PRP Records

Probable Primes Top 10000

(211563 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 ?
27512^351599+15015105842Lelio R Paula01/2017
275219^82763+90105834Lelio R Paula01/2017
2753(9179*2^351540-1)/221105826Lelio R Paula05/2015
275420^81329-51105812Lelio R Paula01/2017
2755(5*10^105811+211)/9105811Robert Price02/2018
27562^351483+28425105807Lelio R Paula01/2017
275715^89960+86105802Lelio R Paula02/2017
27582^351460-17289105801Enzo Doria05/2013
275919^82735+22105798Lelio R Paula01/2017
27602^351435-109077105793Enzo Doria04/2014
27612^351393+1089105780Lelio R Paula01/2017
27622^351364+72631105772Enzo Doria04/2016
27642^351305+1872467105754Enzo Doria05/2016
27633^221649+16105754Lelio R Paula11/2016
27658*3^221637-5105749Lelio R Paula09/2014
27662^351279-2780449105746Enzo Doria03/2016
276715^89903-26105735Lelio R Paula02/2017
27682^351213-73105726Lelio R Paula10/2011
27692^351192-4589105720Yves Minet07/2011
277020^81250-33105709Lelio R Paula12/2016
27712^351076-113159105685Enzo Doria07/2014
277293^53688-2105684Lelio R Paula09/2013
27732^351060-4559105680Yves Minet07/2011
277411^101473-750105674Enzo Doria11/2012
27753*5^151181-8105672Lelio R Paula11/2014
277615^89831-34105650Lelio R Paula02/2017
277711^101448-360105648Enzo Doria08/2012
27783*7^125011+4105648Lelio R Paula11/2014
27792^350943-113269105645Enzo Doria07/2014
27802^350868-19725105622Enzo Doria06/2013
27812^350858-59291105619Enzo Doria10/2015
27822^350851+135105617Lelio R Paula10/2011
27832^350841-741105614Lelio R Paula01/2017
27848*10^105571+3105572Robert Price08/2015
27852^350674-78557105564Jorge Menendez03/2018
27862*5^151026-3105563Lelio R Paula11/2014
2787(2^350702+5)/34264674063105562Lelio R Paula12/2013
27886^135647-5^135647105554Jean-Louis Charton02/2009
27893^221211+236105545Lelio R Paula11/2016
2790(32*10^105530-77)/9105531Robert Price06/2018
279110^105515+33105516Lelio R Paula11/2016
279210^105515-41033105515Patrick De Geest12/2016
2793(29*2^350473-1)/267927105499Lelio R Paula03/2014
279417^85732-72105489Lelio R Paula01/2017
27952^350307-110329105453Enzo Doria05/2014
27962^350253-20365105437Enzo Doria06/2013
2797(3*29^72089-1075)/4105423Curtis Bright05/2015
27982^350139-109009105403Enzo Doria04/2014
27993*5^150763+4105380Lelio R Paula11/2014
280012^97643+91105375Lelio R Paula02/2017
28016*5^150744-7105367Lelio R Paula11/2014
28022^349996-112169105360Enzo Doria06/2014
280311^101142-1080105329Enzo Doria12/2012
2804(68*10^105320-41)/9105321Robert Price10/2013
28053^220712-9934105307Enzo Doria05/2014
28067*10^105296+9105297Robert Price09/2015
28072^349739+1873373105282Enzo Doria06/2016
28087^124574+24105278Lelio R Paula11/2016
28092^349708-20957105273Enzo Doria06/2013
28102^349649-20469105255Enzo Doria06/2013
28112^349607-20109105243Enzo Doria06/2013
28122^349594-19085105239Enzo Doria05/2013
28132^349530+1874479105220Enzo Doria06/2016
2814(3^220528+8)/8081105215Lelio R Paula12/2013
28153^220464-112852105189Enzo Doria07/2014
28162^349419-17349105186Enzo Doria05/2013
28172^349400-2579105180Yves Minet07/2014
28188*5^150471+3105176Lelio R Paula11/2014
281913^94403+94105160Lelio R Paula12/2016
28202^349301-112309105151Enzo Doria06/2014
28219*2^349220+5105127Lelio R Paula09/2014
28227*3^220317+8105119Lelio R Paula09/2014
28237^124386+88105119Lelio R Paula11/2016
28242^349171-19657105111Enzo Doria06/2013
2825(2^(6*58185+1)-5)/3105093Kevin Acres11/2013
2826(2^349111-5)/3105093Lelio R Paula12/2013
28272^348981-2797573105054Enzo Doria04/2016
28282^348869-6555105021Lelio R Paula01/2017
28295^150217+78104998Lelio R Paula11/2016
28302^348703-113005104971Enzo Doria06/2014
28322^348612-809104943Yves Minet05/2013
2831(73*10^104942-1)/9104943Robert Price01/2015
28332^348583-350407104934Enzo Doria06/2015
28342^348531-949104919Yves Minet05/2012
283520^80636-59104910Lelio R Paula12/2016
28362^348437+35104890Lelio R Paula09/2011
28372^348348+135104864Lelio R Paula09/2011
2839(2^348284+9)/25104843Lelio R Paula12/2013
283875^55914-74104843Norbert Schneider01/2015
28402^348268+255255104840Lelio R Paula01/2017
28415^149985-52104836Lelio R Paula11/2016
28422^348224-20249104826Enzo Doria06/2013
28432^348212-20105104823Enzo Doria06/2013
284420^80562+19104814Lelio R Paula12/2016
28452*10^104811-87104812Robert Price04/2018
28462^348149-20053104804Enzo Doria06/2013
28472^348095-171104788Lelio R Paula09/2011
28482^348003-20377104760Enzo Doria06/2013
28492^347994-741104757Lelio R Paula12/2016
2850(13*2^347972-1)/282309104746Lelio R Paula03/2014
28512^347910-109937104732Enzo Doria04/2014
28525^149794+28104702Lelio R Paula11/2016
2853105^51800-2104698Lelio R Paula10/2017
2854(16^86939+3^86939)/19104684Robert Price06/2013
2855(15^89009-1)/14104682Paul Bourdelais03/2010
28562^347731-18609104678Enzo Doria05/2013
28574*6^134519+7104677Lelio R Paula11/2014
28582^347612-18545104642Enzo Doria05/2013
28596^134465+95104635Lelio R Paula11/2016
28602^347517-17301104614Enzo Doria05/2013
28613^219222-310104596Lelio R Paula11/2016
2862(15*2^347399-1)/13104578Lelio R Paula03/2014
28632^347372-17853104570Enzo Doria05/2013
28642^347314+99104552Lelio R Paula09/2011
28652^347300-22233104548Enzo Doria06/2013
28662^347287-19845104544Enzo Doria06/2013
2867(31*2^347254-1)/891104533Lelio R Paula03/2014
28685*F(250091)*(F(250091)-1)+1104532Serge Batalov04/2015
28697*2^347239-3104531Lelio R Paula09/2014
2870(3^219098-8)/514147439969104525Lelio R Paula12/2013
28715*3^219047+8104513Lelio R Paula09/2014
28722^347148-109073104502Enzo Doria04/2014
28732^347129-20145104497Enzo Doria06/2013
28742^346923-19585104435Enzo Doria05/2013
2875(11*2^346864-1)/175104416Lelio R Paula03/2014
28762^346854+346854^2+1104414Robert Price06/2014
28772^346834+11715104408Lelio R Paula04/2015
287879^55009+78104387Norbert Schneider02/2015
28793^218744+58104368Lelio R Paula11/2016
28802^346649+65104352Lelio R Paula09/2011
28812^346638-17265104349Enzo Doria05/2013
28832^346527-111817104316Enzo Doria05/2014
28826^134055+101104316Lelio R Paula11/2016
28846^134013+163104283Lelio R Paula11/2016
288518^83049-89104250Lelio R Paula01/2017
28862^346213+484049104221Enzo Doria04/2017
288718^83021-91104214Lelio R Paula01/2017
288810^104212+128779104213Patrick De Geest05/2016
288910^104212+237447104213Patrick De Geest05/2016
289010^104212+242139104213Patrick De Geest05/2016
289110^104212+269199104213Patrick De Geest05/2016
2892(10^104212-71)/1104212Serge Batalov12/2014
28932^346078+7695104180Lelio R Paula12/2016
28952^346055-19537104173Enzo Doria05/2013
2894(3*2^346057+1)/77104173Lelio R Paula12/2013
28962^346037-20125104168Enzo Doria06/2013
2897(34*10^104168-7)/9/13/551179104162Makoto Morimoto05/2016
28986^133854-17993104159Enzo Doria03/2013
28992^345990+1874239104154Enzo Doria06/2016
29002^345988-20373104153Enzo Doria06/2013
29013*5^148968+8104125Lelio R Paula11/2014
2902(7*10^104113+53)/3104114Robert Price05/2018
2903p(21253)#/2+8104113Robert Price01/2017
2904322^41507+41507^322104094Norbert Schneider12/2014
29056^133768-17423104092Enzo Doria03/2013
29062^345786-19557104092Enzo Doria05/2013
2907171^46606-2104072Lelio R Paula10/2017
29082^345704-149104068Lelio R Paula09/2011
29096^133704-17273104042Enzo Doria02/2013
2910(3*2^345590-1)/23104033Lelio R Paula03/2014
2911(19*2^345590+1)/33859104030Lelio R Paula12/2013
29122^345547+11104021Lelio R Paula09/2011
29132^345504+723104008Lelio R Paula09/2011
29142^345498-20037104006Enzo Doria06/2013
291518^82854-37104005Lelio R Paula01/2017
29162^345486-109065104002Enzo Doria04/2014
29172^345487-1851507104002Enzo Doria08/2015
29182^345476+777103999Lelio R Paula09/2011
2919(5*2^345321-1)/3103953Lelio R Paula03/2014
2920(2^345267-9)/539049127103927Lelio R Paula12/2013
2921(78557*2^345163+1)/78589103905Lelio R Paula07/2014
29222^345106-112181103888Enzo Doria06/2014
29232^345079+99103880Lelio R Paula09/2011
292411^99736-1500103865Enzo Doria12/2012
29252^344842-20157103808Enzo Doria06/2013
2926(47*2^344822+1)/1071103801Lelio R Paula05/2015
29272^344802-20765103796Enzo Doria06/2013
29282^344794-3821103794Yves Minet05/2011
29292^344782-109103103790Enzo Doria04/2014
29303^217521-112292103784Enzo Doria06/2014
29312^344759-3505103783Lelio R Paula11/2016
29322^344735-147103776Lelio R Paula09/2011
2933L(496533)-p(496533)103770Robert Price02/2018
29342*10^103749-69103750Robert Price03/2018
2935(55459*2^344617+1)/3103745Lelio R Paula07/2014
29362^344607-108891103738Enzo Doria03/2014
29372^344541-19561103718Enzo Doria05/2013
2938(1017*2^344529-1)/569103714Lelio R Paula05/2015
2939(4*10^103703-1)/3103704Serge Batalov08/2009
29402^344444-455103688Yves Minet03/2012
2941(13*53^238539*617^9)/10^307661103673Hans Havermann06/2017
29422^344317-109933103650Enzo Doria04/2014
29432^344309-1852033103648Enzo Doria08/2015
29442^344213-21253103619Enzo Doria06/2013
29452^344196-465103614Lelio R Paula11/2016
29462^344187-20001103611Enzo Doria06/2013
2947(117191#+(355573#)/(117191#))/(200233679)103602Makoto Morimoto10/2017
294820^79621-19^79621103590Jean-Louis Charton03/2011
2949Phi(155391,10)/1243129103586Maksym Voznyy09/2015
29502^344085-20365103580Enzo Doria06/2013
29515^148169+54103566Lelio R Paula11/2016
29522^344017-108795103560Enzo Doria03/2014
29532^343971-5077103546Lelio R Paula09/2011
2954(7*10^103531+71)/3103532Robert Price05/2018
29552^343899+141103524Lelio R Paula08/2011
29566^133029-67103517Lelio R Paula11/2016
2957(17*2^343877+1)/13625103515Lelio R Paula12/2013
2958(136*10^103474-1)/9103476Serge Batalov12/2014
29595^148014-24103458Lelio R Paula11/2016
29602^343604+9931103436Yves Minet01/2011
29612^343601-21189103435Enzo Doria06/2013
29622^343508-115229103407Enzo Doria06/2015
2963(509203*2^343491-1)/16147103403Lelio R Paula05/2015
29643^216685-113056103386Enzo Doria07/2014
296544^62903-43^62903103379Jean-Louis Charton08/2012
296611^99262-20103371Lelio R Paula12/2016
2967(509203*2^343357-1)/5103366Lelio R Paula05/2015
29692^343356-2791889103361Enzo Doria03/2016
2968(25*10^103360-241)/9103361Robert Price05/2018
2970Phi(104989,10)/2939693103350Maksym Voznyy09/2015
29712^343182-171103309Lelio R Paula08/2011
2972(23619^23619+23620^23620)/7187103294David Broadhurst09/2009
29732^343079-1835611103278Enzo Doria05/2015
29742^343063-1147103273Yves Minet06/2013
29759*6^132689+7103254Lelio R Paula11/2014
29762^342979-18085103247Enzo Doria05/2013
29772^342966-16995103244Lelio R Paula11/2016
29785^147650+16103203Lelio R Paula11/2016
2979gcd(Phi(852060,10),(10^42603+1)^3*(10^42603+1-10^21302)+(10^85206+10^42603)*(10^21302+1)+10^127809)103201Serge Batalov04/2015
29802^342817+2707067103199Enzo Doria03/2016
298143^63177-42103198Theodore Burton02/2007
29822^342805-21025103195Enzo Doria06/2013
29832^342714+12285103168Lelio R Paula11/2016
298418^82178-4481103156Enzo Doria03/2013
29852^342665-17349103153Enzo Doria05/2013
29862^342612+175103137Lelio R Paula08/2011
29875*2^342585-3103130Lelio R Paula09/2014
29882^342503-19209103104Enzo Doria05/2013
29892^342476+51103096Lelio R Paula08/2011
29902^342460-18885103091Enzo Doria05/2013
29917^121968+82103075Lelio R Paula10/2016
29922^342392-108863103071Enzo Doria03/2014
29933^216014+28103065Lelio R Paula11/2016
29942^342353-108879103059Enzo Doria03/2014
299510^103055+276081103056Patrick De Geest12/2016
299610^103055-53103055Lelio R Paula11/2016
29977^121933+4103046Lelio R Paula11/2014
299819^80560-68103017Lelio R Paula10/2016
29992^342209+76607103016Enzo Doria05/2016
300012^95454-91103013Lelio R Paula10/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 18 2018 23:06 (Time in France)

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