809104943Yves Minet05/2013
3241(73*10^104942-1)/9104943Robert Price01/2015
32432^348583-350407104934Enzo Doria06/2015
32442^348531-949104919Yves Minet05/2012
324520^80636-59104910Lelio R Paula12/2016
32468*10^104893-13104894Robert Price08/2019
32472^348437+35104890Lelio R Paula09/2011
32482^348348+135104864Lelio R Paula09/2011
3250(2^348284+9)/25104843Lelio R Paula12/2013
324975^55914-74104843Norbert Schneider01/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 25 2019 15:53 (Time in France)

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