PRP Records

Probable Primes Top 10000

(252675 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 ?
300120^81649-19^81649106228Jean-Louis Charton03/2011
3002(55*10^106222+377)/9106223Robert Price02/2019
30032^352814-131106208Lelio R Paula10/2011
30042^352752+73951106189Enzo Doria04/2016
30056^136434+5106167Lelio R Paula11/2014
30067*5^151872-8106155Lelio R Paula11/2014
3007105^52520-2106153Lelio R Paula10/2017
30082^352601-1604809106144Enzo Doria05/2015
300912^98353-43106141Lelio R Paula02/2017
30102^352585-18901106139Enzo Doria05/2013
3011(2^352554-3)/193106128Lelio R Paula12/2013
30122^352540+15015106126Lelio R Paula01/2017
30132^352524-3149106121Yves Minet10/2014
30142^352486-1858781106109Enzo Doria04/2016
30152^352444+12705106097Lelio R Paula01/2017
30162^352228-18953106032Enzo Doria05/2013
30172^352107+1872533105995Enzo Doria05/2016
30182^352066-2591105983Yves Minet07/2014
30192^352030+715105972Lelio R Paula10/2011
30209*6^136176-5105967Lelio R Paula11/2014
302117099*2^351991+58329105965Paul Vanderveen12/2017
3022155^48377+2105962Lelio R Paula08/2013
30232^351865+1869707105922Enzo Doria05/2016
30242^351831+23105912Lelio R Paula10/2011
30259*2^351784-5105899Lelio R Paula09/2014
30262^351671-112387105864Enzo Doria06/2014
30272^351669-109501105863Enzo Doria04/2014
30282^351644+74731105856Enzo Doria04/2016
302913^95025-42105853Lelio R Paula12/2016
30302^351599+15015105842Lelio R Paula01/2017
303119^82763+90105834Lelio R Paula01/2017
3032(9179*2^351540-1)/221105826Lelio R Paula05/2015
303320^81329-51105812Lelio R Paula01/2017
3034(5*10^105811+211)/9105811Robert Price02/2018
30352^351483+28425105807Lelio R Paula01/2017
303615^89960+86105802Lelio R Paula02/2017
30372^351460-17289105801Enzo Doria05/2013
303819^82735+22105798Lelio R Paula01/2017
30392^351435-109077105793Enzo Doria04/2014
30402^351393+1089105780Lelio R Paula01/2017
30412^351364+72631105772Enzo Doria04/2016
30422^351305+1872467105754Enzo Doria05/2016
30433^221649+16105754Lelio R Paula11/2016
30448*3^221637-5105749Lelio R Paula09/2014
30452^351279-2780449105746Enzo Doria03/2016
304615^89903-26105735Lelio R Paula02/2017
30472^351213-73105726Lelio R Paula10/2011
30482^351192-4589105720Yves Minet07/2011
304920^81250-33105709Lelio R Paula12/2016
30502^351076-113159105685Enzo Doria07/2014
305193^53688-2105684Lelio R Paula09/2013
30522^351060-4559105680Yves Minet07/2011
305311^101473-750105674Enzo Doria11/2012
30543*5^151181-8105672Lelio R Paula11/2014
305515^89831-34105650Lelio R Paula02/2017
305711^101448-360105648Enzo Doria08/2012
30563*7^125011+4105648Lelio R Paula11/2014
30582^350943-113269105645Enzo Doria07/2014
30592^350868-19725105622Enzo Doria06/2013
30602^350858-59291105619Enzo Doria10/2015
30612^350851+135105617Lelio R Paula10/2011
30622^350841-741105614Lelio R Paula01/2017
30633*10^105582+77105583Robert Price09/2018
30648*10^105571+3105572Robert Price08/2015
30652^350674-78557105564Jorge Menendez03/2018
30662*5^151026-3105563Lelio R Paula11/2014
3067(2^350702+5)/34264674063105562Lelio R Paula12/2013
30686^135647-5^135647105554Jean-Louis Charton02/2009
30693^221211+236105545Lelio R Paula11/2016
3070(32*10^105530-77)/9105531Robert Price06/2018
307110^105515+33105516Lelio R Paula11/2016
307210^105515-41033105515Patrick De Geest12/2016
3073(29*2^350473-1)/267927105499Lelio R Paula03/2014
307417^85732-72105489Lelio R Paula01/2017
30752^350307-110329105453Enzo Doria05/2014
30762^350253-20365105437Enzo Doria06/2013
3077(3*29^72089-1075)/4105423Curtis Bright05/2015
30782^350139-109009105403Enzo Doria04/2014
30793*5^150763+4105380Lelio R Paula11/2014
308012^97643+91105375Lelio R Paula02/2017
30816*5^150744-7105367Lelio R Paula11/2014
30822^349996-112169105360Enzo Doria06/2014
308311^101142-1080105329Enzo Doria12/2012
3084(68*10^105320-41)/9105321Robert Price10/2013
30853^220712-9934105307Enzo Doria05/2014
30867*10^105296+9105297Robert Price09/2015
30872^349739+1873373105282Enzo Doria06/2016
30887^124574+24105278Lelio R Paula11/2016
30892^349708-20957105273Enzo Doria06/2013
30902^349649-20469105255Enzo Doria06/2013
30912^349607-20109105243Enzo Doria06/2013
30922^349594-19085105239Enzo Doria05/2013
30932^349530+1874479105220Enzo Doria06/2016
3094(3^220528+8)/8081105215Lelio R Paula12/2013
30953^220464-112852105189Enzo Doria07/2014
30962^349419-17349105186Enzo Doria05/2013
30972^349400-2579105180Yves Minet07/2014
30988*5^150471+3105176Lelio R Paula11/2014
3099655^37342+37342^655105165Norbert Schneider08/2018
310013^94403+94105160Lelio R Paula12/2016
31012^349301-112309105151Enzo Doria06/2014
31029*2^349220+5105127Lelio R Paula09/2014
31037*3^220317+8105119Lelio R Paula09/2014
31047^124386+88105119Lelio R Paula11/2016
31052^349171-19657105111Enzo Doria06/2013
3106(2^(6*58185+1)-5)/3105093Kevin Acres11/2013
3107(2^349111-5)/3105093Lelio R Paula12/2013
3108675^37142+37142^675105087Norbert Schneider08/2018
31092^348981-2797573105054Enzo Doria04/2016
31102^348869-6555105021Lelio R Paula01/2017
31115^150217+78104998Lelio R Paula11/2016
31122^348703-113005104971Enzo Doria06/2014
31142^348612-809104943Yves Minet05/2013
3113(73*10^104942-1)/9104943Robert Price01/2015
31152^348583-350407104934Enzo Doria06/2015
31162^348531-949104919Yves Minet05/2012
311720^80636-59104910Lelio R Paula12/2016
31182^348437+35104890Lelio R Paula09/2011
31192^348348+135104864Lelio R Paula09/2011
3121(2^348284+9)/25104843Lelio R Paula12/2013
312075^55914-74104843Norbert Schneider01/2015
31222^348268+255255104840Lelio R Paula01/2017
31235^149985-52104836Lelio R Paula11/2016
31242^348224-20249104826Enzo Doria06/2013
31252^348212-20105104823Enzo Doria06/2013
312620^80562+19104814Lelio R Paula12/2016
31272*10^104811-87104812Robert Price04/2018
31282^348149-20053104804Enzo Doria06/2013
31292^348095-171104788Lelio R Paula09/2011
31302^348003-20377104760Enzo Doria06/2013
31312^347994-741104757Lelio R Paula12/2016
3132(13*2^347972-1)/282309104746Lelio R Paula03/2014
31332^347910-109937104732Enzo Doria04/2014
31345^149794+28104702Lelio R Paula11/2016
3135105^51800-2104698Lelio R Paula10/2017
3136(16^86939+3^86939)/19104684Robert Price06/2013
3137(15^89009-1)/14104682Paul Bourdelais03/2010
31382^347731-18609104678Enzo Doria05/2013
31394*6^134519+7104677Lelio R Paula11/2014
31402^347612-18545104642Enzo Doria05/2013
31416^134465+95104635Lelio R Paula11/2016
31422^347517-17301104614Enzo Doria05/2013
31433^219222-310104596Lelio R Paula11/2016
3144(15*2^347399-1)/13104578Lelio R Paula03/2014
31452^347372-17853104570Enzo Doria05/2013
31462^347314+99104552Lelio R Paula09/2011
31472^347300-22233104548Enzo Doria06/2013
31482^347287-19845104544Enzo Doria06/2013
3149(31*2^347254-1)/891104533Lelio R Paula03/2014
31505*F(250091)*(F(250091)-1)+1104532Serge Batalov04/2015
31517*2^347239-3104531Lelio R Paula09/2014
3152(3^219098-8)/514147439969104525Lelio R Paula12/2013
31535*3^219047+8104513Lelio R Paula09/2014
31542^347148-109073104502Enzo Doria04/2014
31552^347129-20145104497Enzo Doria06/2013
31564*10^104461-57104462Robert Price10/2018
31572^346923-19585104435Enzo Doria05/2013
3158(11*2^346864-1)/175104416Lelio R Paula03/2014
31592^346854+346854^2+1104414Robert Price06/2014
31602^346834+11715104408Lelio R Paula04/2015
316179^55009+78104387Norbert Schneider02/2015
31623^218744+58104368Lelio R Paula11/2016
31632^346649+65104352Lelio R Paula09/2011
31642^346638-17265104349Enzo Doria05/2013
31655*10^104326+77104327Robert Price12/2018
31672^346527-111817104316Enzo Doria05/2014
31666^134055+101104316Lelio R Paula11/2016
31686^134013+163104283Lelio R Paula11/2016
316918^83049-89104250Lelio R Paula01/2017
31702^346213+484049104221Enzo Doria04/2017
317118^83021-91104214Lelio R Paula01/2017
317210^104212+128779104213Patrick De Geest05/2016
317310^104212+237447104213Patrick De Geest05/2016
317410^104212+242139104213Patrick De Geest05/2016
317510^104212+269199104213Patrick De Geest05/2016
3176(10^104212-71)/1104212Serge Batalov12/2014
31772^346078+7695104180Lelio R Paula12/2016
31792^346055-19537104173Enzo Doria05/2013
3178(3*2^346057+1)/77104173Lelio R Paula12/2013
31802^346037-20125104168Enzo Doria06/2013
3181(34*10^104168-7)/9/13/551179104162Makoto Morimoto05/2016
31826^133854-17993104159Enzo Doria03/2013
31832^345990+1874239104154Enzo Doria06/2016
31842^345988-20373104153Enzo Doria06/2013
3185(26*10^104132-503)/9104133Robert Price07/2018
31863*5^148968+8104125Lelio R Paula11/2014
3187(7*10^104113+53)/3104114Robert Price05/2018
3188p(21253)#/2+8104113Robert Price01/2017
3189322^41507+41507^322104094Norbert Schneider12/2014
31906^133768-17423104092Enzo Doria03/2013
31912^345786-19557104092Enzo Doria05/2013
3192171^46606-2104072Lelio R Paula10/2017
31932^345704-149104068Lelio R Paula09/2011
31946^133704-17273104042Enzo Doria02/2013
3195(3*2^345590-1)/23104033Lelio R Paula03/2014
3196(19*2^345590+1)/33859104030Lelio R Paula12/2013
31972^345547+11104021Lelio R Paula09/2011
31982^345504+723104008Lelio R Paula09/2011
31992^345498-20037104006Enzo Doria06/2013
320018^82854-37104005Lelio R Paula01/2017
32012^345486-109065104002Enzo Doria04/2014
32022^345487-1851507104002Enzo Doria08/2015
32032^345476+777103999Lelio R Paula09/2011
32044*10^103981-83103982Robert Price10/2018
3205(5*2^345321-1)/3103953Lelio R Paula03/2014
3206(2^345267-9)/539049127103927Lelio R Paula12/2013
3207(78557*2^345163+1)/78589103905Lelio R Paula07/2014
32082^345106-112181103888Enzo Doria06/2014
32092^345079+99103880Lelio R Paula09/2011
321011^99736-1500103865Enzo Doria12/2012
32112^344842-20157103808Enzo Doria06/2013
3212(47*2^344822+1)/1071103801Lelio R Paula05/2015
32132^344802-20765103796Enzo Doria06/2013
32142^344794-3821103794Yves Minet05/2011
32152^344782-109103103790Enzo Doria04/2014
32163^217521-112292103784Enzo Doria06/2014
32172^344759-3505103783Lelio R Paula11/2016
32182^344735-147103776Lelio R Paula09/2011
3219L(496533)-p(496533)103770Robert Price02/2018
32202*10^103749-69103750Robert Price03/2018
3221(55459*2^344617+1)/3103745Lelio R Paula07/2014
32222^344607-108891103738Enzo Doria03/2014
32232^344541-19561103718Enzo Doria05/2013
3224(1017*2^344529-1)/569103714Lelio R Paula05/2015
3225(4*10^103703-1)/3103704Serge Batalov08/2009
32262^344444-455103688Yves Minet03/2012
3227(13*53^238539*617^9)/10^307661103673Hans Havermann06/2017
32282^344317-109933103650Enzo Doria04/2014
32292^344309-1852033103648Enzo Doria08/2015
32302^344213-21253103619Enzo Doria06/2013
32312^344196-465103614Lelio R Paula11/2016
32322^344187-20001103611Enzo Doria06/2013
3233(117191#+(355573#)/(117191#))/(200233679)103602Makoto Morimoto10/2017
323420^79621-19^79621103590Jean-Louis Charton03/2011
3235Phi(155391,10)/1243129103586Maksym Voznyy09/2015
32362^344085-20365103580Enzo Doria06/2013
32375^148169+54103566Lelio R Paula11/2016
32382^344017-108795103560Enzo Doria03/2014
32392^343971-5077103546Lelio R Paula09/2011
3240(7*10^103531+71)/3103532Robert Price05/2018
32412^343899+141103524Lelio R Paula08/2011
3242(2^343933+1)/(3*98294339989393)103520Gord Palameta08/2018
32436^133029-67103517Lelio R Paula11/2016
3244(17*2^343877+1)/13625103515Lelio R Paula12/2013
3245(136*10^103474-1)/9103476Serge Batalov12/2014
32465^148014-24103458Lelio R Paula11/2016
32472^343604+9931103436Yves Minet01/2011
32482^343601-21189103435Enzo Doria06/2013
32492^343508-115229103407Enzo Doria06/2015
3250(509203*2^343491-1)/16147103403Lelio R Paula05/2015


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 20 2019 09:21 (Time in France)

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