PRP Records

Probable Primes Top 10000

(294613 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 ?
10012^946274+218407284857Enzo Doria03/2024
10027*10^284751+9284752Robert Price04/2023
10032^944561-21284342Stefano Morozzi07/2022
1004(4*10^284330-31)/9284330Serge Batalov11/2022
1005(32*10^283826-23)/9283827Serge Batalov01/2023
10062^942533+82067283731Enzo Doria09/2016
10072^941469+39283411Jon Grantham08/2023
1008(10^283342-31)/3283342Robert Price03/2023
10092^940950+1874989283255Enzo Doria06/2016
10102^940426-2786141283097Enzo Doria11/2015
1011(2*10^282948-11)/9282948Serge Batalov11/2022
10122^939881-114115282933Enzo Doria12/2014
1013(14*10^282673-143)/3282674Robert Price05/2023
101410^282493+632551282494Patrick De Geest02/2017
101610^282493-9^282493282493Jean-Louis Charton03/2007
101510^282493-132327282493Patrick De Geest02/2017
10173^591827-2^591827282374Mike Oakes08/2009
1018Tau(509^18946)282048Nik Lygeros / Olivier Rozier05/2015
10192^936716-1835519281980Enzo Doria04/2015
10202^936588+79411281942Enzo Doria06/2016
10212^936047+1877423281779Enzo Doria08/2016
10222^935713+1869377281678Enzo Doria05/2016
10232^933082+1877059280886Enzo Doria08/2016
1024(5*10^280710+1)/3280711Serge Batalov10/2014
10252^932064+26521280580Enzo Doria12/2023
10262^931976+25280553Stefano Morozzi05/2021
1027(42^172663+1)/43280274Paul Bourdelais07/2019
1028(10^279978+11)/3279978Serge Batalov07/2015
10292^929524-1864829279815Enzo Doria01/2016
10302^929329+22697279756Enzo Doria09/2023
10312^929152+60181279703Enzo Doria02/2016
10322^928621-2787883279543Enzo Doria11/2015
1033(2^927763+lucasV(-1,2,927763)+1)/2279285Mike Oakes04/2017
10342^927429+1882277279184Enzo Doria12/2016
10352^926766-11278985Stefano Morozzi07/2022
1036(71^150697-1)/70278978Paul Bourdelais07/2019
1037(33^183661-1)/32278891Paul Bourdelais12/2018
1038(166*10^278633-7)/3278635Robert Price02/2023
1039(2^925391+lucasV(-1,2,925391)+1)/2278571Mike Oakes03/2017
10402^925330-1301278553Yves Minet06/2015
1041(299*10^278546+1)/3278548Robert Price01/2023
10422^925299+216053278543Enzo Doria11/2023
1043(21^210599+1)/22278457Paul Bourdelais08/2013
1044(266*10^278325+1)/3278327Robert Price01/2023
10452^923261-69175277930Enzo Doria11/2015
1046757^96487-756^96487277796Jean-Louis Charton12/2012
10472^922301+57277641Stefano Morozzi05/2021
10487*10^277478-39277479Robert Price07/2023
1049((((((((((((((291487327^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2277369Serge Batalov07/2016
1050(5^396413-1)/4277081Paul Bourdelais06/2010
10512^920318+2792299277044Enzo Doria02/2016
1052(16*10^276537-31)/3276538Robert Price03/2023
10532^918596-2786939276525Enzo Doria11/2015
10542^917910+28369276319Enzo Doria01/2024
1055(6737^72361-1)/(6737^269-1)276002Ryan Propper11/2023
10562^916639+60563275936Enzo Doria04/2016
1057(2*10^275922+1)/3275922Serge Batalov11/2022
10582^916385-2786383275860Enzo Doria11/2015
10592^915928+82081275722Enzo Doria09/2016
1060(4*10^275671+11)/3275672Tyler Busby02/2023
10612^915576-114137275616Enzo Doria01/2015
10622^914828+1876741275391Enzo Doria07/2016
10632^914757-2203275370Yves Minet12/2015
10647*10^275157-27275158Robert Price11/2022
10652^912744+20011274764Enzo Doria06/2023
10662^911900+1871245274510Enzo Doria05/2016
1067(16*10^274251-91)/3274252Robert Price11/2022
10682^910999+9274239Stefano Morozzi05/2021
1069(2^910869-7)/5274199Stefano Morozzi08/2022
10702^910490+283429274085Enzo Doria01/2017
10717*10^273983+39273984Robert Price01/2023
10722^909988-1862249273934Enzo Doria12/2015
10732^909297+1879157273726Enzo Doria08/2016
10742^909257-1864423273714Enzo Doria01/2016
10752^908739-7273558Stefano Morozzi07/2022
10762^908579-1861747273510Enzo Doria12/2015
10773*2^908005-5273338Jon Grantham07/2023
10782^907635-2791597273226Enzo Doria01/2016
10792^907059+211193273052Enzo Doria08/2023
1080(53^158341+1)/54273022Paul Bourdelais07/2019
10812^906594-113201272912Enzo Doria08/2014
10829*10^272800+91272801Robert Price05/2023
10832*10^272710-49272711Robert Price05/2023
10842*10^272403-91272404Robert Price02/2023
10852^904773+1872167272364Enzo Doria06/2016
10866^349903+5272278Paul Bourdelais02/2021
10872^904149-1862473272176Enzo Doria12/2015
1088(7*10^271757-61)/9271757Erik Branger03/2012
10892^902497+1880117271679Enzo Doria09/2016
10902^901858+77689271487Enzo Doria06/2016
10912^901372+1875301271341Enzo Doria06/2016
10922^901146+219049271272Enzo Doria02/2024
1093(8*10^271039-77)/3271040Robert Price04/2023
10942^899999+1144031270927Norman Luhn09/2023
10952*10^270802-91270803Robert Price02/2023
109623*10^270799-7270801Robert Price10/2022
10972^899121-115033270663Enzo Doria07/2015
10982^898900+883021270596Enzo Doria12/2016
10992^898762-251511270555Enzo Doria12/2013
11002^898589+47270503Lelio R Paula03/2016
1101187322*10^270343-187321270349Danilo Nitsche09/2013
110248358*10^270343-48357270348Danilo Nitsche09/2013
1103(10^270343-1)/9270343Maksym Voznyy07/2007
11042^897867-3217270285Yves Minet12/2016
11052^897849-115273270280Enzo Doria07/2015
11062^897367+26289270135Enzo Doria03/2024
11072^896616-114179269909Enzo Doria12/2014
1108(12648^66049-1)/(12648^257-1)269881Ryan Propper11/2023
1109(22*10^269517-19)/3269518Robert Price07/2023
111010^(2*134739+1)-7*10^134739-1269479Robert Price07/2023
11112^894928+583561269401Enzo Doria04/2017
11122^894673-39343269324Enzo Doria08/2015
11132^893836+23221269072Enzo Doria10/2023
11142^892718+29539268735Enzo Doria03/2024
11152^892660+213901268718Enzo Doria10/2023
1116F(1285607)268676Henri Lifchitz11/2008
11172^892234+22189268590Enzo Doria09/2023
11182^892151+24863268565Enzo Doria11/2023
11192^892112+187663268553Enzo Doria08/2016
1120(266*10^268407-17)/3268409Robert Price02/2023
1121(10^268207+1)/11268206Paul Bourdelais02/2010
11222^890957-69583268205Enzo Doria12/2015
112332841!^2+32840!^2+...+2!^2+1!^2268128Serge Batalov07/2017
11242^890122-351401267954Enzo Doria07/2015
1125(19^209359-1)/18267718Paul Bourdelais08/2010
1126(85^138647+1)/86267507Paul Bourdelais07/2019
1127(1005^89087-1)/1004267451Jinyuan Wang01/2024
1128(485^99523-1)/484267291Michael Stocker05/2020
11292^886324+77791266811Enzo Doria06/2016
11307*10^266731+87266732Robert Price11/2022
11312^886040+213901266725Enzo Doria10/2023
11322^885242+217909266485Enzo Doria01/2024
11332^884738+26809266333Enzo Doria12/2023
11342^884714+1880527266326Enzo Doria10/2016
11357*10^266024-47266025Robert Price08/2023
113611^255426+255426^11265999Serge Batalov05/2014
11372^883462-343421265949Enzo Doria07/2015
11382^883442+1875019265943Enzo Doria06/2016
11392^883333-291583265910Enzo Doria07/2015
114010^265566+3593037265567Paul Bourdelais08/2023
1141(2*10^265321-17)/3265321Serge Batalov11/2022
1142(16*10^265052-91)/3265053Robert Price11/2022
11432^880411+1882673265031Enzo Doria12/2016
1144(14*10^264791-11)/3264792Robert Price08/2022
11452^879530-2788031264765Enzo Doria12/2015
11462^879292+25171264694Enzo Doria11/2023
1147(2*10^264539+61)/9264539Serge Batalov11/2022
11482^878118+2793079264340Enzo Doria02/2016
1149(2^878073-7)/5264326Stefano Morozzi08/2022
1150(37^168527-1)/36264283Paul Bourdelais08/2019
11515^377865+3^377865-1264117Jon Grantham08/2023
1152(19*10^263971+131)/3263972Robert Price08/2023
11532^876202-17263764Stefano Morozzi07/2022
1154(14*10^263720-11)/3263721Robert Price08/2022
11552^875748-461129263627Enzo Doria07/2015
11562^875518-15263558Stefano Morozzi07/2022
1157(29*10^263523-17)/3263524Robert Price01/2023
11582^875181-2789923263456Enzo Doria12/2015
11592^875101-350083263432Enzo Doria08/2015
11602^874684+1883587263307Enzo Doria01/2017
11612^874616+1872211263286Enzo Doria05/2016
11623^551491+16263129Robert Price04/2020
11632^874073+2792957263123Enzo Doria02/2016
1164(7*10^263006-19)/3263007Robert Price10/2023
11652^873628+1878751262989Enzo Doria08/2016
11662^873497+20837262949Enzo Doria08/2023
11672^873288-269262886Yves Minet01/2015
1168(2*10^262874+7)/9262874Rytis Slatkevicius01/2023
1169(28*10^262655-43)/3262656Robert Price04/2023
1170(2*10^262603-11)/9262603Serge Batalov11/2022
11712^871991-4207262496Yves Minet03/2021
1172(23*10^262324+7)/3262325Robert Price05/2023
11732^871146-3173262242Yves Minet07/2016
11742^869601-163261776Yves Minet01/2015
1175(2*10^261704+61)/9261704Serge Batalov11/2022
11762^869326+282859261694Enzo Doria11/2016
11772^869035-114181261606Enzo Doria12/2014
11782^868817+26777261540Enzo Doria12/2023
11793^547850+9000004261391Enzo Doria10/2023
11804*10^261248+91261249Robert Price11/2022
11812^865715+80303260607Enzo Doria07/2016
11822^865474+23209260534Enzo Doria10/2023
11832^865238+214759260463Enzo Doria11/2023
11842^865048+1882411260406Enzo Doria12/2016
11852^864899-113871260361Enzo Doria10/2014
1186(16*10^260256-91)/3260257Robert Price11/2022
1187(7*10^260198-61)/9260198Erik Branger11/2011
11882^864298-2788421260180Enzo Doria12/2015
11892^864039-2791357260102Enzo Doria01/2016
11902^863621-113833259976Enzo Doria10/2014
119110^259945-11259945Mischa Rodermond04/2023
1192(28*10^259897+113)/3259898Robert Price06/2023
11932^862837+75767259740Enzo Doria05/2016
11942^862637-31259680Jorge Menendez05/2019
11952^862088+1874941259515Enzo Doria06/2016
11962^861987-134557259484Hans Havermann10/2018
1197(14*10^259431-143)/3259432Robert Price05/2023
11982^861516-1854029259343Enzo Doria09/2015
11992^860975-1853977259180Enzo Doria09/2015
12003^543128+16259138Robert Price04/2020
12012^860625-1858843259074Enzo Doria10/2015
12022^860110+77689258919Enzo Doria05/2016
12032^859600+1880371258766Enzo Doria10/2016
12042^859433+494711258716Makoto Morimoto10/2013
1205(2^859433-44)/(2^2*3)258715Makoto Morimoto08/2019
1206(2^859431-11)/3258715Stefano Morozzi08/2022
1207(13*10^258710-43)/3258711Robert Price08/2023
1208(2^859433+39899)/(73*3907*46301)258705Makoto Morimoto10/2016
12092^859240+1875271258658Enzo Doria06/2016
1210Tau(971^15738)258571Nik Lygeros / Olivier Rozier05/2015
1211(23*10^258494-47)/3258495Robert Price09/2023
1212(144^119671+1)/145258292Paul Bourdelais08/2019
12132^857608+105258166Stefano Morozzi05/2021
1214(11*2^857159-13)/15258031Renaud Lifchitz08/2011
12152^857016-633113257988Enzo Doria12/2013
12162^855732-113969257602Enzo Doria10/2014
1217(5*10^257431+91)/3257432Robert Price08/2023
12182^853682-3911256984Enzo Doria05/2014
121911^246668-90256879Enzo Doria12/2012
12205*2^852698+3256689Jon Grantham07/2023
1221(23*10^256654+7)/3256655Robert Price05/2023
12222^851904-113939256449Enzo Doria10/2014
12232^851725-851725^2256395Henri Lifchitz03/2019
122411^246167-90256357Enzo Doria12/2012
1225(85*10^256301-1)/3256303Robert Price12/2022
1226(10^256187+7)/63443/148782853256175Alfred Reich10/2021
12272^850700-569049256087Enzo Doria11/2013
12282^850675+153256079Stefano Morozzi05/2021
122921^193601-20^193601255983Jean-Louis Charton02/2015
1230(37^163193+1)/38255918Paul Bourdelais07/2019
1231(14*10^255805-83)/3255806Robert Price11/2022
12322^849316+25861255670Enzo Doria12/2023
12332^849177-114025255628Enzo Doria12/2014
12342*10^255442-21255443Robert Price08/2023
12352^848502-3173255425Yves Minet07/2016
12362^848178-140291255328Enzo Doria01/2014
12377*10^255167+87255168Robert Price11/2022
12382^847622-2441255160Yves Minet02/2016
12392^847291+182843255061Enzo Doria11/2016
12402^847174+1879429255025Enzo Doria09/2016
12412^846881+215837254937Enzo Doria12/2023
124224*29^174239+13361254809Curtis Bright04/2015
124322*10^254639+7254641Robert Price10/2022
12442^845633-933075254561Paul Bourdelais11/2021
12452^845610-1868591254554Enzo Doria04/2016
12462^845484+81931254517Enzo Doria08/2016
12472^845402-114761254492Enzo Doria05/2015
124898*10^254173-9254175Robert Price05/2023
12492^844334-2792441254170Enzo Doria02/2016
12502*10^254162+69254163Robert Price08/2023


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 04 2024 15:31 (Time in France)

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