PRP Records

Probable Primes Top 10000

(253476 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 ?
3501(55459*2^340090+1)/1591102379Lelio R Paula07/2014
350289^52511-88^52511102365Robert Price06/2015
35033^214539-112756102362Enzo Doria07/2014
35042^340000-19877102351Enzo Doria06/2013
35052^339990-114845102348Enzo Doria05/2015
3506(3^214516-2)/51383102346Lelio R Paula12/2013
350720^78661-99102341Lelio R Paula09/2016
35082^339951-19585102336Enzo Doria05/2013
3509(13*2^339943+1)/45102333Lelio R Paula12/2013
35102^339889+29327102317Yves Minet06/2010
351126348^7641+7641^26348102314Hans Havermann03/2019
35122^339834-109493102301Enzo Doria04/2014
3513(16*10^102299-19)/3102300Robert Price02/2019
3514(11^98221-5^98221)/6102286Robert Price01/2013
35153^214365+1820102279Lelio R Paula10/2016
351631978^1579+1579^31978102278Hans Havermann03/2019
3517(11*2^339705-1)/183102261Lelio R Paula03/2014
35182^339694-16995102259Lelio R Paula09/2016
3519(56*10^102255+691)/9102256Robert Price05/2019
3520122^49008+121102249Norbert Schneider10/2018
35227^120985-38102245Lelio R Paula10/2016
352110^102244+122961102245Patrick De Geest12/2016
352310^102244-27102244Lelio R Paula09/2016
35247^120982-62102242Lelio R Paula10/2016
35254*6^131382-5102236Lelio R Paula11/2014
35262^339586-1091102226Yves Minet11/2012
352711^98161-3072000102225Enzo Doria12/2012
35289*7^120961-4102225Lelio R Paula11/2014
35295*3^214250+2102224Serge Batalov10/2010
353012^94713-59102213Lelio R Paula10/2016
353112^94705+89102204Lelio R Paula10/2016
35322^339407-177102172Lelio R Paula08/2011
35334*10^102163-57102164Robert Price10/2018
35342^339355+65102157Lelio R Paula07/2011
3535(2^339323+47)/880715102141Lelio R Paula12/2013
35372^339168+21102100Lelio R Paula07/2011
35362^339167-108807102100Enzo Doria03/2014
35382^339156+163102097Lelio R Paula08/2011
3539(25*10^102076-67)/3102077Robert Price06/2019
35402^339081-4543102074Yves Minet03/2019
354124327^15668+15668^24327102053Hans Havermann02/2019
354225080^11711+11711^25080102041Hans Havermann02/2019
3543(2^338982-7)/1754517102038Lelio R Paula12/2013
35442^338891-18885102017Enzo Doria05/2013
35458*10^102000+51102001Robert Price08/2019
35462^338829-113239101998Enzo Doria07/2014
35472^338828-113297101998Enzo Doria07/2014
35482^338796+93101988Donovan Johnson06/2008
3549lucasU(1373,1,32502)-lucasU(1373,1,32501)101978Mike Oakes05/2009
355025295^10744+10744^25295101969Hans Havermann01/2019
355125712^9243+9243^25712101969Hans Havermann01/2019
3552(71^55079-1)/70101964Paul Bourdelais08/2017
35532^338682-19865101954Enzo Doria06/2013
3554(2^(112895*3+1)+243)/7101954Kevin Acres12/2013
355528594^3673+3673^28594101939Hans Havermann02/2019
35562^338568+37101920Lelio R Paula07/2011
35572^338559-1858777101917Enzo Doria04/2016
3558(9*2^338520+1)/365101904Lelio R Paula12/2013
355924502^14419+14419^24502101903Hans Havermann01/2019
35602^338497-17041101898Enzo Doria05/2013
35612^338475+54615101892Lelio R Paula10/2016
35622^338426-19797101877Enzo Doria06/2013
35632^338368-20369101859Enzo Doria06/2013
35642^338366+74179101859Enzo Doria04/2016
356527088^5755+5755^27088101853Hans Havermann01/2019
35662^338280-19745101833Enzo Doria06/2013
3567(3*2^338236-1)/347101818Lelio R Paula03/2014
35686^130841+103101815Lelio R Paula10/2016
35692^338122-20117101785Enzo Doria06/2013
3570(2^338139+5)/905333101785Lelio R Paula12/2013
357135^65917-7092101781Enzo Doria03/2013
35722^338010-19833101752Enzo Doria06/2013
35733^213215-76101730Lelio R Paula09/2016
357423907^17998+17998^23907101730Hans Havermann01/2019
35752^337930+63101728Lelio R Paula07/2011
35762^337920+1869661101725Enzo Doria05/2016
357724116^16509+16509^24116101715Hans Havermann01/2019
35782^337859-19645101706Enzo Doria05/2013
35792^337754+1869169101675Enzo Doria05/2016
35803*10^101657-37101658Robert Price07/2018
3581(31*2^337677-1)/593101650Lelio R Paula03/2014
358211^97605-24101646Lelio R Paula10/2016
35838^112539-112539101633Robert Price01/2014
358425694^9003+9003^25694101605Hans Havermann12/2018
35852^337515-19869101603Enzo Doria06/2013
35862^337473+719101590Lelio R Paula08/2011
3587(2^337485-509203)/656647157101585Lelio R Paula12/2013
35882^337452-108815101584Enzo Doria03/2014
35892^337453+1185101584Lelio R Paula09/2016
35902^337410-113561101571Enzo Doria08/2014
35912^337387+855101564Lelio R Paula09/2016
35922^337367-17295101558Lelio R Paula09/2016
35932^337342-109035101551Enzo Doria04/2014
359423703^19238+19238^23703101548Hans Havermann12/2018
35952^337267-19101528Lelio R Paula07/2011
35962^337183-19989101503Enzo Doria06/2013
35972^337149+72425101492Enzo Doria04/2016
359824041^16642+16642^24041101483Hans Havermann12/2018
359933982^969+969^33982101482Hans Havermann12/2018
36002^337101-20241101478Enzo Doria06/2013
36012^337035-20001101458Enzo Doria06/2013
36022^337017-16995101453Lelio R Paula09/2016
36032^336979-115315101441Enzo Doria06/2015
36042^336970-20885101439Enzo Doria06/2013
36052^336958+79101435Lelio R Paula10/2009
36062^336942+169101430Lelio R Paula10/2009
3607(15185*2^336894-1)/7939101416Lelio R Paula05/2015
36084*10^101415-89101416Robert Price11/2018
36092^336871+257463101409Tony Prest / Never Odd Or Even04/2016
36102^336871+318105101409Tony Prest / Never Odd Or Even04/2016
36112^336871+1010813101409Tony Prest / Never Odd Or Even04/2016
36122^336871+2302245101409Tony Prest / Never Odd Or Even04/2016
36132^336871+389273101409Tony Prest / Never Odd Or Even04/2016
36142^336871+1685475101409Tony Prest / Never Odd Or Even04/2016
36152^336871+1068119101409Tony Prest / Never Odd Or Even04/2016
36162^336871+586905101409Tony Prest / Never Odd Or Even04/2016
36172^336871+674571101409Tony Prest / Never Odd Or Even04/2016
36182^336871+707009101409Tony Prest / Never Odd Or Even04/2016
36192^336871+1210299101409Tony Prest / Never Odd Or Even04/2016
36202^336871+1921185101409Tony Prest / Never Odd Or Even04/2016
36212^336871+2003973101409Tony Prest / Never Odd Or Even04/2016
36222^336871+2656475101409Tony Prest / Never Odd Or Even04/2016
36232^336871+2703023101409Tony Prest / Never Odd Or Even04/2016
36242^336871+2704545101409Tony Prest / Never Odd Or Even04/2016
36252^336871+2766801101409Tony Prest / Never Odd Or Even04/2016
36262^336871+2127735101409Tony Prest / Never Odd Or Even04/2016
3627(2^336871+821089)/3101408Tony Prest / Never Odd Or Even05/2016
3628(2^336871+119567)/5101408Tony Prest / Never Odd Or Even05/2016
3629(2^336871+398161)/3101408Tony Prest / Never Odd Or Even05/2016
3630(2^336871+625889)/7101408Tony Prest / Never Odd Or Even05/2016
363124097^16150+16150^24097101405Hans Havermann12/2018
36322^336842+94065101400Lelio R Paula09/2016
3633(2^336871+904417)/3/3/3/5/19/9287177/9690011663/29993043103101378Tony Prest / Never Odd Or Even04/2016
3634(2^336871+631971)/13/251/1601/294277/614362921/30324278867101377Tony Prest / Never Odd Or Even04/2016
3635(2^336871+1443541)/3/89/1655197/11018131/47972707/468862691879101374Tony Prest / Never Odd Or Even04/2016
3636(2^336871+689863)/3/11/109/137/1867/7151/20800501/29243857/127778489101373Tony Prest / Never Odd Or Even04/2016
3637(2^336871+219839)/191/643/3011/9479/117127/175750007/4578271757101373Tony Prest / Never Odd Or Even04/2016
3638(2^336871+272895)/19/661/977572033/95853078653/520779768241101373Tony Prest / Never Odd Or Even04/2016
3639(2^336871+1023429)/2311/415873/991889/3630648341/207732189179101373Tony Prest / Never Odd Or Even04/2016
364010^101369+203811101370Patrick De Geest11/2016
364110^101369-99101369Lelio R Paula09/2016
3642(2^336871+1832627)/5/5/23/181/4397/91373/3746673331/115602484097/279351383917101363Tony Prest / Never Odd Or Even04/2016
36432^336701-113563101358Enzo Doria08/2014
36442^336644-109023101340Enzo Doria04/2014
36452^336601-21081101327Enzo Doria06/2013
364620^77869+63101310Lelio R Paula09/2016
3647(13*2^336523-1)/19101304Lelio R Paula03/2014
36496^130179-137101299Lelio R Paula10/2016
3648(2^336506+lucasV(1,2,336506)+1)/2101299Mike Oakes11/2016
3650(24737*2^336485+1)/7285101293Lelio R Paula07/2014
3651(2^336448+9)/497405101276Lelio R Paula12/2013
36522^336369-19753101258Enzo Doria05/2013
365323842^17653+17653^23842101253Hans Havermann11/2018
36542^336350-344291101252Enzo Doria07/2015
3655(56*10^101222-47)/9101223Robert Price02/2019
36562^336243-108777101220Enzo Doria03/2014
3657(31*2^336189-1)/19101204Lelio R Paula03/2014
365823535^19954+19954^23535101202Hans Havermann11/2018
3659(78557*2^336178+1)/1268757101199Lelio R Paula07/2014
36602^336150-20393101192Enzo Doria06/2013
366123996^16473+16473^23996101186Hans Havermann11/2018
36622^336112-1865249101180Enzo Doria03/2016
36632^336103-109015101178Enzo Doria04/2014
366413^90809-96101157Lelio R Paula10/2016
366526199^7258+7258^26199101150Hans Havermann11/2018
366619^79098-30101147Lelio R Paula10/2016
366719^79095+88101144Lelio R Paula10/2016
366815^85976+32101116Lelio R Paula10/2016
36692^335872-2776215101108Tony Prest / Never Odd Or Even01/2019
3670(3^211950+7)/28854513015920697088101107Lelio R Paula11/2013
3671(4^167933+17)/3101106Robert Price02/2017
36732^335858+153101104Lelio R Paula10/2009
3672(2^335872-2776871)/5/5/479101104Tony Prest / Never Odd Or Even01/2019
3674(2^335872-2758787)/23/31/20809101101Tony Prest / Never Odd Or Even01/2019
3675(2^335872-2795083)/3/3/113/283/148367101097Tony Prest / Never Odd Or Even01/2019
36766^129918-35101096Lelio R Paula10/2016
36773^211885-70101095Lelio R Paula09/2016
3679(29*2^335835-1)/550599101093Lelio R Paula03/2014
3678(2^335872-2794771)/3/5/5/61/232312440293101093Tony Prest / Never Odd Or Even01/2019
36802^335818-20033101092Enzo Doria06/2013
36812^335813-110083101090Enzo Doria04/2014
36822^335804+2155101088Lelio R Paula09/2016
3683(2^335872-2756679)/7/7/7/13/31/4987/437653/8734021101087Tony Prest / Never Odd Or Even01/2019
36842^335784-16145101082Enzo Doria04/2013
368511^97051+62101069Lelio R Paula10/2016
36863*10^101065+11101066Robert Price07/2018
368727820^4293+4293^27820101064Hans Havermann10/2018
3688(2^335691-3)/26515101049Lelio R Paula12/2013
36892^335658-94395101044Lelio R Paula09/2016
369024514^13215+13215^24514101024Hans Havermann11/2018
36912^335586+169101022Lelio R Paula10/2009
3692(56^57787-1)/55101021Paul Bourdelais08/2017
3693(19*10^100997+737)/9100998Robert Price07/2018
369447599!2+1024100991Robert Price02/2015
36952^335468-18629100986Enzo Doria05/2013
36962^335454-20961100982Enzo Doria06/2013
369710^100978+61100979Lelio R Paula09/2016
369810^100978-156437100978Patrick De Geest11/2016
3699(15*2^335417+1)/481100970Lelio R Paula12/2013
37002^335403-1859167100967Enzo Doria03/2016
370123599^18976+18976^23599100962Hans Havermann10/2018
37029*2^335364-5100956Lelio R Paula08/2014
37032^335349+72287100951Enzo Doria04/2016
37042^335329+16095100945Lelio R Paula09/2016
3705232823#+233663100937Makoto Morimoto10/2017
3706(232823#+10141)/(10141*1674461)100927Makoto Morimoto06/2019
37072^335237-20893100917Enzo Doria06/2013
37082^335222-19337100912Enzo Doria05/2013
37092^335222-109985100912Enzo Doria04/2014
37102^335182-17237100900Enzo Doria05/2013
37112^335043-16737100858Enzo Doria05/2013
3712(21181*2^335049+1)/1343811100858Lelio R Paula07/2014
37132^335038-20633100857Enzo Doria06/2013
37142^335031+1873373100855Enzo Doria06/2016
371523489^19650+19650^23489100847Hans Havermann10/2018
37163^211354-8816100842Enzo Doria05/2014
37172^334984-112757100841Enzo Doria06/2014
371829451^2648+2648^29451100809Hans Havermann09/2018
371925583^8716+8716^25583100806Hans Havermann08/2018
37212^334857+48527100803Lelio R Paula08/2011
372012^93406+29100803Lelio R Paula10/2016
372228780^3179+3179^28780100796Hans Havermann09/2018
3723(5*2^334825+1)/47100792Lelio R Paula12/2013
37242^334809-13100788Lelio R Paula04/2011
3725(82*10^100780-1)/9100781Robert Price12/2014
372631395^1622+1622^31395100780Hans Havermann09/2018
3727(2^334779+47)/5100778Lelio R Paula12/2013
37282^334751+2049100771Lelio R Paula09/2016
372913^90443-98100749Lelio R Paula10/2016
3730(7*10^100737+71)/3100738Robert Price05/2018
3731(24737*2^334628+1)/3100737Lelio R Paula07/2014
373215^85639-28100720Lelio R Paula10/2016
373327068^5259+5259^27068100718Hans Havermann08/2018
37342^334562+577294575100711Lelio R Paula09/2016
37354*3^211077-5100710Lelio R Paula08/2014
37362^334524+145100702Lelio R Paula07/2009
373727648^4375+4375^27648100666Hans Havermann09/2018
3738(1017*2^334391-1)/3535100662Lelio R Paula05/2015
37392^334294-113111100633Enzo Doria07/2014
374025581^8582+8582^25581100626Hans Havermann08/2018
37416^129308-17723100622Enzo Doria03/2013
37426^129305+95100619Lelio R Paula10/2016
37432^334244-1167100618Lelio R Paula09/2016
3744(26*10^100566+49)/3100567Robert Price08/2019
3745(21*2^334050+1)/935100558Lelio R Paula12/2013
374624885^10984+10984^24885100555Hans Havermann07/2018
3747(78557*2^334018+1)/4326021100548Lelio R Paula07/2014
3748(35*10^100542+1)/9100543Serge Batalov11/2010
374923578^18367+18367^23578100538Hans Havermann07/2018
375013^90251+24100535Lelio R Paula10/2016


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: August, 25 2019 15:53 (Time in France)

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