PRP Records

Probable Primes Top 10000

(294627 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 ?
100122845^65536+22844^65536285658Kellen Shenton03/2021
1002(11*2^948635-13)/15285568Renaud Lifchitz11/2011
1003(54^164839+1)/55285565Paul Bourdelais07/2019
10042^948510+782569285530Enzo Doria10/2016
10052^948374-114137285490Enzo Doria01/2015
10062^947739+1872923285298Enzo Doria06/2016
10072^946274+218407284857Enzo Doria03/2024
10087*10^284751+9284752Robert Price04/2023
10092^944561-21284342Stefano Morozzi07/2022
1010(4*10^284330-31)/9284330Serge Batalov11/2022
1011(32*10^283826-23)/9283827Serge Batalov01/2023
10122^942533+82067283731Enzo Doria09/2016
10132^941469+39283411Jon Grantham08/2023
1014(10^283342-31)/3283342Robert Price03/2023
10152^940950+1874989283255Enzo Doria06/2016
10162^940426-2786141283097Enzo Doria11/2015
1017(2*10^282948-11)/9282948Serge Batalov11/2022
10182^939881-114115282933Enzo Doria12/2014
1019(14*10^282673-143)/3282674Robert Price05/2023
102010^282493+632551282494Patrick De Geest02/2017
102210^282493-9^282493282493Jean-Louis Charton03/2007
102110^282493-132327282493Patrick De Geest02/2017
10233^591827-2^591827282374Mike Oakes08/2009
1024Tau(509^18946)282048Nik Lygeros / Olivier Rozier05/2015
10252^936716-1835519281980Enzo Doria04/2015
10262^936588+79411281942Enzo Doria06/2016
10272^936047+1877423281779Enzo Doria08/2016
10282^935713+1869377281678Enzo Doria05/2016
10292^933082+1877059280886Enzo Doria08/2016
1030(5*10^280710+1)/3280711Serge Batalov10/2014
10312^932064+26521280580Enzo Doria12/2023
10322^931976+25280553Stefano Morozzi05/2021
1033(42^172663+1)/43280274Paul Bourdelais07/2019
1034(10^279978+11)/3279978Serge Batalov07/2015
10352^929524-1864829279815Enzo Doria01/2016
10362^929329+22697279756Enzo Doria09/2023
10372^929152+60181279703Enzo Doria02/2016
10382^928621-2787883279543Enzo Doria11/2015
1039(2^927763+lucasV(-1,2,927763)+1)/2279285Mike Oakes04/2017
10402^927429+1882277279184Enzo Doria12/2016
10412^926766-11278985Stefano Morozzi07/2022
1042(71^150697-1)/70278978Paul Bourdelais07/2019
1043(33^183661-1)/32278891Paul Bourdelais12/2018
1044(166*10^278633-7)/3278635Robert Price02/2023
1045(2^925391+lucasV(-1,2,925391)+1)/2278571Mike Oakes03/2017
10462^925330-1301278553Yves Minet06/2015
1047(299*10^278546+1)/3278548Robert Price01/2023
10482^925299+216053278543Enzo Doria11/2023
1049(21^210599+1)/22278457Paul Bourdelais08/2013
1050(266*10^278325+1)/3278327Robert Price01/2023
10512^923261-69175277930Enzo Doria11/2015
1052757^96487-756^96487277796Jean-Louis Charton12/2012
10532^922301+57277641Stefano Morozzi05/2021
10547*10^277478-39277479Robert Price07/2023
1055((((((((((((((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
1056(5^396413-1)/4277081Paul Bourdelais06/2010
10572^920318+2792299277044Enzo Doria02/2016
1058(16*10^276537-31)/3276538Robert Price03/2023
10592^918596-2786939276525Enzo Doria11/2015
10602^917910+28369276319Enzo Doria01/2024
1061(6737^72361-1)/(6737^269-1)276002Ryan Propper11/2023
10622^916639+60563275936Enzo Doria04/2016
1063(2*10^275922+1)/3275922Serge Batalov11/2022
10642^916385-2786383275860Enzo Doria11/2015
10652^915928+82081275722Enzo Doria09/2016
1066(4*10^275671+11)/3275672Tyler Busby02/2023
10672^915576-114137275616Enzo Doria01/2015
10682^914828+1876741275391Enzo Doria07/2016
10692^914757-2203275370Yves Minet12/2015
10707*10^275157-27275158Robert Price11/2022
10712^912744+20011274764Enzo Doria06/2023
10722^911900+1871245274510Enzo Doria05/2016
1073(16*10^274251-91)/3274252Robert Price11/2022
10742^910999+9274239Stefano Morozzi05/2021
1075(2^910869-7)/5274199Stefano Morozzi08/2022
10762^910490+283429274085Enzo Doria01/2017
10777*10^273983+39273984Robert Price01/2023
10782^909988-1862249273934Enzo Doria12/2015
10792^909297+1879157273726Enzo Doria08/2016
10802^909257-1864423273714Enzo Doria01/2016
10812^908739-7273558Stefano Morozzi07/2022
10822^908579-1861747273510Enzo Doria12/2015
10833*2^908005-5273338Jon Grantham07/2023
10842^907635-2791597273226Enzo Doria01/2016
10852^907059+211193273052Enzo Doria08/2023
1086(53^158341+1)/54273022Paul Bourdelais07/2019
10872^906594-113201272912Enzo Doria08/2014
10889*10^272800+91272801Robert Price05/2023
10892*10^272710-49272711Robert Price05/2023
10902*10^272403-91272404Robert Price02/2023
10912^904773+1872167272364Enzo Doria06/2016
10926^349903+5272278Paul Bourdelais02/2021
10932^904149-1862473272176Enzo Doria12/2015
1094(7*10^271757-61)/9271757Erik Branger03/2012
10952^902497+1880117271679Enzo Doria09/2016
10962^901858+77689271487Enzo Doria06/2016
10972^901372+1875301271341Enzo Doria06/2016
10982^901146+219049271272Enzo Doria02/2024
1099(8*10^271039-77)/3271040Robert Price04/2023
11002^899999+1144031270927Norman Luhn09/2023
11012*10^270802-91270803Robert Price02/2023
110223*10^270799-7270801Robert Price10/2022
11032^899121-115033270663Enzo Doria07/2015
11042^898900+883021270596Enzo Doria12/2016
11052^898762-251511270555Enzo Doria12/2013
11062^898589+47270503Lelio R Paula03/2016
1107187322*10^270343-187321270349Danilo Nitsche09/2013
110848358*10^270343-48357270348Danilo Nitsche09/2013
1109(10^270343-1)/9270343Maksym Voznyy07/2007
11102^897867-3217270285Yves Minet12/2016
11112^897849-115273270280Enzo Doria07/2015
11122^897367+26289270135Enzo Doria03/2024
11132^896616-114179269909Enzo Doria12/2014
1114(12648^66049-1)/(12648^257-1)269881Ryan Propper11/2023
1115(22*10^269517-19)/3269518Robert Price07/2023
111610^(2*134739+1)-7*10^134739-1269479Robert Price07/2023
11172^894928+583561269401Enzo Doria04/2017
11182^894673-39343269324Enzo Doria08/2015
11192^893836+23221269072Enzo Doria10/2023
11202^892718+29539268735Enzo Doria03/2024
11212^892660+213901268718Enzo Doria10/2023
1122F(1285607)268676Henri Lifchitz11/2008
11232^892234+22189268590Enzo Doria09/2023
11242^892151+24863268565Enzo Doria11/2023
11252^892112+187663268553Enzo Doria08/2016
1126(266*10^268407-17)/3268409Robert Price02/2023
1127(10^268207+1)/11268206Paul Bourdelais02/2010
11282^890957-69583268205Enzo Doria12/2015
112932841!^2+32840!^2+...+2!^2+1!^2268128Serge Batalov07/2017
11302^890122-351401267954Enzo Doria07/2015
1131(19^209359-1)/18267718Paul Bourdelais08/2010
1132(85^138647+1)/86267507Paul Bourdelais07/2019
1133(1005^89087-1)/1004267451Jinyuan Wang01/2024
1134(485^99523-1)/484267291Michael Stocker05/2020
11352^886324+77791266811Enzo Doria06/2016
11367*10^266731+87266732Robert Price11/2022
11372^886040+213901266725Enzo Doria10/2023
11382^885242+217909266485Enzo Doria01/2024
11392^884738+26809266333Enzo Doria12/2023
11402^884714+1880527266326Enzo Doria10/2016
11417*10^266024-47266025Robert Price08/2023
114211^255426+255426^11265999Serge Batalov05/2014
11432^883462-343421265949Enzo Doria07/2015
11442^883442+1875019265943Enzo Doria06/2016
11452^883333-291583265910Enzo Doria07/2015
114610^265566+3593037265567Paul Bourdelais08/2023
1147(2*10^265321-17)/3265321Serge Batalov11/2022
1148(16*10^265052-91)/3265053Robert Price11/2022
11492^880411+1882673265031Enzo Doria12/2016
1150(14*10^264791-11)/3264792Robert Price08/2022
11512^879530-2788031264765Enzo Doria12/2015
11522^879292+25171264694Enzo Doria11/2023
1153(2*10^264539+61)/9264539Serge Batalov11/2022
11542^878118+2793079264340Enzo Doria02/2016
1155(2^878073-7)/5264326Stefano Morozzi08/2022
1156(37^168527-1)/36264283Paul Bourdelais08/2019
11575^377865+3^377865-1264117Jon Grantham08/2023
1158(19*10^263971+131)/3263972Robert Price08/2023
11592^876202-17263764Stefano Morozzi07/2022
1160(14*10^263720-11)/3263721Robert Price08/2022
11612^875748-461129263627Enzo Doria07/2015
11622^875518-15263558Stefano Morozzi07/2022
1163(29*10^263523-17)/3263524Robert Price01/2023
11642^875181-2789923263456Enzo Doria12/2015
11652^875101-350083263432Enzo Doria08/2015
11662^874684+1883587263307Enzo Doria01/2017
11672^874616+1872211263286Enzo Doria05/2016
11682^874566+30049263271Enzo Doria03/2024
11693^551491+16263129Robert Price04/2020
11702^874073+2792957263123Enzo Doria02/2016
1171(7*10^263006-19)/3263007Robert Price10/2023
11722^873628+1878751262989Enzo Doria08/2016
11732^873497+20837262949Enzo Doria08/2023
11742^873288-269262886Yves Minet01/2015
1175(2*10^262874+7)/9262874Rytis Slatkevicius01/2023
1176(28*10^262655-43)/3262656Robert Price04/2023
1177(2*10^262603-11)/9262603Serge Batalov11/2022
11782^871991-4207262496Yves Minet03/2021
1179(23*10^262324+7)/3262325Robert Price05/2023
11802^871146-3173262242Yves Minet07/2016
11812^869601-163261776Yves Minet01/2015
1182(2*10^261704+61)/9261704Serge Batalov11/2022
11832^869326+282859261694Enzo Doria11/2016
11842^869035-114181261606Enzo Doria12/2014
11852^868817+26777261540Enzo Doria12/2023
11863^547850+9000004261391Enzo Doria10/2023
11874*10^261248+91261249Robert Price11/2022
11882^865715+80303260607Enzo Doria07/2016
11892^865474+23209260534Enzo Doria10/2023
11902^865238+214759260463Enzo Doria11/2023
11912^865048+1882411260406Enzo Doria12/2016
11922^864899-113871260361Enzo Doria10/2014
1193(16*10^260256-91)/3260257Robert Price11/2022
1194(7*10^260198-61)/9260198Erik Branger11/2011
11952^864298-2788421260180Enzo Doria12/2015
11962^864039-2791357260102Enzo Doria01/2016
11972^863621-113833259976Enzo Doria10/2014
119810^259945-11259945Mischa Rodermond04/2023
1199(28*10^259897+113)/3259898Robert Price06/2023
12002^862837+75767259740Enzo Doria05/2016
12012^862637-31259680Jorge Menendez05/2019
12022^862088+1874941259515Enzo Doria06/2016
12032^861987-134557259484Hans Havermann10/2018
1204(14*10^259431-143)/3259432Robert Price05/2023
12052^861516-1854029259343Enzo Doria09/2015
12062^860975-1853977259180Enzo Doria09/2015
12073^543128+16259138Robert Price04/2020
12082^860625-1858843259074Enzo Doria10/2015
12092^860110+77689258919Enzo Doria05/2016
12102^859600+1880371258766Enzo Doria10/2016
12112^859433+494711258716Makoto Morimoto10/2013
1213(2^859433-44)/(2^2*3)258715Makoto Morimoto08/2019
1212(2^859431-11)/3258715Stefano Morozzi08/2022
1214(13*10^258710-43)/3258711Robert Price08/2023
1215(2^859433+39899)/(73*3907*46301)258705Makoto Morimoto10/2016
12162^859240+1875271258658Enzo Doria06/2016
1217Tau(971^15738)258571Nik Lygeros / Olivier Rozier05/2015
1218(23*10^258494-47)/3258495Robert Price09/2023
1219(144^119671+1)/145258292Paul Bourdelais08/2019
12202^857608+105258166Stefano Morozzi05/2021
1221(11*2^857159-13)/15258031Renaud Lifchitz08/2011
12222^857016-633113257988Enzo Doria12/2013
12232^855732-113969257602Enzo Doria10/2014
1224(5*10^257431+91)/3257432Robert Price08/2023
12252^853682-3911256984Enzo Doria05/2014
122611^246668-90256879Enzo Doria12/2012
12275*2^852698+3256689Jon Grantham07/2023
1228(23*10^256654+7)/3256655Robert Price05/2023
12292^851904-113939256449Enzo Doria10/2014
12302^851725-851725^2256395Henri Lifchitz03/2019
123111^246167-90256357Enzo Doria12/2012
1232(85*10^256301-1)/3256303Robert Price12/2022
1233(10^256187+7)/63443/148782853256175Alfred Reich10/2021
12342^850700-569049256087Enzo Doria11/2013
12352^850675+153256079Stefano Morozzi05/2021
123621^193601-20^193601255983Jean-Louis Charton02/2015
1237(37^163193+1)/38255918Paul Bourdelais07/2019
1238(14*10^255805-83)/3255806Robert Price11/2022
12392^849316+25861255670Enzo Doria12/2023
12402^849177-114025255628Enzo Doria12/2014
12412*10^255442-21255443Robert Price08/2023
12422^848502-3173255425Yves Minet07/2016
12432^848178-140291255328Enzo Doria01/2014
12447*10^255167+87255168Robert Price11/2022
12452^847622-2441255160Yves Minet02/2016
12462^847291+182843255061Enzo Doria11/2016
12472^847174+1879429255025Enzo Doria09/2016
12482^846881+215837254937Enzo Doria12/2023
124924*29^174239+13361254809Curtis Bright04/2015
125022*10^254639+7254641Robert Price10/2022


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 12 2024 13:37 (Time in France)

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