PRP Records

Probable Primes Top 10000

(277054 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 ?
200138655^6176+6176^38655146530Hans Havermann11/2020
200232820^29059+29059^32820146485Hans Havermann12/2020
200337261^8530+8530^37261146472Hans Havermann12/2020
200466953^154+154^66953146462Hans Havermann12/2020
200596^73877-95^73877146445Robert Price10/2015
20068*10^146421+81146422Robert Price08/2019
200733153^26090+26090^33153146420Hans Havermann11/2020
2008(52^85259+1)/53146304Paul Bourdelais09/2017
2009179^64935+2146290Lelio R Paula10/2017
201032595^30758+30758^32595146285Hans Havermann11/2020
201134972^15157+15157^34972146205Hans Havermann12/2020
2012(19*10^146181-49)/3146182Robert Price05/2019
20132^485531-114621146160Enzo Doria05/2015
2014(2^485461-9)/4249146135Lelio R Paula09/2015
20152^485389+81887146117Enzo Doria08/2016
201632554^30773+30773^32554146108Hans Havermann11/2020
2017(10^146063+71)/9146063Serge Batalov07/2015
2018(2^485119+7)/2745146032Lelio R Paula09/2015
2019(22*10^146029+257)/9146030Robert Price06/2018
20207*10^145982-53145983Robert Price06/2020
20212^484743+1872923145923Enzo Doria05/2016
202233140^25287+25287^33140145913Hans Havermann01/2021
202337875^7112+7112^37875145895Hans Havermann01/2021
202432862^27473+27473^32862145872Hans Havermann01/2021
202532836^27587+27587^32836145815Hans Havermann01/2021
20262^484341+1879157145802Enzo Doria08/2016
20272*10^145784-91145785Robert Price04/2020
20282^484271-51145781Lelio R Paula11/2017
202970^78989-69^78989145743Robert Price01/2014
203051^85334+2145714Robert Price07/2015
20312^483886-1857101145665Enzo Doria10/2015
203233350^23307+23307^33350145656Hans Havermann01/2021
2033(19*10^145585+131)/3145586Robert Price06/2020
20342^483563-1863457145567Enzo Doria12/2015
20352^483516-1861409145553Enzo Doria11/2015
20362^483384-115019145514Enzo Doria06/2015
2037(259*10^145501-1)/3145503Robert Price12/2020
2038(19*10^145499-61)/3145500Robert Price05/2019
20392^483302-3221145489Lelio R Paula12/2012
204035523^12434+12434^35523145453Hans Havermann01/2021
20412^483046+1874029145412Enzo Doria06/2016
20422^482991-2789317145395Enzo Doria12/2015
20432^482978-2789711145391Enzo Doria12/2015
20442^482966-2789711145388Enzo Doria12/2015
20452^482817-1858843145343Enzo Doria10/2015
20462^482751-113635145323Enzo Doria08/2014
20472^482705-459763145309Enzo Doria05/2015
2048(4^241306+11)/3145281Robert Price03/2017
2049(238*10^145276-1)/3145278Robert Price04/2020
2050(19*2^482534+1)/7145258Lelio R Paula09/2015
205153^84239-52^84239145252Robert Price01/2013
205247952^1067+1067^47952145207Hans Havermann01/2021
2053(2^482333+5)/9287145193Lelio R Paula09/2015
20542^482087+72623145123Enzo Doria04/2016
20552^482016-286565145102Enzo Doria07/2015
2056(19*10^145093+101)/3145094Robert Price09/2019
20572^481840+15145049Robert Price09/2015
20582^481801-481801145037Henri Lifchitz03/2005
20592^481775+1869083145029Enzo Doria05/2016
206029^99167+2145022Ray Chandler08/2011
20612^481663+1875653144996Enzo Doria07/2016
206236486^9379+9379^36486144929Hans Havermann12/2020
206335111^13378+13378^35111144882Hans Havermann01/2021
20642^481149-459073144841Enzo Doria05/2015
206534619^15246+15246^34619144817Hans Havermann01/2021
20662^481045-113215144809Enzo Doria07/2014
2067(64*10^144797+287)/9144798Robert Price04/2019
20682^480859-113695144753Enzo Doria09/2014
20692^480766-2787191144725Enzo Doria11/2015
2070(21*27^101106-151)/26144720Curtis Bright05/2015
20712^480678+1874239144699Enzo Doria06/2016
2072(8*10^144683+1)/9144683Serge Batalov05/2010
2073L(692147)144651Henri Lifchitz10/2008
2074(76*10^144648+77)/9144649Robert Price10/2019
207532672^26721+26721^32672144635Hans Havermann01/2021
20762^480417+35144620Robert Price11/2015
20772^480296-59879144584Enzo Doria10/2015
207833157^22878+22878^33157144546Hans Havermann12/2020
207945494^1497+1497^45494144454Hans Havermann12/2020
20802^479844+3144448Donovan Johnson06/2006
208133442^20803+20803^33442144407Hans Havermann01/2021
2082(27*2^479642+1)/733144386Lelio R Paula08/2015
208344917^1638+1638^44917144378Hans Havermann12/2020
2084(21*2^479605-1)/11144376Lelio R Paula09/2015
20852^479348-2792219144299Enzo Doria02/2016
20863^302389-6242144277Enzo Doria05/2014
208733778^18641+18641^33778144248Hans Havermann01/2021
20882*10^144220-3144221Robert Price07/2015
20892^478904-109109144165Enzo Doria04/2014
209043698^1987+1987^43698144125Hans Havermann12/2020
209136128^9723+9723^36128144072Hans Havermann01/2021
209232817^24518+24518^32817144050Hans Havermann12/2020
209334295^15828+15828^34295144020Hans Havermann01/2021
20942^478337-115333143994Enzo Doria07/2015
2095(7*2^478330-1)/3143993Lelio R Paula08/2015
209688^74047-87^74047143984Robert Price05/2015
209733242^21441+21441^33242143980Hans Havermann01/2021
2098(19*10^143963+467)/9143964Robert Price02/2018
2099(71^77761+1)/72143954Paul Bourdelais09/2017
210033490^19859+19859^33490143939Hans Havermann01/2021
21012^478088+27143919Robert Price11/2015
21027*10^143857-93143858Robert Price08/2020
21033*10^143844+61143845Robert Price09/2020
210441358^3005+3005^41358143837Hans Havermann01/2021
21052^477475-22071143735Enzo Doria07/2013
21062^477417-22123143717Enzo Doria07/2013
21072^477359-3577143700Yves Minet03/2017
210839435^4402+4402^39435143688Hans Havermann01/2021
2109(14*10^143662-71)/3143663Robert Price12/2018
211046371^1252+1252^46371143640Hans Havermann12/2020
211134975^12748+12748^34975143588Hans Havermann01/2021
21122^476936-396765143573Enzo Doria07/2013
21132^476888-2791229143558Enzo Doria01/2016
21142^476868-1859939143552Enzo Doria11/2015
211540807^3294+3294^40807143548Hans Havermann12/2020
2116755^49878+49878^755143547Norbert Schneider04/2019
21172^476558-113627143459Enzo Doria08/2014
21182^476478-45143435Lelio R Paula11/2017
2119(2^475854+9)/73143245Lelio R Paula08/2015
21202^475813-113239143234Enzo Doria07/2014
21212^475624-114059143178Enzo Doria11/2014
2122(11*2^475553-7)/15143156Renaud Lifchitz03/2011
21232^475480-2786129143134Enzo Doria10/2015
2124(19*10^143129-43)/3143130Robert Price05/2019
2125(14*10^143097+73)/3143098Robert Price12/2018
21262^475299-111937143080Enzo Doria05/2014
21272^475160-2797859143038Enzo Doria04/2016
2128(2^475069+3)/395143008Lelio R Paula08/2015
21292^475027-461437142998Enzo Doria07/2015
2130(2^474958+78557)/3142977Lelio R Paula07/2015
2131(8*10^142932+43)/3142933Robert Price06/2018
2132(54^82471-1)/53142871Paul Bourdelais09/2017
2133(11*2^474432-1)/95142818Lelio R Paula09/2015
21342^474417-59923142814Enzo Doria10/2015
21354*10^142810-21142811Robert Price09/2018
2136(3*2^474166+1)/7142738Lelio R Paula08/2015
21372^474053+2897142705Lelio R Paula08/2012
2138(10^142699+359)/9142699Serge Batalov12/2014
2139898^48311-897^48311142676Jean-Louis Charton12/2012
21402^473740-1856639142610Enzo Doria09/2015
2141(25*10^142573-403)/9142574Robert Price12/2020
21422^473617-114223142573Enzo Doria12/2014
21432^473257+1873217142465Enzo Doria06/2016
2144(19*2^473242+1)/11142461Lelio R Paula09/2015
2145(61*10^142446-1)/3142448Robert Price01/2020
2146(14*10^142440+61)/3142441Robert Price12/2018
2147(10^142425+359)/9142425Serge Batalov12/2014
21482^473101+773027142418Enzo Doria05/2016
2149(13*2^472838-1)/3142340Lelio R Paula09/2015
2150(17*2^472789-1)/187347142320Lelio R Paula09/2015
21512^472634-109511142278Enzo Doria04/2014
2152(48^84589+1)/49142213Robert Price01/2014
21537*10^142189+87142190Robert Price07/2019
21542^472258+7142164Lelio R Paula08/2015
2155(23*10^142105+91)/3142106Robert Price08/2019
2156tau(317^10330)142098Nik Lygeros / Olivier Rozier / LR team10/2013
2157(11*2^471913-1)/21142060Lelio R Paula09/2015
2158(16*10^142058+197)/3142059Robert Price04/2019
21599*10^142037+91142038Robert Price10/2020
21602^471792+1880881142024Enzo Doria11/2016
2161(31*2^471580-1)/135141960Lelio R Paula08/2015
2162(4*10^141926-79)/3141927Robert Price02/2018
2163(904*19^110984-1)/3141924Curtis Bright05/2015
2164(14*10^141853+37)/3141854Robert Price12/2018
2165(41*10^141836-59)/9141837Robert Price10/2018
21664*5^202913-9141831Lelio R Paula04/2015
21672*7^167812-3141818Lelio R Paula12/2014
21682^471043+35141799Robert Price11/2015
2169(11*2^470956-1)/7945141770Lelio R Paula08/2015
2170(11*10^141718-131)/3141719Robert Price09/2018
21712^470692+76771141693Enzo Doria05/2016
2172(21*2^470391+1)/533141601Lelio R Paula09/2015
21732^470305-459373141576Enzo Doria05/2015
21742^470183+72623141540Enzo Doria04/2016
21752^470173-16465141537Enzo Doria04/2013
217644*10^141476+9141478Robert Price10/2020
21772^469974-1841141477Enzo Doria05/2014
2178(23*2^469939+1)/25141466Lelio R Paula08/2015
21792*10^141448+63141449Robert Price05/2018
21802^469824+43141432Lelio R Paula09/2017
21812*10^141407-27141408Robert Price05/2018
2182(214*10^141385-1)/3141387Robert Price01/2021
21832^469630-59711141373Enzo Doria10/2015
2184(25*10^141366-331)/9141367Robert Price08/2018
2185(2^469564-3)/611141351Lelio R Paula08/2015
2186197^61601+2141342Lelio R Paula08/2017
21872^469372-112949141296Enzo Doria07/2014
21883^296115+4141283Tyler NeSmith01/2021
2190143^(2^16)+106^(2^16)141253Valeryi Kuryshev02/2011
2189143^65536+106^65536141253Serge Batalov03/2018
21912^469198+782569141243Enzo Doria10/2016
21922^469076-2786939141206Enzo Doria11/2015
21932^468804+1874941141125Enzo Doria06/2016
21942^468787+81353141119Enzo Doria08/2016
21952^468595-350407141062Enzo Doria06/2015
21962^468564+87855141052Lelio R Paula01/2016
21972^468551-21987141048Enzo Doria07/2013
21982^468523-7141040Lelio R Paula08/2015
2199(25*10^141019-13)/3141020Robert Price09/2019
22002^468405+87855141004Lelio R Paula01/2016
22012^467978-113051140876Enzo Doria07/2014
22022^467780-344429140816Enzo Doria07/2015
22039*10^140802-89140803Robert Price04/2020
22042^467605-1855603140764Enzo Doria09/2015
22055*10^140744-7140745Robert Price09/2015
2206(5^201359-1)/4140744Paul Bourdelais12/2008
22072^467401-1850023140702Enzo Doria08/2015
2208(266*10^140681-17)/3140683Robert Price07/2020
2209(2^467270+78557)/23247140658Lelio R Paula07/2015
2210(29*2^467205+1)/2780517107140635Lelio R Paula08/2015
22112^467166-1854941140631Enzo Doria09/2015
2212(203*10^140615-11)/3140617Robert Price12/2020
2213(85*10^140609+473)/9140610Robert Price01/2020
22142^466866-1840571140541Enzo Doria06/2015
22152^466829-459523140530Enzo Doria05/2015
22162^466692-113213140489Enzo Doria07/2014
2217(44*10^140410-503)/9140411Robert Price12/2018
2218153^64265-2140400Lelio R Paula11/2017
2219(112*10^140357-1)/3140359Serge Batalov12/2014
2220(29*10^140337-17)/3140338Robert Price09/2019
22212^466181-112735140335Enzo Doria07/2014
2222(5*10^140281-119)/3140282Robert Price03/2018
2223(27*2^465872+1)/691140241Lelio R Paula08/2015
22242^465803-114817140221Enzo Doria05/2015
2225floor(Pi*10^140344)%10^140165140165Serge Batalov08/2012
22262^465503-112735140131Enzo Doria07/2014
2227(16*10^140091+167)/3140092Robert Price06/2019
22286^179964+179964^6-1140040Robert Price04/2014
2229(89*10^140008-179)/9140009Robert Price12/2019
2230(29*2^465077-1)/9140003Lelio R Paula08/2015
22312^465072-344789140001Enzo Doria07/2015
22325*10^139945+81139946Robert Price03/2019
22332^464864-17139939Lelio R Paula09/2017
22348*10^139920+51139921Robert Price08/2019
2235(85*10^139913-1)/3139915Robert Price02/2020
2236(17^113621+1)/18139804Paul Bourdelais09/2011
22372*10^139800-21139801Robert Price09/2020
2238(13*10^139782+191)/3139783Robert Price11/2018
2239(19*2^464312-1)/3139773Lelio R Paula08/2015
2240(74*10^139723+133)/9139724Robert Price06/2019
22413*10^139722+13139723Robert Price07/2018
224277*10^139692+3139694Robert Price06/2020
2243(31*2^463970+1)/5139670Lelio R Paula08/2015
2244(18203^(2^15)+(18201)^(2^15))/2139597Robert Price05/2018
22452^463633-2788423139568Enzo Doria11/2015
22462^463271-109501139459Enzo Doria04/2014
2247(5*10^139457+79)/3139458Robert Price03/2018
22482^463237-99139449Lelio R Paula09/2017
2249(49*10^139442+383)/9139443Robert Price04/2019
2250(7*10^139417-547)/9139417Robert Price01/2018


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 25 2021 11:23 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!