PRP Records

Probable Primes Top 10000

(190562 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 ?
25012^353992-57106563Lelio R Paula10/2011
25022^353832-1853849106515Enzo Doria09/2015
2503(7^126037-1)/6106513Paul Bourdelais09/2008
25042^353794-18453106503Enzo Doria05/2013
25052^353728+7695106483Lelio R Paula01/2017
25062^353672-303106466Yves Minet02/2012
25076^136811+101106460Lelio R Paula02/2017
25082^353641+1871981106457Enzo Doria05/2016
25092^353553+54615106431Lelio R Paula01/2017
25102^353544-18897106428Enzo Doria05/2013
25116^136729-133106396Lelio R Paula02/2017
25122^353418+1605106390Lelio R Paula01/2017
25132^353387+65106381Lelio R Paula10/2011
25142^353372+74311106376Enzo Doria04/2016
25152^353344-3693106368Yves Minet03/2017
25162^353277-20089106347Enzo Doria06/2013
25172^353275+72173106347Enzo Doria04/2016
25182^353268-17705106345Enzo Doria05/2013
25192^353267-19857106344Enzo Doria06/2013
2520222748^3+3^222748106278Anatoly F. Selevich12/2010
2521(9179*2^353019-1)/9106273Lelio R Paula05/2015
25222^353025+72257106272Enzo Doria04/2016
25232^352932-20345106244Enzo Doria06/2013
2524(2^353011-3)/745325861246794515484535106244Lelio R Paula12/2013
25252^352883-187106229Lelio R Paula10/2011
252620^81649-19^81649106228Jean-Louis Charton03/2011
25272^352814-131106208Lelio R Paula10/2011
25282^352752+73951106189Enzo Doria04/2016
25296^136434+5106167Lelio R Paula11/2014
25307*5^151872-8106155Lelio R Paula11/2014
2531105^52520-2106153Lelio R Paula10/2017
25322^352601-1604809106144Enzo Doria05/2015
253312^98353-43106141Lelio R Paula02/2017
25342^352585-18901106139Enzo Doria05/2013
2535(2^352554-3)/193106128Lelio R Paula12/2013
25362^352540+15015106126Lelio R Paula01/2017
25372^352524-3149106121Yves Minet10/2014
25382^352486-1858781106109Enzo Doria04/2016
25392^352444+12705106097Lelio R Paula01/2017
25402^352228-18953106032Enzo Doria05/2013
25412^352107+1872533105995Enzo Doria05/2016
25422^352066-2591105983Yves Minet07/2014
25432^352030+715105972Lelio R Paula10/2011
25449*6^136176-5105967Lelio R Paula11/2014
2545155^48377+2105962Lelio R Paula08/2013
25462^351865+1869707105922Enzo Doria05/2016
25472^351831+23105912Lelio R Paula10/2011
25489*2^351784-5105899Lelio R Paula09/2014
25492^351671-112387105864Enzo Doria06/2014
25502^351669-109501105863Enzo Doria04/2014
25512^351644+74731105856Enzo Doria04/2016
255213^95025-42105853Lelio R Paula12/2016
25532^351599+15015105842Lelio R Paula01/2017
255419^82763+90105834Lelio R Paula01/2017
2555(9179*2^351540-1)/221105826Lelio R Paula05/2015
255620^81329-51105812Lelio R Paula01/2017
25572^351483+28425105807Lelio R Paula01/2017
255815^89960+86105802Lelio R Paula02/2017
25592^351460-17289105801Enzo Doria05/2013
256019^82735+22105798Lelio R Paula01/2017
25612^351435-109077105793Enzo Doria04/2014
25622^351393+1089105780Lelio R Paula01/2017
25632^351364+72631105772Enzo Doria04/2016
25642^351305+1872467105754Enzo Doria05/2016
25653^221649+16105754Lelio R Paula11/2016
25668*3^221637-5105749Lelio R Paula09/2014
25672^351279-2780449105746Enzo Doria03/2016
256815^89903-26105735Lelio R Paula02/2017
25692^351213-73105726Lelio R Paula10/2011
25702^351192-4589105720Yves Minet07/2011
257120^81250-33105709Lelio R Paula12/2016
25722^351076-113159105685Enzo Doria07/2014
257393^53688-2105684Lelio R Paula09/2013
25742^351060-4559105680Yves Minet07/2011
257511^101473-750105674Enzo Doria11/2012
25763*5^151181-8105672Lelio R Paula11/2014
257715^89831-34105650Lelio R Paula02/2017
257911^101448-360105648Enzo Doria08/2012
25783*7^125011+4105648Lelio R Paula11/2014
25802^350943-113269105645Enzo Doria07/2014
25812^350868-19725105622Enzo Doria06/2013
25822^350858-59291105619Enzo Doria10/2015
25832^350851+135105617Lelio R Paula10/2011
25842^350841-741105614Lelio R Paula01/2017
25858*10^105571+3105572Robert Price08/2015
25862*5^151026-3105563Lelio R Paula11/2014
2587(2^350702+5)/34264674063105562Lelio R Paula12/2013
25886^135647-5^135647105554Jean-Louis Charton02/2009
25893^221211+236105545Lelio R Paula11/2016
259010^105515+33105516Lelio R Paula11/2016
259110^105515-41033105515Patrick De Geest12/2016
2592(29*2^350473-1)/267927105499Lelio R Paula03/2014
259317^85732-72105489Lelio R Paula01/2017
25942^350307-110329105453Enzo Doria05/2014
25952^350253-20365105437Enzo Doria06/2013
2596(3*29^72089-1075)/4105423Curtis Bright05/2015
25972^350139-109009105403Enzo Doria04/2014
25983*5^150763+4105380Lelio R Paula11/2014
259912^97643+91105375Lelio R Paula02/2017
26006*5^150744-7105367Lelio R Paula11/2014
26012^349996-112169105360Enzo Doria06/2014
260211^101142-1080105329Enzo Doria12/2012
2603(68*10^105320-41)/9105321Robert Price10/2013
26043^220712-9934105307Enzo Doria05/2014
26057*10^105296+9105297Robert Price09/2015
26062^349739+1873373105282Enzo Doria06/2016
26077^124574+24105278Lelio R Paula11/2016
26082^349708-20957105273Enzo Doria06/2013
26092^349649-20469105255Enzo Doria06/2013
26102^349607-20109105243Enzo Doria06/2013
26112^349594-19085105239Enzo Doria05/2013
26122^349530+1874479105220Enzo Doria06/2016
2613(3^220528+8)/8081105215Lelio R Paula12/2013
26143^220464-112852105189Enzo Doria07/2014
26152^349419-17349105186Enzo Doria05/2013
26162^349400-2579105180Yves Minet07/2014
26178*5^150471+3105176Lelio R Paula11/2014
261813^94403+94105160Lelio R Paula12/2016
26192^349301-112309105151Enzo Doria06/2014
26209*2^349220+5105127Lelio R Paula09/2014
26217*3^220317+8105119Lelio R Paula09/2014
26227^124386+88105119Lelio R Paula11/2016
26232^349171-19657105111Enzo Doria06/2013
2624(2^(6*58185+1)-5)/3105093Kevin Acres11/2013
2625(2^349111-5)/3105093Lelio R Paula12/2013
26262^348981-2797573105054Enzo Doria04/2016
26272^348869-6555105021Lelio R Paula01/2017
26285^150217+78104998Lelio R Paula11/2016
26292^348703-113005104971Enzo Doria06/2014
26312^348612-809104943Yves Minet05/2013
2630(73*10^104942-1)/9104943Robert Price01/2015
26322^348583-350407104934Enzo Doria06/2015
26332^348531-949104919Yves Minet05/2012
263420^80636-59104910Lelio R Paula12/2016
26352^348437+35104890Lelio R Paula09/2011
26362^348348+135104864Lelio R Paula09/2011
2637(2^348284+9)/25104843Lelio R Paula12/2013
263875^55914-74104843Norbert Schneider01/2015
26392^348268+255255104840Lelio R Paula01/2017
26405^149985-52104836Lelio R Paula11/2016
26412^348224-20249104826Enzo Doria06/2013
26422^348212-20105104823Enzo Doria06/2013
264320^80562+19104814Lelio R Paula12/2016
26442^348149-20053104804Enzo Doria06/2013
26452^348095-171104788Lelio R Paula09/2011
26462^348003-20377104760Enzo Doria06/2013
26472^347994-741104757Lelio R Paula12/2016
2648(13*2^347972-1)/282309104746Lelio R Paula03/2014
26492^347910-109937104732Enzo Doria04/2014
26505^149794+28104702Lelio R Paula11/2016
2651105^51800-2104698Lelio R Paula10/2017
2652(16^86939+3^86939)/19104684Robert Price06/2013
2653(15^89009-1)/14104682Paul Bourdelais03/2010
26542^347731-18609104678Enzo Doria05/2013
26554*6^134519+7104677Lelio R Paula11/2014
26562^347612-18545104642Enzo Doria05/2013
26576^134465+95104635Lelio R Paula11/2016
26582^347517-17301104614Enzo Doria05/2013
26593^219222-310104596Lelio R Paula11/2016
2660(15*2^347399-1)/13104578Lelio R Paula03/2014
26612^347372-17853104570Enzo Doria05/2013
26622^347314+99104552Lelio R Paula09/2011
26632^347300-22233104548Enzo Doria06/2013
26642^347287-19845104544Enzo Doria06/2013
2665(31*2^347254-1)/891104533Lelio R Paula03/2014
26665*F(250091)*(F(250091)-1)+1104532Serge Batalov04/2015
26677*2^347239-3104531Lelio R Paula09/2014
2668(3^219098-8)/514147439969104525Lelio R Paula12/2013
26695*3^219047+8104513Lelio R Paula09/2014
26702^347148-109073104502Enzo Doria04/2014
26712^347129-20145104497Enzo Doria06/2013
26722^346923-19585104435Enzo Doria05/2013
2673(11*2^346864-1)/175104416Lelio R Paula03/2014
26742^346854+346854^2+1104414Robert Price06/2014
26752^346834+11715104408Lelio R Paula04/2015
267679^55009+78104387Norbert Schneider02/2015
26773^218744+58104368Lelio R Paula11/2016
26782^346649+65104352Lelio R Paula09/2011
26792^346638-17265104349Enzo Doria05/2013
26812^346527-111817104316Enzo Doria05/2014
26806^134055+101104316Lelio R Paula11/2016
26826^134013+163104283Lelio R Paula11/2016
268318^83049-89104250Lelio R Paula01/2017
26842^346213+484049104221Enzo Doria04/2017
268518^83021-91104214Lelio R Paula01/2017
268610^104212+128779104213Patrick De Geest05/2016
268710^104212+237447104213Patrick De Geest05/2016
268810^104212+242139104213Patrick De Geest05/2016
268910^104212+269199104213Patrick De Geest05/2016
2690(10^104212-71)/1104212Serge Batalov12/2014
26912^346078+7695104180Lelio R Paula12/2016
26922^346055-19537104173Enzo Doria05/2013
2693(3*2^346057+1)/77104173Lelio R Paula12/2013
26942^346037-20125104168Enzo Doria06/2013
2695(34*10^104168-7)/9/13/551179104162Makoto Morimoto05/2016
26966^133854-17993104159Enzo Doria03/2013
26972^345990+1874239104154Enzo Doria06/2016
26982^345988-20373104153Enzo Doria06/2013
26993*5^148968+8104125Lelio R Paula11/2014
2700p(21253)#/2+8104113Robert Price01/2017
2701322^41507+41507^322104094Norbert Schneider12/2014
27026^133768-17423104092Enzo Doria03/2013
27032^345786-19557104092Enzo Doria05/2013
2704171^46606-2104072Lelio R Paula10/2017
27052^345704-149104068Lelio R Paula09/2011
27066^133704-17273104042Enzo Doria02/2013
2707(3*2^345590-1)/23104033Lelio R Paula03/2014
2708(19*2^345590+1)/33859104030Lelio R Paula12/2013
27092^345547+11104021Lelio R Paula09/2011
27102^345504+723104008Lelio R Paula09/2011
27112^345498-20037104006Enzo Doria06/2013
271218^82854-37104005Lelio R Paula01/2017
27132^345486-109065104002Enzo Doria04/2014
27142^345487-1851507104002Enzo Doria08/2015
27152^345476+777103999Lelio R Paula09/2011
2716(5*2^345321-1)/3103953Lelio R Paula03/2014
2717(2^345267-9)/539049127103927Lelio R Paula12/2013
2718(78557*2^345163+1)/78589103905Lelio R Paula07/2014
27192^345106-112181103888Enzo Doria06/2014
27202^345079+99103880Lelio R Paula09/2011
272111^99736-1500103865Enzo Doria12/2012
27222^344842-20157103808Enzo Doria06/2013
2723(47*2^344822+1)/1071103801Lelio R Paula05/2015
27242^344802-20765103796Enzo Doria06/2013
27252^344794-3821103794Yves Minet05/2011
27262^344782-109103103790Enzo Doria04/2014
27273^217521-112292103784Enzo Doria06/2014
27282^344759-3505103783Lelio R Paula11/2016
27292^344735-147103776Lelio R Paula09/2011
2730(55459*2^344617+1)/3103745Lelio R Paula07/2014
27312^344607-108891103738Enzo Doria03/2014
27322^344541-19561103718Enzo Doria05/2013
2733(1017*2^344529-1)/569103714Lelio R Paula05/2015
2734(4*10^103703-1)/3103704Serge Batalov08/2009
27352^344444-455103688Yves Minet03/2012
2736(13*53^238539*617^9)/10^307661103673Hans Havermann06/2017
27372^344317-109933103650Enzo Doria04/2014
27382^344309-1852033103648Enzo Doria08/2015
27392^344213-21253103619Enzo Doria06/2013
27402^344196-465103614Lelio R Paula11/2016
27412^344187-20001103611Enzo Doria06/2013
2742(117191#+(355573#)/(117191#))/(200233679)103602Makoto Morimoto10/2017
274320^79621-19^79621103590Jean-Louis Charton03/2011
2744Phi(155391,10)/1243129103586Maksym Voznyy09/2015
27452^344085-20365103580Enzo Doria06/2013
27465^148169+54103566Lelio R Paula11/2016
27472^344017-108795103560Enzo Doria03/2014
27482^343971-5077103546Lelio R Paula09/2011
27492^343899+141103524Lelio R Paula08/2011
27506^133029-67103517Lelio R Paula11/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: November, 17 2017 23:50 (Time in France)

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