PRP Records

Probable Primes Top 10000

(247113 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 ?
32519*7^120961-4102225Lelio R Paula11/2014
32525*3^214250+2102224Serge Batalov10/2010
325312^94713-59102213Lelio R Paula10/2016
325412^94705+89102204Lelio R Paula10/2016
32552^339407-177102172Lelio R Paula08/2011
32564*10^102163-57102164Robert Price10/2018
32572^339355+65102157Lelio R Paula07/2011
3258(2^339323+47)/880715102141Lelio R Paula12/2013
32592^339168+21102100Lelio R Paula07/2011
32602^339167-108807102100Enzo Doria03/2014
32612^339156+163102097Lelio R Paula08/2011
3262(2^338982-7)/1754517102038Lelio R Paula12/2013
32632^338891-18885102017Enzo Doria05/2013
32642^338829-113239101998Enzo Doria07/2014
32652^338828-113297101998Enzo Doria07/2014
32662^338796+93101988Donovan Johnson06/2008
3267lucasU(1373,1,32502)-lucasU(1373,1,32501)101978Mike Oakes05/2009
3268(71^55079-1)/70101964Paul Bourdelais08/2017
32692^338682-19865101954Enzo Doria06/2013
3270(2^(112895*3+1)+243)/7101954Kevin Acres12/2013
32712^338568+37101920Lelio R Paula07/2011
32722^338559-1858777101917Enzo Doria04/2016
3273(9*2^338520+1)/365101904Lelio R Paula12/2013
32742^338497-17041101898Enzo Doria05/2013
32752^338475+54615101892Lelio R Paula10/2016
32762^338426-19797101877Enzo Doria06/2013
32772^338368-20369101859Enzo Doria06/2013
32782^338366+74179101859Enzo Doria04/2016
32792^338280-19745101833Enzo Doria06/2013
3280(3*2^338236-1)/347101818Lelio R Paula03/2014
32816^130841+103101815Lelio R Paula10/2016
32822^338122-20117101785Enzo Doria06/2013
3283(2^338139+5)/905333101785Lelio R Paula12/2013
328435^65917-7092101781Enzo Doria03/2013
32852^338010-19833101752Enzo Doria06/2013
32863^213215-76101730Lelio R Paula09/2016
32872^337930+63101728Lelio R Paula07/2011
32882^337920+1869661101725Enzo Doria05/2016
32892^337859-19645101706Enzo Doria05/2013
32902^337754+1869169101675Enzo Doria05/2016
32913*10^101657-37101658Robert Price07/2018
3292(31*2^337677-1)/593101650Lelio R Paula03/2014
329311^97605-24101646Lelio R Paula10/2016
32948^112539-112539101633Robert Price01/2014
329525694^9003+9003^25694101605Hans Havermann12/2018
32962^337515-19869101603Enzo Doria06/2013
32972^337473+719101590Lelio R Paula08/2011
3298(2^337485-509203)/656647157101585Lelio R Paula12/2013
32992^337452-108815101584Enzo Doria03/2014
33002^337453+1185101584Lelio R Paula09/2016
33012^337410-113561101571Enzo Doria08/2014
33022^337387+855101564Lelio R Paula09/2016
33032^337367-17295101558Lelio R Paula09/2016
33042^337342-109035101551Enzo Doria04/2014
33052^337267-19101528Lelio R Paula07/2011
33062^337183-19989101503Enzo Doria06/2013
33072^337149+72425101492Enzo Doria04/2016
33082^337101-20241101478Enzo Doria06/2013
33092^337035-20001101458Enzo Doria06/2013
33102^337017-16995101453Lelio R Paula09/2016
33112^336979-115315101441Enzo Doria06/2015
33122^336970-20885101439Enzo Doria06/2013
33132^336958+79101435Lelio R Paula10/2009
33142^336942+169101430Lelio R Paula10/2009
3316(15185*2^336894-1)/7939101416Lelio R Paula05/2015
33154*10^101415-89101416Robert Price11/2018
33172^336871+257463101409Tony Prest / Never Odd Or Even04/2016
33182^336871+318105101409Tony Prest / Never Odd Or Even04/2016
33192^336871+1010813101409Tony Prest / Never Odd Or Even04/2016
33202^336871+2302245101409Tony Prest / Never Odd Or Even04/2016
33212^336871+389273101409Tony Prest / Never Odd Or Even04/2016
33222^336871+1685475101409Tony Prest / Never Odd Or Even04/2016
33232^336871+1068119101409Tony Prest / Never Odd Or Even04/2016
33242^336871+586905101409Tony Prest / Never Odd Or Even04/2016
33252^336871+674571101409Tony Prest / Never Odd Or Even04/2016
33262^336871+707009101409Tony Prest / Never Odd Or Even04/2016
33272^336871+1210299101409Tony Prest / Never Odd Or Even04/2016
33282^336871+1921185101409Tony Prest / Never Odd Or Even04/2016
33292^336871+2003973101409Tony Prest / Never Odd Or Even04/2016
33302^336871+2656475101409Tony Prest / Never Odd Or Even04/2016
33312^336871+2703023101409Tony Prest / Never Odd Or Even04/2016
33322^336871+2704545101409Tony Prest / Never Odd Or Even04/2016
33332^336871+2766801101409Tony Prest / Never Odd Or Even04/2016
33342^336871+2127735101409Tony Prest / Never Odd Or Even04/2016
3335(2^336871+821089)/3101408Tony Prest / Never Odd Or Even05/2016
3336(2^336871+119567)/5101408Tony Prest / Never Odd Or Even05/2016
3337(2^336871+398161)/3101408Tony Prest / Never Odd Or Even05/2016
3338(2^336871+625889)/7101408Tony Prest / Never Odd Or Even05/2016
33392^336842+94065101400Lelio R Paula09/2016
3340(2^336871+904417)/3/3/3/5/19/9287177/9690011663/29993043103101378Tony Prest / Never Odd Or Even04/2016
3341(2^336871+631971)/13/251/1601/294277/614362921/30324278867101377Tony Prest / Never Odd Or Even04/2016
3342(2^336871+1443541)/3/89/1655197/11018131/47972707/468862691879101374Tony Prest / Never Odd Or Even04/2016
3343(2^336871+689863)/3/11/109/137/1867/7151/20800501/29243857/127778489101373Tony Prest / Never Odd Or Even04/2016
3344(2^336871+219839)/191/643/3011/9479/117127/175750007/4578271757101373Tony Prest / Never Odd Or Even04/2016
3345(2^336871+272895)/19/661/977572033/95853078653/520779768241101373Tony Prest / Never Odd Or Even04/2016
3346(2^336871+1023429)/2311/415873/991889/3630648341/207732189179101373Tony Prest / Never Odd Or Even04/2016
334710^101369+203811101370Patrick De Geest11/2016
334810^101369-99101369Lelio R Paula09/2016
3349(2^336871+1832627)/5/5/23/181/4397/91373/3746673331/115602484097/279351383917101363Tony Prest / Never Odd Or Even04/2016
33502^336701-113563101358Enzo Doria08/2014
33512^336644-109023101340Enzo Doria04/2014
33522^336601-21081101327Enzo Doria06/2013
335320^77869+63101310Lelio R Paula09/2016
3354(13*2^336523-1)/19101304Lelio R Paula03/2014
33556^130179-137101299Lelio R Paula10/2016
3356(2^336506+lucasV(1,2,336506)+1)/2101299Mike Oakes11/2016
3357(24737*2^336485+1)/7285101293Lelio R Paula07/2014
3358(2^336448+9)/497405101276Lelio R Paula12/2013
33592^336369-19753101258Enzo Doria05/2013
336023842^17653+17653^23842101253Hans Havermann11/2018
33612^336350-344291101252Enzo Doria07/2015
33622^336243-108777101220Enzo Doria03/2014
3363(31*2^336189-1)/19101204Lelio R Paula03/2014
336423535^19954+19954^23535101202Hans Havermann11/2018
3365(78557*2^336178+1)/1268757101199Lelio R Paula07/2014
33662^336150-20393101192Enzo Doria06/2013
336723996^16473+16473^23996101186Hans Havermann11/2018
33682^336112-1865249101180Enzo Doria03/2016
33692^336103-109015101178Enzo Doria04/2014
337013^90809-96101157Lelio R Paula10/2016
337126199^7258+7258^26199101150Hans Havermann11/2018
337219^79098-30101147Lelio R Paula10/2016
337319^79095+88101144Lelio R Paula10/2016
337415^85976+32101116Lelio R Paula10/2016
3375(3^211950+7)/28854513015920697088101107Lelio R Paula11/2013
3376(4^167933+17)/3101106Robert Price02/2017
33772^335858+153101104Lelio R Paula10/2009
33786^129918-35101096Lelio R Paula10/2016
33793^211885-70101095Lelio R Paula09/2016
3380(29*2^335835-1)/550599101093Lelio R Paula03/2014
33812^335818-20033101092Enzo Doria06/2013
33822^335813-110083101090Enzo Doria04/2014
33832^335804+2155101088Lelio R Paula09/2016
33842^335784-16145101082Enzo Doria04/2013
338511^97051+62101069Lelio R Paula10/2016
33863*10^101065+11101066Robert Price07/2018
338727820^4293+4293^27820101064Hans Havermann10/2018
3388(2^335691-3)/26515101049Lelio R Paula12/2013
33892^335658-94395101044Lelio R Paula09/2016
339024514^13215+13215^24514101024Hans Havermann11/2018
33912^335586+169101022Lelio R Paula10/2009
3392(56^57787-1)/55101021Paul Bourdelais08/2017
3393(19*10^100997+737)/9100998Robert Price07/2018
339447599!2+1024100991Robert Price02/2015
33952^335468-18629100986Enzo Doria05/2013
33962^335454-20961100982Enzo Doria06/2013
339710^100978+61100979Lelio R Paula09/2016
339810^100978-156437100978Patrick De Geest11/2016
3399(15*2^335417+1)/481100970Lelio R Paula12/2013
34002^335403-1859167100967Enzo Doria03/2016
340123599^18976+18976^23599100962Hans Havermann10/2018
34029*2^335364-5100956Lelio R Paula08/2014
34032^335349+72287100951Enzo Doria04/2016
34042^335329+16095100945Lelio R Paula09/2016
3405232823#+233663100937Makoto Morimoto10/2017
34062^335237-20893100917Enzo Doria06/2013
34072^335222-19337100912Enzo Doria05/2013
34082^335222-109985100912Enzo Doria04/2014
34092^335182-17237100900Enzo Doria05/2013
34102^335043-16737100858Enzo Doria05/2013
3411(21181*2^335049+1)/1343811100858Lelio R Paula07/2014
34122^335038-20633100857Enzo Doria06/2013
34132^335031+1873373100855Enzo Doria06/2016
341423489^19650+19650^23489100847Hans Havermann10/2018
34153^211354-8816100842Enzo Doria05/2014
34162^334984-112757100841Enzo Doria06/2014
341729451^2648+2648^29451100809Hans Havermann09/2018
341825583^8716+8716^25583100806Hans Havermann08/2018
34192^334857+48527100803Lelio R Paula08/2011
342012^93406+29100803Lelio R Paula10/2016
342128780^3179+3179^28780100796Hans Havermann09/2018
3422(5*2^334825+1)/47100792Lelio R Paula12/2013
34232^334809-13100788Lelio R Paula04/2011
3424(82*10^100780-1)/9100781Robert Price12/2014
342531395^1622+1622^31395100780Hans Havermann09/2018
3426(2^334779+47)/5100778Lelio R Paula12/2013
34272^334751+2049100771Lelio R Paula09/2016
342813^90443-98100749Lelio R Paula10/2016
3429(7*10^100737+71)/3100738Robert Price05/2018
3430(24737*2^334628+1)/3100737Lelio R Paula07/2014
343115^85639-28100720Lelio R Paula10/2016
343227068^5259+5259^27068100718Hans Havermann08/2018
34332^334562+577294575100711Lelio R Paula09/2016
34344*3^211077-5100710Lelio R Paula08/2014
34352^334524+145100702Lelio R Paula07/2009
343627648^4375+4375^27648100666Hans Havermann09/2018
3437(1017*2^334391-1)/3535100662Lelio R Paula05/2015
34382^334294-113111100633Enzo Doria07/2014
343925581^8582+8582^25581100626Hans Havermann08/2018
34406^129308-17723100622Enzo Doria03/2013
34416^129305+95100619Lelio R Paula10/2016
34422^334244-1167100618Lelio R Paula09/2016
3443(21*2^334050+1)/935100558Lelio R Paula12/2013
344424885^10984+10984^24885100555Hans Havermann07/2018
3445(78557*2^334018+1)/4326021100548Lelio R Paula07/2014
3446(35*10^100542+1)/9100543Serge Batalov11/2010
344723578^18367+18367^23578100538Hans Havermann07/2018
344813^90251+24100535Lelio R Paula10/2016
34492^333963+789100533Lelio R Paula08/2011
34502^333919-1840087100520Enzo Doria06/2015
34512^333911+72623100518Enzo Doria04/2016
345224605^12168+12168^24605100517Hans Havermann08/2018
345318^80064-67100503Lelio R Paula10/2016
34545^143742-48100472Lelio R Paula10/2016
345524095^14784+14784^24095100472Hans Havermann08/2018
34562^333757-112123100471Enzo Doria06/2014
345727358^4693+4693^27358100444Hans Havermann07/2018
34582^333603-108861100425Enzo Doria03/2014
34599*7^118818-2100414Lelio R Paula11/2014
34602^333546-17097100408Enzo Doria05/2013
346117^81597+72100401Lelio R Paula10/2016
3462p(20559)#/2+8100384Robert Price01/2017
346311^96390-24100380Lelio R Paula10/2016
34654832563059*2^333333+30029100353Donovan Johnson01/2008
346423565^18136+18136^23565100353Hans Havermann07/2018
34662^333354+763100350Lelio R Paula08/2011
34672^333289-109483100330Enzo Doria04/2014
34682^333240-2790209100316Enzo Doria03/2016
346923601^17798+17798^23601100314Hans Havermann05/2018
3471(2^333227-2^166614+1)/510031111/2006
34702^333225+719100311Lelio R Paula08/2011
34722^333221-2785333100310Enzo Doria10/2015
347376^53332-75100308Norbert Schneider02/2015
34746^128892-17573100298Enzo Doria03/2013
34752^333105-113215100275Enzo Doria07/2014
3476(31*2^333102+1)/2375100272Lelio R Paula11/2013
34774*10^100257-83100258Robert Price10/2018
347817^81476-74100253Lelio R Paula10/2016
347923392^19207+19207^23392100199Hans Havermann06/2018
348017^81417-16100180Theodore Burton11/2005
34812^332739-113215100165Enzo Doria07/2014
34822^332730-1865621100162Enzo Doria03/2016
348391^51127-2100160Lelio R Paula09/2013
348415^85159-32100155Lelio R Paula10/2016
34856^128661+97100118Lelio R Paula10/2016
348619^78285+40100108Lelio R Paula07/2016
34876^128640+5100102Lelio R Paula11/2014
3488(14*10^100075+61)/3100076Robert Price12/2018
348928562^3189+3189^28562100072Hans Havermann05/2018
34906^128565-127100044Lelio R Paula08/2016
34912^332309-133100035Lelio R Paula02/2011
34922^332307+731100035Lelio R Paula07/2011
34932^332301+12927100033Lelio R Paula04/2013
349423406^18781+18781^23406100031Hans Havermann04/2018
349512^92684-13100023Lelio R Paula07/2016
349610^100002+236023100003Stefano Morozzi05/2018
349710^100002+433741100003Stefano Morozzi05/2018
3498(10^100002-1)/9-10^33441100002Akihiko Yoshida03/2018
3499(10^100002-1)/9-10^44692100002Akihiko Yoshida03/2018
350010^100002-249519100002Patrick De Geest07/2018


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: December, 11 2018 05:54 (Time in France)

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