PRP Records

Probable Primes Top 10000

(295829 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 (> 50000) Who ? When ?
40012^466829-459523140530Enzo Doria05/2015
40022^466692-113213140489Enzo Doria07/2014
400323*10^140464-3140466Robert Price10/2021
4004(2*10^140461-17)/3140461Serge Batalov11/2022
400531335^30364+30364^31335140455Hans Havermann05/2021
400628511^31524-31524^28511140440Frank Doornink06/2024
400732795^19126+19126^32795140416Hans Havermann05/2021
4008(44*10^140410-503)/9140411Robert Price12/2018
400928332^31535-31535^28332140403Frank Doornink06/2024
4010153^64265-2140400Lelio R Paula11/2017
401130323^31322-31322^30323140379Frank Doornink06/2024
4012(112*10^140357-1)/3140359Serge Batalov12/2014
4013(29*10^140337-17)/3140338Robert Price09/2019
40142^466181-112735140335Enzo Doria07/2014
4015(16*10^140290-37)/3140291Robert Price05/2021
4016(5*10^140281-119)/3140282Robert Price03/2018
401734568^11415+11415^34568140259Hans Havermann05/2021
4018(27*2^465872+1)/691140241Lelio R Paula08/2015
401933632^14781+14781^33632140236Hans Havermann05/2021
402031803^25670+25670^31803140233Hans Havermann05/2021
40212^465803-114817140221Enzo Doria05/2015
4022floor(Pi*10^140344)%10^140165140165Serge Batalov08/2012
40232^465503-112735140131Enzo Doria07/2014
4024(16*10^140091+167)/3140092Robert Price06/2019
4025(8*10^140087-137)/3140088Robert Price03/2022
40266^179964+179964^6-1140040Robert Price04/2014
4027(89*10^140008-179)/9140009Robert Price12/2019
4028(29*2^465077-1)/9140003Lelio R Paula08/2015
40292^465072-344789140001Enzo Doria07/2015
403034742^10683+10683^34742139965Hans Havermann05/2021
40315*10^139945+81139946Robert Price03/2019
403232648^19335+19335^32648139941Hans Havermann05/2021
40332^464864-17139939Lelio R Paula09/2017
40348*10^139920+51139921Robert Price08/2019
4035(85*10^139913-1)/3139915Robert Price02/2020
403631203^30436+30436^31203139896Hans Havermann04/2021
40372^464642+22189139872Enzo Doria09/2023
403826138^31663-31663^26138139865Frank Doornink03/2024
4039(16^116139+619)/5139845Anonymous08/2022
4040(2^464556+619)/5139845Eric Chen10/2023
40414*10^139839-27139840Robert Price08/2021
404233582^14573+14573^33582139821Hans Havermann05/2021
4043(17^113621+1)/18139804Paul Bourdelais09/2011
40452*10^139800-21139801Robert Price09/2020
404432628^19261+19261^32628139801Hans Havermann04/2021
4046(13*10^139782+191)/3139783Robert Price11/2018
4047(64*10^139776+791)/9139777Robert Price01/2022
4048(695*10^139772+7)/9139774Robert Price12/2021
4049(19*2^464312-1)/3139773Lelio R Paula08/2015
4050(74*10^139723+133)/9139724Robert Price06/2019
40513*10^139722+13139723Robert Price07/2018
405231577^26592+26592^31577139721Hans Havermann05/2021
405377*10^139692+3139694Robert Price06/2020
4054(31*2^463970+1)/5139670Lelio R Paula08/2015
4055(18203^(2^15)+(18201)^(2^15))/2139597Robert Price05/2018
405639640^3321+3321^39640139584Hans Havermann05/2021
405736663^6410+6410^36663139571Hans Havermann05/2021
40582^463633-2788423139568Enzo Doria11/2015
405933659^13978+13978^33659139532Hans Havermann05/2021
406031811^24318+24318^31811139521Hans Havermann04/2021
406134149^12172+12172^34149139512Hans Havermann04/2021
4062(29*10^139476+313)/9139477Robert Price04/2021
406331721^24940+24940^31721139474Hans Havermann05/2021
406432833^17698+17698^32833139473Hans Havermann05/2021
40652^463271-109501139459Enzo Doria04/2014
4066(5*10^139457+79)/3139458Robert Price03/2018
40672^463237-99139449Lelio R Paula09/2017
4068(49*10^139442+383)/9139443Robert Price04/2019
406931155^29902+29902^31155139441Hans Havermann05/2021
4070(7*10^139417-547)/9139417Robert Price01/2018
407129636^31175-31175^29636139409Frank Doornink05/2024
4072(10^139398+191)/3139398Robert Price02/2018
407323*10^139386-3139388Robert Price10/2021
40742^463019+79463139383Enzo Doria06/2016
40753^292129-112756139381Enzo Doria07/2014
4076(15*2^462951+1)/527139361Lelio R Paula08/2015
407731922^23205+23205^31922139359Hans Havermann05/2021
4078(19*10^139336+503)/9139337Alfred Reich11/2023
40802^462855-1865707139334Enzo Doria02/2016
407931237^28876+28876^31237139334Hans Havermann05/2021
4081(86*10^139315+121)/9139316Robert Price08/2019
40822^462786-292043139313Enzo Doria08/2015
408338915^3798+3798^38915139299Hans Havermann05/2021
4085(26*10^139289+1)/9139290Serge Batalov05/2010
4084(17*10^139289+7)/3139290Robert Price06/2023
408634065^12248+12248^34065139260Hans Havermann05/2021
408736425^6654+6654^36425139256Hans Havermann05/2021
408839252^3527+3527^39252139243Hans Havermann05/2021
4089(17*10^139239+67)/3139240Robert Price01/2019
409031887^23248+23248^31887139231Hans Havermann05/2021
4091(25*10^139210-97)/9139211Robert Price01/2022
40922^462238-935139148Yves Minet02/2014
4093(29*10^139134-119)/9139135Robert Price12/2021
4094U(687859)/4127153139105Serge Batalov07/2024
4095(109*10^139100-7)/3139102Robert Price03/2021
409638744^3885+3885^38744139068Hans Havermann05/2021
409731112^29499+29499^31112139065Hans Havermann05/2021
40982*10^139043-63139044Robert Price01/2022
409936390^6613+6613^36390139025Hans Havermann04/2021
410030554^30989-30989^30554138988Frank Doornink05/2024
41012*10^138975+33138976Robert Price11/2021
410242437^1882+1882^42437138966Hans Havermann05/2021
410332151^20990+20990^32151138958Hans Havermann05/2021
410432154^20933+20933^32154138933Hans Havermann04/2021
410531082^29499+29499^31082138931Hans Havermann04/2021
410630573^30962-30962^30573138876Frank Doornink05/2024
41072^461228+1870441138844Enzo Doria05/2016
41082^461204-113675138837Enzo Doria08/2014
4109(2^461139-7)/47138815Lelio R Paula08/2015
4110(17*10^138812-521)/9138813Robert Price04/2018
41113*10^138811-11138812Robert Price07/2018
411229109^31088-31088^29109138778Frank Doornink05/2024
4113(28*10^138768+173)/3138769Robert Price12/2019
4114(17*2^460963+1)/124051613138757Lelio R Paula08/2015
4115(379*10^138737-1)/9138739Robert Price02/2020
4116(43*10^138648+101)/9138649Robert Price11/2018
41172^460567-113541138645Enzo Doria08/2014
41182^460539+224789138637Enzo Doria07/2024
4119(10^138622+161)/9138622Robert Price09/2021
41207*10^138604+3138605Robert Price08/2015
4121(133*10^138600+17)/3138602Robert Price11/2021
412233912^12203+12203^33912138581Hans Havermann05/2021
41232^460330+69138574Lelio R Paula09/2017
4124(17*10^138569-77)/3138570Robert Price08/2019
412531186^27725+27725^31186138556Hans Havermann05/2021
4126(16*10^138545+89)/3138546Robert Price03/2021
412739753^3056+3056^39753138546Hans Havermann05/2021
412831282^26847+26847^31282138545Hans Havermann05/2021
41296*10^138520-37138521Robert Price02/2021
41312^460078-69581138498Enzo Doria12/2015
413031830^22447+22447^31830138498Hans Havermann05/2021
413237384^5065+5065^37384138492Hans Havermann05/2021
413328736^31055-31055^28736138457Frank Doornink05/2024
413434774^9585+9585^34774138456Hans Havermann05/2021
413510^138444-5001138444Robert Price12/2021
41362^459768+1531138404Lelio R Paula06/2012
4137(266*10^138328-17)/3138330Robert Price07/2020
413827200^31193-31193^27200138328Frank Doornink01/2024
413928782^31019-31019^28782138318Frank Doornink05/2024
414032963^15696+15696^32963138306Hans Havermann05/2021
41412^459343-113611138277Enzo Doria08/2014
4142(28*10^138240+113)/3138241Robert Price03/2020
41432^459199+1874393138233Enzo Doria06/2016
414433339^14002+14002^33339138230Hans Havermann05/2021
414530137^30860-30860^30137138226Frank Doornink05/2024
41462^459063-345307138192Enzo Doria06/2015
41472*10^138162-43138163Robert Price04/2018
41482^458927-112747138151Enzo Doria06/2014
41492^458927-69217138151Enzo Doria11/2015
415030907^29458+29458^30907138130Hans Havermann05/2021
415132882^15837+15837^32882138094Hans Havermann05/2021
415239252^3295+3295^39252138083Hans Havermann05/2021
415333789^12190+12190^33789138062Hans Havermann06/2021
4154555555*2^458524+1513138036Darren Bedwell08/2009
415528095^31028-31028^28095138033Frank Doornink05/2024
415630931^29002+29002^30931138028Hans Havermann05/2021
41572^458465+2^32+1138012T. D. Noe06/2007
415832206^19275+19275^32206138003Hans Havermann05/2021
41592^458321-113053137969Enzo Doria07/2014
41606^177298+323137965Riley Fisher03/2023
41612^458298+79459137962Enzo Doria06/2016
416230254^30789-30789^30254137959Frank Doornink05/2024
41632^458248-21815137947Enzo Doria07/2013
41642^458194+1876549137931Enzo Doria07/2016
4165(318259#+325270)/(2^2*5*11*2957)137907Makoto Morimoto10/2017
4166(318259#+2625)/(3^2*5*7^5*22965193)137899Makoto Morimoto06/2019
4167(793*10^137887+53)/9137889Robert Price01/2022
41682^457937+57137853Lelio R Paula09/2017
416928714^30921-30921^28714137849Frank Doornink05/2024
4170(8*10^137845+13)/3137846Robert Price06/2018
41712^457822+105137819Donovan Johnson06/2006
41722^457754-113711137798Enzo Doria09/2014
417311^132315-360137792Enzo Doria09/2012
417432072^19689+19689^32072137725Hans Havermann06/2021
417526529^31132-31132^26529137720Frank Doornink03/2024
417644592^1225+1225^44592137707Hans Havermann05/2021
417728986^30857-30857^28986137690Frank Doornink05/2024
41782^457347-37137676Lelio R Paula09/2017
41792^457322-2786393137668Enzo Doria10/2015
4180gcd(Phi(699340,10),(10^34967+1)^3*(10^34967+1+10^17484)-(10^69934+10^34967)*(10^17484-1)+10^104901)137664Serge Batalov04/2015
418134015^11134+11134^34015137647Hans Havermann06/2021
41822^457240-59939137643Enzo Doria10/2015
4183(856*10^137633-1)/9137635Robert Price03/2020
418436232^6289+6289^36232137631Hans Havermann05/2021
41852^457120-21575137607Enzo Doria07/2013
4186(11*2^456978+1)/15137564Lelio R Paula07/2015
418730963^27722+27722^30963137564Hans Havermann04/2021
418833722^12003+12003^33722137562Hans Havermann06/2021
4189(7*25^98399+10613)/12137556Curtis Bright05/2015
419041901^1918+1918^41901137555Hans Havermann06/2021
4191(7*10^137551-1)/3137552Robert Price08/2022
419232930^15021+15021^32930137539Hans Havermann05/2021
419331178^25785+25785^31178137538Hans Havermann05/2021
4194419^52446+52446^419137525Norbert Schneider11/2020
41952^456813+214175137515Enzo Doria10/2023
41962^456796-113513137510Enzo Doria08/2014
419731788^21137+21137^31788137485Hans Havermann04/2021
4198(7*2^456655+1)/39137467Lelio R Paula07/2015
419927151^31004-31004^27151137466Frank Doornink01/2024
42002^456503-114361137422Enzo Doria01/2015
4201(11*2^456387+1)/19137386Lelio R Paula07/2015
420230618^30618-5^5137352Serge Batalov04/2024
420336248^6147+6147^36248137332Hans Havermann05/2021
420431986^19651+19651^31986137329Hans Havermann05/2021
42052^456167+22313137320Enzo Doria09/2023
420631817^20656+20656^31817137292Hans Havermann05/2021
4207(71*10^137250+1)/9137251Serge Batalov05/2010
42082^455922+76249137247Enzo Doria05/2016
420931310^24171+24171^31310137241Hans Havermann05/2021
421014^119741-119741^14137239Serge Batalov04/2016
421135014^8297+8297^35014137218Hans Havermann05/2021
4212(19*2^455760+1)/3455137196Lelio R Paula07/2015
4214124^(2^16)+57^(2^16)137195Valeryi Kuryshev02/2011
4213124^65536+57^65536137195Serge Batalov03/2018
42152^455689+72677137177Enzo Doria04/2016
4216(17948!)^2+Prime(17948)137118Robert Price08/2014
421731287^24128+24128^31287137116Hans Havermann05/2021
4218(37^87421-1)/36137093Robert Price03/2012
421936233^6070+6070^36233137077Hans Havermann05/2021
4220(8*10^137073-17)/9137073Serge Batalov11/2022
422138418^3697+3697^38418137070Hans Havermann04/2021
42222^455323-57137066Lelio R Paula09/2017
4223(56*10^137019+583)/9137020Robert Price08/2021
422425017^31148-31148^25017136997Frank Doornink12/2023
4225(73*17^111333-9)/16136991Curtis Bright05/2015
42262^455025-112723136977Enzo Doria06/2014
422733876^11039+11039^33876136959Hans Havermann05/2021
4228(19860^32041-1)/(19860^179-1)136943Ryan Propper11/2023
4229(251^57059-1)/250136921Anonymous04/2024
423035142^7873+7873^35142136919Hans Havermann05/2021
4231(4997*31^91805-1)/2136918Eric Chen05/2024
423266*10^136894+7136896Robert Price07/2020
423328766^30697-30697^28766136875Frank Doornink05/2024
42342^454675-1777136871Yves Minet10/2011
423531676^20931+20931^31676136866Hans Havermann05/2021
42363*10^136829+29136830Robert Price05/2018
42374*10^136813-57136814Robert Price10/2018
4238(6092*28^94536-143)/9136812Curtis Bright05/2015
4239fibonacci(654572)-2136798Jon Grantham08/2023
424037359^4588+4588^37359136795Hans Havermann05/2021
42412^454348-53136773Lelio R Paula09/2017
424231^91680-2136729Lelio R Paula05/2017
42432^454199-113697136728Enzo Doria09/2014
424430785^27622+27622^30785136725Hans Havermann05/2021
424532973^14014+14014^32973136725Hans Havermann05/2021
42477*10^136716+69136717Robert Price07/2019
424636002^6273+6273^36002136717Hans Havermann05/2021
42486*10^136692+53136693Robert Price05/2020
4249(13*10^136687+47)/3136688Robert Price10/2018
42502^453935-2791357136649Enzo Doria01/2016


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 18 2024 11:41 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!