PRP Records

Probable Primes Top 10000

(191107 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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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 ?
27515^148169+54103566Lelio R Paula11/2016
27522^344017-108795103560Enzo Doria03/2014
27532^343971-5077103546Lelio R Paula09/2011
27542^343899+141103524Lelio R Paula08/2011
27556^133029-67103517Lelio R Paula11/2016
2756(17*2^343877+1)/13625103515Lelio R Paula12/2013
2757(136*10^103474-1)/9103476Serge Batalov12/2014
27585^148014-24103458Lelio R Paula11/2016
27592^343604+9931103436Yves Minet01/2011
27602^343601-21189103435Enzo Doria06/2013
27612^343508-115229103407Enzo Doria06/2015
2762(509203*2^343491-1)/16147103403Lelio R Paula05/2015
27633^216685-113056103386Enzo Doria07/2014
276444^62903-43^62903103379Jean-Louis Charton08/2012
276511^99262-20103371Lelio R Paula12/2016
2766(509203*2^343357-1)/5103366Lelio R Paula05/2015
27672^343356-2791889103361Enzo Doria03/2016
2768Phi(104989,10)/2939693103350Maksym Voznyy09/2015
27692^343182-171103309Lelio R Paula08/2011
2770(23619^23619+23620^23620)/7187103294David Broadhurst09/2009
27712^343079-1835611103278Enzo Doria05/2015
27722^343063-1147103273Yves Minet06/2013
27739*6^132689+7103254Lelio R Paula11/2014
27742^342979-18085103247Enzo Doria05/2013
27752^342966-16995103244Lelio R Paula11/2016
27765^147650+16103203Lelio R Paula11/2016
2777gcd(Phi(852060,10),(10^42603+1)^3*(10^42603+1-10^21302)+(10^85206+10^42603)*(10^21302+1)+10^127809)103201Serge Batalov04/2015
27782^342817+2707067103199Enzo Doria03/2016
277943^63177-42103198Theodore Burton02/2007
27802^342805-21025103195Enzo Doria06/2013
27812^342714+12285103168Lelio R Paula11/2016
278218^82178-4481103156Enzo Doria03/2013
27832^342665-17349103153Enzo Doria05/2013
27842^342612+175103137Lelio R Paula08/2011
27855*2^342585-3103130Lelio R Paula09/2014
27862^342503-19209103104Enzo Doria05/2013
27872^342476+51103096Lelio R Paula08/2011
27882^342460-18885103091Enzo Doria05/2013
27897^121968+82103075Lelio R Paula10/2016
27902^342392-108863103071Enzo Doria03/2014
27913^216014+28103065Lelio R Paula11/2016
27922^342353-108879103059Enzo Doria03/2014
279310^103055+276081103056Patrick De Geest12/2016
279410^103055-53103055Lelio R Paula11/2016
27957^121933+4103046Lelio R Paula11/2014
279619^80560-68103017Lelio R Paula10/2016
27972^342209+76607103016Enzo Doria05/2016
2799328^40945+40945^328103013Norbert Schneider12/2014
279812^95454-91103013Lelio R Paula10/2016
280065^56809-64^56809102990Robert Price08/2013
28015^147338-6102985Lelio R Paula11/2014
28022^342084-112739102978Enzo Doria06/2014
28039*6^132330+7102974Lelio R Paula11/2014
28042^342034-16737102963Enzo Doria05/2013
2805(9787*2^342011-1)/25102959Lelio R Paula05/2015
2806(3^215802-5)/124343756102956Lelio R Paula12/2013
28072^341991-17421102950Enzo Doria05/2013
28082^341969-112225102943Enzo Doria06/2014
2809(9787*2^341864-1)/3102915Lelio R Paula05/2015
28102^341859+1869413102910Enzo Doria05/2016
281110^102909+61102910Lelio R Paula11/2016
281210^102909-67049102909Patrick De Geest12/2016
28132^341659+1836773102850Enzo Doria03/2016
28142^341608-110639102835Enzo Doria05/2014
281510^102824+49102825Lelio R Paula11/2016
281610^102824-168011102824Patrick De Geest12/2016
281711^98708-8102794Lelio R Paula10/2016
28182^341466+4429102792Lelio R Paula09/2011
28192^341460-107102790Lelio R Paula08/2011
2820(2^341388+47)/21014943102761Lelio R Paula12/2013
28212^341355+21102759Lelio R Paula08/2011
28222^341246+40755102726Lelio R Paula11/2016
2823(2^341256-5)/991699102723Lelio R Paula12/2013
28247^121547+78102720Lelio R Paula10/2016
28252^341223-461197102719Enzo Doria06/2015
28272^341190-20577102709Enzo Doria06/2013
2826(27*2^341212+1)/84674449102709Lelio R Paula12/2013
28286^131976-65102698Lelio R Paula10/2016
28292^341134+2533102692Henri Lifchitz09/2005
283013^92184-54102688Lelio R Paula10/2016
28312^341116-20873102687Enzo Doria06/2013
28322^341094-19953102680Enzo Doria06/2013
28332^341053+129102668Lelio R Paula08/2011
2835(31*2^341006-1)/3102655Lelio R Paula03/2014
28347^121471+94102655Lelio R Paula10/2016
28372^341004-173102653Lelio R Paula08/2011
283620^78901+3102653Lelio R Paula10/2016
28385^146853-52102646Lelio R Paula10/2016
28392^340969-216931102642Enzo Doria05/2014
28402^340952+1870021102637Enzo Doria05/2016
28415*2^340940-3102634Lelio R Paula08/2014
2842(6^131891+1)/7102631Paul Bourdelais01/2010
284375^54717+74102598Norbert Schneider01/2015
28442^340806-20393102593Enzo Doria06/2013
2845(2^340790+5)/138267102583Lelio R Paula12/2013
28466^131821+77102577Lelio R Paula10/2016
28472^340688-29102558Henri Lifchitz05/2005
28482^340685-109101102557Enzo Doria04/2014
284965^56567-64102552Norbert Schneider11/2014
28502^340547-108897102515Enzo Doria03/2014
28517^121268+82102484Lelio R Paula10/2016
2852(6883*2^340443-1)/162401102483Lelio R Paula05/2015
28532^340434-5955102481Lelio R Paula11/2016
2854(2^340381+47)/7102465Lelio R Paula12/2013
2855111^50095+110102461Norbert Schneider04/2017
28562^340291-20301102438Enzo Doria06/2013
285712^94915+89102431Lelio R Paula10/2016
28582^340208-20373102413Enzo Doria06/2013
28596^131598-17273102404Enzo Doria02/2013
28602^340115-21181102385Enzo Doria06/2013
2861(55459*2^340090+1)/1591102379Lelio R Paula07/2014
286289^52511-88^52511102365Robert Price06/2015
28633^214539-112756102362Enzo Doria07/2014
28642^340000-19877102351Enzo Doria06/2013
28652^339990-114845102348Enzo Doria05/2015
2866(3^214516-2)/51383102346Lelio R Paula12/2013
286720^78661-99102341Lelio R Paula09/2016
28682^339951-19585102336Enzo Doria05/2013
2869(13*2^339943+1)/45102333Lelio R Paula12/2013
28702^339889+29327102317Yves Minet06/2010
28712^339834-109493102301Enzo Doria04/2014
2872(11^98221-5^98221)/6102286Robert Price01/2013
28733^214365+1820102279Lelio R Paula10/2016
2874(11*2^339705-1)/183102261Lelio R Paula03/2014
28752^339694-16995102259Lelio R Paula09/2016
28767^120985-38102245Lelio R Paula10/2016
287710^102244+122961102245Patrick De Geest12/2016
287810^102244-27102244Lelio R Paula09/2016
28797^120982-62102242Lelio R Paula10/2016
28804*6^131382-5102236Lelio R Paula11/2014
28812^339586-1091102226Yves Minet11/2012
288211^98161-3072000102225Enzo Doria12/2012
28839*7^120961-4102225Lelio R Paula11/2014
28845*3^214250+2102224Serge Batalov10/2010
288512^94713-59102213Lelio R Paula10/2016
288612^94705+89102204Lelio R Paula10/2016
28872^339407-177102172Lelio R Paula08/2011
28882^339355+65102157Lelio R Paula07/2011
2889(2^339323+47)/880715102141Lelio R Paula12/2013
28902^339168+21102100Lelio R Paula07/2011
28912^339167-108807102100Enzo Doria03/2014
28922^339156+163102097Lelio R Paula08/2011
2893(2^338982-7)/1754517102038Lelio R Paula12/2013
28942^338891-18885102017Enzo Doria05/2013
28952^338829-113239101998Enzo Doria07/2014
28962^338828-113297101998Enzo Doria07/2014
28972^338796+93101988Donovan Johnson06/2008
2898lucasU(1373,1,32502)-lucasU(1373,1,32501)101978Mike Oakes05/2009
2899(71^55079-1)/70101964Paul Bourdelais08/2017
29012^338682-19865101954Enzo Doria06/2013
2900(2^(112895*3+1)+243)/7101954Kevin Acres12/2013
29022^338568+37101920Lelio R Paula07/2011
29032^338559-1858777101917Enzo Doria04/2016
2904(9*2^338520+1)/365101904Lelio R Paula12/2013
29052^338497-17041101898Enzo Doria05/2013
29062^338475+54615101892Lelio R Paula10/2016
29072^338426-19797101877Enzo Doria06/2013
29082^338368-20369101859Enzo Doria06/2013
29092^338366+74179101859Enzo Doria04/2016
29102^338280-19745101833Enzo Doria06/2013
2911(3*2^338236-1)/347101818Lelio R Paula03/2014
29126^130841+103101815Lelio R Paula10/2016
29142^338122-20117101785Enzo Doria06/2013
2913(2^338139+5)/905333101785Lelio R Paula12/2013
291535^65917-7092101781Enzo Doria03/2013
29162^338010-19833101752Enzo Doria06/2013
29173^213215-76101730Lelio R Paula09/2016
29182^337930+63101728Lelio R Paula07/2011
29192^337920+1869661101725Enzo Doria05/2016
29202^337859-19645101706Enzo Doria05/2013
29212^337754+1869169101675Enzo Doria05/2016
2922(31*2^337677-1)/593101650Lelio R Paula03/2014
292311^97605-24101646Lelio R Paula10/2016
29248^112539-112539101633Robert Price01/2014
29252^337515-19869101603Enzo Doria06/2013
29262^337473+719101590Lelio R Paula08/2011
2927(2^337485-509203)/656647157101585Lelio R Paula12/2013
29282^337452-108815101584Enzo Doria03/2014
29292^337453+1185101584Lelio R Paula09/2016
29302^337410-113561101571Enzo Doria08/2014
29312^337387+855101564Lelio R Paula09/2016
29322^337367-17295101558Lelio R Paula09/2016
29332^337342-109035101551Enzo Doria04/2014
29342^337267-19101528Lelio R Paula07/2011
29352^337183-19989101503Enzo Doria06/2013
29362^337149+72425101492Enzo Doria04/2016
29372^337101-20241101478Enzo Doria06/2013
29382^337035-20001101458Enzo Doria06/2013
29392^337017-16995101453Lelio R Paula09/2016
29402^336979-115315101441Enzo Doria06/2015
29412^336970-20885101439Enzo Doria06/2013
29422^336958+79101435Lelio R Paula10/2009
29432^336942+169101430Lelio R Paula10/2009
2944(15185*2^336894-1)/7939101416Lelio R Paula05/2015
29452^336871+257463101409Tony Prest / Never Odd Or Even04/2016
29462^336871+318105101409Tony Prest / Never Odd Or Even04/2016
29472^336871+1010813101409Tony Prest / Never Odd Or Even04/2016
29482^336871+2302245101409Tony Prest / Never Odd Or Even04/2016
29492^336871+389273101409Tony Prest / Never Odd Or Even04/2016
29502^336871+1685475101409Tony Prest / Never Odd Or Even04/2016
29512^336871+1068119101409Tony Prest / Never Odd Or Even04/2016
29522^336871+586905101409Tony Prest / Never Odd Or Even04/2016
29532^336871+674571101409Tony Prest / Never Odd Or Even04/2016
29542^336871+707009101409Tony Prest / Never Odd Or Even04/2016
29552^336871+1210299101409Tony Prest / Never Odd Or Even04/2016
29562^336871+1921185101409Tony Prest / Never Odd Or Even04/2016
29572^336871+2003973101409Tony Prest / Never Odd Or Even04/2016
29582^336871+2656475101409Tony Prest / Never Odd Or Even04/2016
29592^336871+2703023101409Tony Prest / Never Odd Or Even04/2016
29602^336871+2704545101409Tony Prest / Never Odd Or Even04/2016
29612^336871+2766801101409Tony Prest / Never Odd Or Even04/2016
29622^336871+2127735101409Tony Prest / Never Odd Or Even04/2016
2963(2^336871+821089)/3101408Tony Prest / Never Odd Or Even05/2016
2964(2^336871+119567)/5101408Tony Prest / Never Odd Or Even05/2016
2965(2^336871+398161)/3101408Tony Prest / Never Odd Or Even05/2016
2966(2^336871+625889)/7101408Tony Prest / Never Odd Or Even05/2016
29672^336842+94065101400Lelio R Paula09/2016
2968(2^336871+904417)/3/3/3/5/19/9287177/9690011663/29993043103101378Tony Prest / Never Odd Or Even04/2016
2969(2^336871+631971)/13/251/1601/294277/614362921/30324278867101377Tony Prest / Never Odd Or Even04/2016
2970(2^336871+1443541)/3/89/1655197/11018131/47972707/468862691879101374Tony Prest / Never Odd Or Even04/2016
2971(2^336871+689863)/3/11/109/137/1867/7151/20800501/29243857/127778489101373Tony Prest / Never Odd Or Even04/2016
2972(2^336871+219839)/191/643/3011/9479/117127/175750007/4578271757101373Tony Prest / Never Odd Or Even04/2016
2973(2^336871+272895)/19/661/977572033/95853078653/520779768241101373Tony Prest / Never Odd Or Even04/2016
2974(2^336871+1023429)/2311/415873/991889/3630648341/207732189179101373Tony Prest / Never Odd Or Even04/2016
297510^101369+203811101370Patrick De Geest11/2016
297610^101369-99101369Lelio R Paula09/2016
2977(2^336871+1832627)/5/5/23/181/4397/91373/3746673331/115602484097/279351383917101363Tony Prest / Never Odd Or Even04/2016
29782^336701-113563101358Enzo Doria08/2014
29792^336644-109023101340Enzo Doria04/2014
29802^336601-21081101327Enzo Doria06/2013
298120^77869+63101310Lelio R Paula09/2016
2982(13*2^336523-1)/19101304Lelio R Paula03/2014
29836^130179-137101299Lelio R Paula10/2016
2984(2^336506+lucasV(1,2,336506)+1)/2101299Mike Oakes11/2016
2985(24737*2^336485+1)/7285101293Lelio R Paula07/2014
2986(2^336448+9)/497405101276Lelio R Paula12/2013
29872^336369-19753101258Enzo Doria05/2013
29882^336350-344291101252Enzo Doria07/2015
29892^336243-108777101220Enzo Doria03/2014
2990(31*2^336189-1)/19101204Lelio R Paula03/2014
2991(78557*2^336178+1)/1268757101199Lelio R Paula07/2014
29922^336150-20393101192Enzo Doria06/2013
29932^336112-1865249101180Enzo Doria03/2016
29942^336103-109015101178Enzo Doria04/2014
299513^90809-96101157Lelio R Paula10/2016
299619^79098-30101147Lelio R Paula10/2016
299719^79095+88101144Lelio R Paula10/2016
299815^85976+32101116Lelio R Paula10/2016
2999(3^211950+7)/28854513015920697088101107Lelio R Paula11/2013
3000(4^167933+17)/3101106Robert Price02/2017


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: November, 22 2017 23:29 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!