PRP Records

Probable Primes Top 10000

(255244 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 ?
3502328^40945+40945^328103013Norbert Schneider12/2014
350112^95454-91103013Lelio R Paula10/2016
350325833^9716+9716^25833103009Hans Havermann01/2019
350465^56809-64^56809102990Robert Price08/2013
35055^147338-6102985Lelio R Paula11/2014
35062^342084-112739102978Enzo Doria06/2014
35079*6^132330+7102974Lelio R Paula11/2014
35082^342034-16737102963Enzo Doria05/2013
3509(9787*2^342011-1)/25102959Lelio R Paula05/2015
3510(3^215802-5)/124343756102956Lelio R Paula12/2013
35112^341991-17421102950Enzo Doria05/2013
35122^341969-112225102943Enzo Doria06/2014
3513(9787*2^341864-1)/3102915Lelio R Paula05/2015
35142^341859+1869413102910Enzo Doria05/2016
351510^102909+61102910Lelio R Paula11/2016
351610^102909-67049102909Patrick De Geest12/2016
351723814^20935+20935^23814102898Hans Havermann02/2019
351828345^4264+4264^28345102888Hans Havermann02/2019
351925665^10204+10204^25665102886Hans Havermann02/2019
352026288^8181+8181^26288102860Hans Havermann02/2019
35212^341659+1836773102850Enzo Doria03/2016
35222^341608-110639102835Enzo Doria05/2014
352310^102824+49102825Lelio R Paula11/2016
352410^102824-168011102824Patrick De Geest12/2016
352511^98708-8102794Lelio R Paula10/2016
35262^341466+4429102792Lelio R Paula09/2011
35272^341460-107102790Lelio R Paula08/2011
3528(2^341388+47)/21014943102761Lelio R Paula12/2013
35292^341355+21102759Lelio R Paula08/2011
35302^341246+40755102726Lelio R Paula11/2016
3531(2^341256-5)/991699102723Lelio R Paula12/2013
35327^121547+78102720Lelio R Paula10/2016
35332^341223-461197102719Enzo Doria06/2015
353427838^4893+4893^27838102711Hans Havermann03/2019
35362^341190-20577102709Enzo Doria06/2013
3535(27*2^341212+1)/84674449102709Lelio R Paula12/2013
35376^131976-65102698Lelio R Paula10/2016
35382^341134+2533102692Henri Lifchitz09/2005
353913^92184-54102688Lelio R Paula10/2016
35402^341116-20873102687Enzo Doria06/2013
35412^341094-19953102680Enzo Doria06/2013
354223761^20950+20950^23761102676Hans Havermann03/2019
35432^341053+129102668Lelio R Paula08/2011
3544(31*2^341006-1)/3102655Lelio R Paula03/2014
35457^121471+94102655Lelio R Paula10/2016
35472^341004-173102653Lelio R Paula08/2011
354620^78901+3102653Lelio R Paula10/2016
35485^146853-52102646Lelio R Paula10/2016
35492^340969-216931102642Enzo Doria05/2014
3550122^49196+121102641Norbert Schneider10/2018
35512^340952+1870021102637Enzo Doria05/2016
35525*2^340940-3102634Lelio R Paula08/2014
3553(6^131891+1)/7102631Paul Bourdelais01/2010
355425876^9239+9239^25876102615Hans Havermann02/2019
3555(4*10^102612+83)/3102613Robert Price02/2018
355675^54717+74102598Norbert Schneider01/2015
3557(17*10^102597+13)/3102598Robert Price01/2019
35582^340806-20393102593Enzo Doria06/2013
3559(2^340790+5)/138267102583Lelio R Paula12/2013
35606^131821+77102577Lelio R Paula10/2016
35612^340688-29102558Henri Lifchitz05/2005
35622^340685-109101102557Enzo Doria04/2014
356365^56567-64102552Norbert Schneider11/2014
356426230^8121+8121^26230102550Hans Havermann03/2019
35652^340547-108897102515Enzo Doria03/2014
356625592^10119+10119^25592102500Hans Havermann02/2019
35677^121268+82102484Lelio R Paula10/2016
3568(6883*2^340443-1)/162401102483Lelio R Paula05/2015
35692^340434-5955102481Lelio R Paula11/2016
3570(2^340381+47)/7102465Lelio R Paula12/2013
3571111^50095+110102461Norbert Schneider04/2017
35722^340291-20301102438Enzo Doria06/2013
357312^94915+89102431Lelio R Paula10/2016
357424466^15349+15349^24466102417Hans Havermann03/2019
35752^340208-20373102413Enzo Doria06/2013
35766^131598-17273102404Enzo Doria02/2013
35772^340115-21181102385Enzo Doria06/2013
3578(55459*2^340090+1)/1591102379Lelio R Paula07/2014
357989^52511-88^52511102365Robert Price06/2015
35803^214539-112756102362Enzo Doria07/2014
35812^340000-19877102351Enzo Doria06/2013
35822^339990-114845102348Enzo Doria05/2015
3583(3^214516-2)/51383102346Lelio R Paula12/2013
358420^78661-99102341Lelio R Paula09/2016
35852^339951-19585102336Enzo Doria05/2013
3586(13*2^339943+1)/45102333Lelio R Paula12/2013
35872^339889+29327102317Yves Minet06/2010
358826348^7641+7641^26348102314Hans Havermann03/2019
3589Phi(239414,10)/6333218543102303Makoto Kamada08/2019
35902^339834-109493102301Enzo Doria04/2014
3591(16*10^102299-19)/3102300Robert Price02/2019
3592(11^98221-5^98221)/6102286Robert Price01/2013
35933^214365+1820102279Lelio R Paula10/2016
359431978^1579+1579^31978102278Hans Havermann03/2019
3595(11*2^339705-1)/183102261Lelio R Paula03/2014
35962^339694-16995102259Lelio R Paula09/2016
3597(56*10^102255+691)/9102256Robert Price05/2019
3598122^49008+121102249Norbert Schneider10/2018
36007^120985-38102245Lelio R Paula10/2016
359910^102244+122961102245Patrick De Geest12/2016
360110^102244-27102244Lelio R Paula09/2016
36027^120982-62102242Lelio R Paula10/2016
36034*6^131382-5102236Lelio R Paula11/2014
36042^339586-1091102226Yves Minet11/2012
360511^98161-3072000102225Enzo Doria12/2012
36069*7^120961-4102225Lelio R Paula11/2014
36075*3^214250+2102224Serge Batalov10/2010
360812^94713-59102213Lelio R Paula10/2016
360912^94705+89102204Lelio R Paula10/2016
36102^339407-177102172Lelio R Paula08/2011
36114*10^102163-57102164Robert Price10/2018
36122^339355+65102157Lelio R Paula07/2011
3613(2^339323+47)/880715102141Lelio R Paula12/2013
36142^339168+21102100Lelio R Paula07/2011
36152^339167-108807102100Enzo Doria03/2014
36162^339156+163102097Lelio R Paula08/2011
3617(25*10^102076-67)/3102077Robert Price06/2019
36182^339081-4543102074Yves Minet03/2019
361924327^15668+15668^24327102053Hans Havermann02/2019
362025080^11711+11711^25080102041Hans Havermann02/2019
3621(2^338982-7)/1754517102038Lelio R Paula12/2013
36222^338891-18885102017Enzo Doria05/2013
36238*10^102000+51102001Robert Price08/2019
36242^338829-113239101998Enzo Doria07/2014
36252^338828-113297101998Enzo Doria07/2014
36262^338796+93101988Donovan Johnson06/2008
3627lucasU(1373,1,32502)-lucasU(1373,1,32501)101978Mike Oakes05/2009
362825295^10744+10744^25295101969Hans Havermann01/2019
362925712^9243+9243^25712101969Hans Havermann01/2019
3630(71^55079-1)/70101964Paul Bourdelais08/2017
36312^338682-19865101954Enzo Doria06/2013
3632(2^(112895*3+1)+243)/7101954Kevin Acres12/2013
363328594^3673+3673^28594101939Hans Havermann02/2019
36342^338568+37101920Lelio R Paula07/2011
36352^338559-1858777101917Enzo Doria04/2016
3636(9*2^338520+1)/365101904Lelio R Paula12/2013
363724502^14419+14419^24502101903Hans Havermann01/2019
36382^338497-17041101898Enzo Doria05/2013
36392^338475+54615101892Lelio R Paula10/2016
36402^338426-19797101877Enzo Doria06/2013
36412^338368-20369101859Enzo Doria06/2013
36422^338366+74179101859Enzo Doria04/2016
364327088^5755+5755^27088101853Hans Havermann01/2019
36442^338280-19745101833Enzo Doria06/2013
3645(3*2^338236-1)/347101818Lelio R Paula03/2014
36466^130841+103101815Lelio R Paula10/2016
36472^338122-20117101785Enzo Doria06/2013
3648(2^338139+5)/905333101785Lelio R Paula12/2013
364935^65917-7092101781Enzo Doria03/2013
36502^338010-19833101752Enzo Doria06/2013
36513^213215-76101730Lelio R Paula09/2016
365223907^17998+17998^23907101730Hans Havermann01/2019
36532^337930+63101728Lelio R Paula07/2011
36542^337920+1869661101725Enzo Doria05/2016
365524116^16509+16509^24116101715Hans Havermann01/2019
36562^337859-19645101706Enzo Doria05/2013
36572^337754+1869169101675Enzo Doria05/2016
36583*10^101657-37101658Robert Price07/2018
3659(31*2^337677-1)/593101650Lelio R Paula03/2014
366011^97605-24101646Lelio R Paula10/2016
36618^112539-112539101633Robert Price01/2014
366225694^9003+9003^25694101605Hans Havermann12/2018
36632^337515-19869101603Enzo Doria06/2013
36642^337473+719101590Lelio R Paula08/2011
3665(2^337485-509203)/656647157101585Lelio R Paula12/2013
36662^337452-108815101584Enzo Doria03/2014
36672^337453+1185101584Lelio R Paula09/2016
36682^337410-113561101571Enzo Doria08/2014
36692^337387+855101564Lelio R Paula09/2016
36702^337367-17295101558Lelio R Paula09/2016
36712^337342-109035101551Enzo Doria04/2014
367223703^19238+19238^23703101548Hans Havermann12/2018
3673(26*10^101537-167)/3101538Robert Price10/2019
36742^337267-19101528Lelio R Paula07/2011
36752^337183-19989101503Enzo Doria06/2013
36762^337149+72425101492Enzo Doria04/2016
367724041^16642+16642^24041101483Hans Havermann12/2018
367833982^969+969^33982101482Hans Havermann12/2018
36792^337101-20241101478Enzo Doria06/2013
36802^337035-20001101458Enzo Doria06/2013
36812^337017-16995101453Lelio R Paula09/2016
36822^336979-115315101441Enzo Doria06/2015
36832^336970-20885101439Enzo Doria06/2013
36842^336958+79101435Lelio R Paula10/2009
36852^336942+169101430Lelio R Paula10/2009
3686(15185*2^336894-1)/7939101416Lelio R Paula05/2015
36874*10^101415-89101416Robert Price11/2018
36882^336871+257463101409Tony Prest / Never Odd Or Even04/2016
36892^336871+318105101409Tony Prest / Never Odd Or Even04/2016
36902^336871+1010813101409Tony Prest / Never Odd Or Even04/2016
36912^336871+2302245101409Tony Prest / Never Odd Or Even04/2016
36922^336871+389273101409Tony Prest / Never Odd Or Even04/2016
36932^336871+1685475101409Tony Prest / Never Odd Or Even04/2016
36942^336871+1068119101409Tony Prest / Never Odd Or Even04/2016
36952^336871+586905101409Tony Prest / Never Odd Or Even04/2016
36962^336871+674571101409Tony Prest / Never Odd Or Even04/2016
36972^336871+707009101409Tony Prest / Never Odd Or Even04/2016
36982^336871+1210299101409Tony Prest / Never Odd Or Even04/2016
36992^336871+1921185101409Tony Prest / Never Odd Or Even04/2016
37002^336871+2003973101409Tony Prest / Never Odd Or Even04/2016
37012^336871+2656475101409Tony Prest / Never Odd Or Even04/2016
37022^336871+2703023101409Tony Prest / Never Odd Or Even04/2016
37032^336871+2704545101409Tony Prest / Never Odd Or Even04/2016
37042^336871+2766801101409Tony Prest / Never Odd Or Even04/2016
37052^336871+2127735101409Tony Prest / Never Odd Or Even04/2016
3706(2^336871+821089)/3101408Tony Prest / Never Odd Or Even05/2016
3707(2^336871+119567)/5101408Tony Prest / Never Odd Or Even05/2016
3708(2^336871+398161)/3101408Tony Prest / Never Odd Or Even05/2016
3709(2^336871+625889)/7101408Tony Prest / Never Odd Or Even05/2016
371024097^16150+16150^24097101405Hans Havermann12/2018
37112^336842+94065101400Lelio R Paula09/2016
3712(2^336871+904417)/3/3/3/5/19/9287177/9690011663/29993043103101378Tony Prest / Never Odd Or Even04/2016
3713(2^336871+631971)/13/251/1601/294277/614362921/30324278867101377Tony Prest / Never Odd Or Even04/2016
3714(2^336871+1443541)/3/89/1655197/11018131/47972707/468862691879101374Tony Prest / Never Odd Or Even04/2016
3715(2^336871+689863)/3/11/109/137/1867/7151/20800501/29243857/127778489101373Tony Prest / Never Odd Or Even04/2016
3716(2^336871+219839)/191/643/3011/9479/117127/175750007/4578271757101373Tony Prest / Never Odd Or Even04/2016
3717(2^336871+272895)/19/661/977572033/95853078653/520779768241101373Tony Prest / Never Odd Or Even04/2016
3718(2^336871+1023429)/2311/415873/991889/3630648341/207732189179101373Tony Prest / Never Odd Or Even04/2016
371910^101369+203811101370Patrick De Geest11/2016
372010^101369-99101369Lelio R Paula09/2016
3721(2^336871+1832627)/5/5/23/181/4397/91373/3746673331/115602484097/279351383917101363Tony Prest / Never Odd Or Even04/2016
37222^336701-113563101358Enzo Doria08/2014
372389717!4-512101351Robert Price11/2019
37242^336644-109023101340Enzo Doria04/2014
37252^336601-21081101327Enzo Doria06/2013
372620^77869+63101310Lelio R Paula09/2016
3727(13*2^336523-1)/19101304Lelio R Paula03/2014
37286^130179-137101299Lelio R Paula10/2016
3729(2^336506+lucasV(1,2,336506)+1)/2101299Mike Oakes11/2016
3730(24737*2^336485+1)/7285101293Lelio R Paula07/2014
3731(2^336448+9)/497405101276Lelio R Paula12/2013
37322^336369-19753101258Enzo Doria05/2013
373323842^17653+17653^23842101253Hans Havermann11/2018
37342^336350-344291101252Enzo Doria07/2015
3735(56*10^101222-47)/9101223Robert Price02/2019
37362^336243-108777101220Enzo Doria03/2014
3737(31*2^336189-1)/19101204Lelio R Paula03/2014
373823535^19954+19954^23535101202Hans Havermann11/2018
3739(78557*2^336178+1)/1268757101199Lelio R Paula07/2014
37402^336150-20393101192Enzo Doria06/2013
374123996^16473+16473^23996101186Hans Havermann11/2018
37422^336112-1865249101180Enzo Doria03/2016
37432^336103-109015101178Enzo Doria04/2014
374413^90809-96101157Lelio R Paula10/2016
374526199^7258+7258^26199101150Hans Havermann11/2018
374619^79098-30101147Lelio R Paula10/2016
374719^79095+88101144Lelio R Paula10/2016
374815^85976+32101116Lelio R Paula10/2016
37492^335872-2776215101108Tony Prest / Never Odd Or Even01/2019
3750(3^211950+7)/28854513015920697088101107Lelio R Paula11/2013


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: November, 10 2019 12:07 (Time in France)

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