PRP Records

Probable Primes Top 10000

(280932 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 ?
20012^491851+1871453148062Enzo Doria05/2016
2002(68*10^148060-257)/9148061Robert Price07/2019
2003(151*10^148020-1)/3148022Robert Price03/2020
200439153^6032+6032^39153148017Hans Havermann10/2020
200536798^10507+10507^36798147983Hans Havermann12/2020
2006(26*10^147973-23)/3147974Robert Price12/2019
20072^491521-1865323147963Enzo Doria02/2016
2008(2^491476+7)/71147948Lelio R Paula10/2015
20092^491391-7807147924Lelio R Paula01/2013
201039736^5279+5279^39736147920Hans Havermann11/2020
20112^491370-113297147918Enzo Doria07/2014
2012(32760^32760+32759^32759)/95546586737133567708319147900Robert Price07/2016
201344368^2155+2155^44368147899Hans Havermann12/2020
2014(17*10^147890+79)/3147891Robert Price04/2019
201594*10^147871-3147873Robert Price05/2020
201610^147843-50000000001147843Robert Price12/2020
201735805^13346+13346^35805147709Hans Havermann11/2020
20182^490660-17147704Lelio R Paula12/2017
2019(229*10^147699-1)/3147701Robert Price07/2020
202040656^4289+4289^40656147678Hans Havermann11/2020
20212^490550+1179439147671Enzo Doria06/2016
2022(23*10^147649-59)/9147650Robert Price05/2018
20232^490303+2793653147596Enzo Doria03/2016
2024199^64181-2147543Lelio R Paula11/2017
202532849^30958+30958^32849147518Hans Havermann11/2020
20262^489871-286987147466Enzo Doria07/2015
20272^489864-351899147464Enzo Doria07/2015
2028175^65724-2147422Lelio R Paula11/2017
20292^489712+1874851147419Enzo Doria06/2016
203034473^18830+18830^34473147367Hans Havermann11/2020
203163^81896-2147359Lelio R Paula10/2017
203234580^18237+18237^34580147344Hans Havermann11/2020
2033(11*10^147313-107)/3147314Robert Price09/2018
20342^489305-59815147296Enzo Doria10/2015
2035(2^489280-7)/6381147285Lelio R Paula09/2015
20362*10^147260+29147261Robert Price02/2021
203733556^24457+24457^33556147258Hans Havermann11/2020
20382^489125+80357147242Enzo Doria06/2016
203932835^30452+30452^32835147220Hans Havermann12/2020
2040(148*10^147139-1)/3147141Robert Price03/2020
204134338^19255+19255^34338147123Hans Havermann11/2020
20422^488648-112799147098Enzo Doria07/2014
20432^488627-350317147092Enzo Doria06/2015
204433432^25075+25075^33432147076Hans Havermann12/2020
2045(2^488441-1)/(61543567*30051203516986199)147012Dario Alpern12/2014
20462^488280-2165146987Yves Minet07/2014
20472^488278+45146987Lelio R Paula12/2017
20482^487927-39146881Lelio R Paula12/2017
2049(7*10^146860-13)/3146861Robert Price07/2018
2050(26*10^146856-77)/3146857Robert Price11/2019
205132948^28611+28611^32948146834Hans Havermann11/2020
205242596^2799+2799^42596146829Hans Havermann12/2020
20532^487726-1863341146821Enzo Doria12/2015
205443838^2229+2229^43838146775Hans Havermann11/2020
205535005^15594+15594^35005146775Hans Havermann11/2020
2056((10^73362-1)*10000/9+6701)*10^73362+(10^73362-1)/9146728Hans Havermann09/2019
205732963^28234+28234^32963146711Hans Havermann12/2020
2058(22*10^146661-19)/3146662Robert Price04/2019
205933958^20825+20825^33958146651Hans Havermann12/2020
20602^487121-39523146639Enzo Doria09/2015
206161063^252+252^61063146637Hans Havermann12/2020
2062(7*2^486967+1)/39146591Lelio R Paula09/2015
206334099^19900+19900^34099146587Hans Havermann11/2020
20642^486893-79146570Yves Minet09/2017
206536818^9567+9567^36818146565Hans Havermann12/2020
20662^486840+1879141146554Enzo Doria08/2016
20672^486774-87146534Lelio R Paula12/2017
206838655^6176+6176^38655146530Hans Havermann11/2020
20698*10^146522-81146523Robert Price02/2021
207032820^29059+29059^32820146485Hans Havermann12/2020
207137261^8530+8530^37261146472Hans Havermann12/2020
207266953^154+154^66953146462Hans Havermann12/2020
207396^73877-95^73877146445Robert Price10/2015
20748*10^146421+81146422Robert Price08/2019
207533153^26090+26090^33153146420Hans Havermann11/2020
2076(52^85259+1)/53146304Paul Bourdelais09/2017
2077179^64935+2146290Lelio R Paula10/2017
207832595^30758+30758^32595146285Hans Havermann11/2020
207934972^15157+15157^34972146205Hans Havermann12/2020
2080(19*10^146181-49)/3146182Robert Price05/2019
20812^485531-114621146160Enzo Doria05/2015
2082(2^485461-9)/4249146135Lelio R Paula09/2015
20832^485389+81887146117Enzo Doria08/2016
208432554^30773+30773^32554146108Hans Havermann11/2020
2085(10^146063+71)/9146063Serge Batalov07/2015
2086(2^485119+7)/2745146032Lelio R Paula09/2015
2087(22*10^146029+257)/9146030Robert Price06/2018
20887*10^145982-53145983Robert Price06/2020
20892^484743+1872923145923Enzo Doria05/2016
209033140^25287+25287^33140145913Hans Havermann01/2021
209137875^7112+7112^37875145895Hans Havermann01/2021
209232862^27473+27473^32862145872Hans Havermann01/2021
209332836^27587+27587^32836145815Hans Havermann01/2021
20942^484341+1879157145802Enzo Doria08/2016
20952*10^145784-91145785Robert Price04/2020
20962^484271-51145781Lelio R Paula11/2017
209770^78989-69^78989145743Robert Price01/2014
209851^85334+2145714Robert Price07/2015
20992^483886-1857101145665Enzo Doria10/2015
210033350^23307+23307^33350145656Hans Havermann01/2021
2101(19*10^145585+131)/3145586Robert Price06/2020
21022^483563-1863457145567Enzo Doria12/2015
21032^483516-1861409145553Enzo Doria11/2015
21042^483384-115019145514Enzo Doria06/2015
2105(259*10^145501-1)/3145503Robert Price12/2020
2106(19*10^145499-61)/3145500Robert Price05/2019
21072^483302-3221145489Lelio R Paula12/2012
210835523^12434+12434^35523145453Hans Havermann01/2021
21092^483046+1874029145412Enzo Doria06/2016
21102^482991-2789317145395Enzo Doria12/2015
21112^482978-2789711145391Enzo Doria12/2015
21122^482966-2789711145388Enzo Doria12/2015
21132^482817-1858843145343Enzo Doria10/2015
21142^482751-113635145323Enzo Doria08/2014
21152^482705-459763145309Enzo Doria05/2015
2116(4^241306+11)/3145281Robert Price03/2017
2117(238*10^145276-1)/3145278Robert Price04/2020
2118(19*2^482534+1)/7145258Lelio R Paula09/2015
211953^84239-52^84239145252Robert Price01/2013
212047952^1067+1067^47952145207Hans Havermann01/2021
2121(2^482333+5)/9287145193Lelio R Paula09/2015
21222^482087+72623145123Enzo Doria04/2016
21232^482016-286565145102Enzo Doria07/2015
2124(19*10^145093+101)/3145094Robert Price09/2019
21252^481840+15145049Robert Price09/2015
21262^481801-481801145037Henri Lifchitz03/2005
21272^481775+1869083145029Enzo Doria05/2016
212829^99167+2145022Ray Chandler08/2011
21292^481663+1875653144996Enzo Doria07/2016
213036486^9379+9379^36486144929Hans Havermann12/2020
213135111^13378+13378^35111144882Hans Havermann01/2021
21322^481149-459073144841Enzo Doria05/2015
213334619^15246+15246^34619144817Hans Havermann01/2021
21342^481045-113215144809Enzo Doria07/2014
2135(64*10^144797+287)/9144798Robert Price04/2019
21362^480859-113695144753Enzo Doria09/2014
21372^480766-2787191144725Enzo Doria11/2015
2138(21*27^101106-151)/26144720Curtis Bright05/2015
21392^480678+1874239144699Enzo Doria06/2016
2140(8*10^144683+1)/9144683Serge Batalov05/2010
2141L(692147)144651Henri Lifchitz10/2008
2142(76*10^144648+77)/9144649Robert Price10/2019
214332672^26721+26721^32672144635Hans Havermann01/2021
21442^480417+35144620Robert Price11/2015
21452^480296-59879144584Enzo Doria10/2015
214633157^22878+22878^33157144546Hans Havermann12/2020
214745494^1497+1497^45494144454Hans Havermann12/2020
21482^479844+3144448Donovan Johnson06/2006
214933442^20803+20803^33442144407Hans Havermann01/2021
2150(27*2^479642+1)/733144386Lelio R Paula08/2015
215144917^1638+1638^44917144378Hans Havermann12/2020
2152(21*2^479605-1)/11144376Lelio R Paula09/2015
21532^479348-2792219144299Enzo Doria02/2016
21543^302389-6242144277Enzo Doria05/2014
215533778^18641+18641^33778144248Hans Havermann01/2021
21562*10^144220-3144221Robert Price07/2015
21572^478904-109109144165Enzo Doria04/2014
215843698^1987+1987^43698144125Hans Havermann12/2020
215936128^9723+9723^36128144072Hans Havermann01/2021
216032817^24518+24518^32817144050Hans Havermann12/2020
216134295^15828+15828^34295144020Hans Havermann01/2021
21622^478337-115333143994Enzo Doria07/2015
2163(7*2^478330-1)/3143993Lelio R Paula08/2015
216488^74047-87^74047143984Robert Price05/2015
216533242^21441+21441^33242143980Hans Havermann01/2021
2166(19*10^143963+467)/9143964Robert Price02/2018
2167(71^77761+1)/72143954Paul Bourdelais09/2017
216833490^19859+19859^33490143939Hans Havermann01/2021
21692^478088+27143919Robert Price11/2015
21707*10^143857-93143858Robert Price08/2020
21713*10^143844+61143845Robert Price09/2020
217241358^3005+3005^41358143837Hans Havermann01/2021
21732^477475-22071143735Enzo Doria07/2013
21742^477417-22123143717Enzo Doria07/2013
21752^477359-3577143700Yves Minet03/2017
217639435^4402+4402^39435143688Hans Havermann01/2021
2177(14*10^143662-71)/3143663Robert Price12/2018
21786^184614+5143658Paul Bourdelais01/2021
217946371^1252+1252^46371143640Hans Havermann12/2020
218034975^12748+12748^34975143588Hans Havermann01/2021
21812^476936-396765143573Enzo Doria07/2013
21822^476888-2791229143558Enzo Doria01/2016
21832^476868-1859939143552Enzo Doria11/2015
218440807^3294+3294^40807143548Hans Havermann12/2020
2185755^49878+49878^755143547Norbert Schneider04/2019
2186(19^112247-4^112247)/15143536Robert Price03/2021
21872^476558-113627143459Enzo Doria08/2014
21882^476478-45143435Lelio R Paula11/2017
2189(2^475854+9)/73143245Lelio R Paula08/2015
21902^475813-113239143234Enzo Doria07/2014
21912^475624-114059143178Enzo Doria11/2014
2192(11*2^475553-7)/15143156Renaud Lifchitz03/2011
21932^475480-2786129143134Enzo Doria10/2015
2194(19*10^143129-43)/3143130Robert Price05/2019
2195(14*10^143097+73)/3143098Robert Price12/2018
21962^475299-111937143080Enzo Doria05/2014
21972^475160-2797859143038Enzo Doria04/2016
2198(2^475069+3)/395143008Lelio R Paula08/2015
21992^475027-461437142998Enzo Doria07/2015
2200(2^474958+78557)/3142977Lelio R Paula07/2015
2201(8*10^142932+43)/3142933Robert Price06/2018
2202(54^82471-1)/53142871Paul Bourdelais09/2017
2203(11*2^474432-1)/95142818Lelio R Paula09/2015
22042^474417-59923142814Enzo Doria10/2015
22054*10^142810-21142811Robert Price09/2018
2206(3*2^474166+1)/7142738Lelio R Paula08/2015
22072^474053+2897142705Lelio R Paula08/2012
2208(10^142699+359)/9142699Serge Batalov12/2014
2209898^48311-897^48311142676Jean-Louis Charton12/2012
22102^473740-1856639142610Enzo Doria09/2015
2211(25*10^142573-403)/9142574Robert Price12/2020
22122^473617-114223142573Enzo Doria12/2014
22132^473257+1873217142465Enzo Doria06/2016
2214(19*2^473242+1)/11142461Lelio R Paula09/2015
2215(61*10^142446-1)/3142448Robert Price01/2020
2216(14*10^142440+61)/3142441Robert Price12/2018
2217(10^142425+359)/9142425Serge Batalov12/2014
22182^473101+773027142418Enzo Doria05/2016
2219(13*2^472838-1)/3142340Lelio R Paula09/2015
2220(17*2^472789-1)/187347142320Lelio R Paula09/2015
22212^472634-109511142278Enzo Doria04/2014
2222(48^84589+1)/49142213Robert Price01/2014
22237*10^142189+87142190Robert Price07/2019
22242^472258+7142164Lelio R Paula08/2015
2225(23*10^142105+91)/3142106Robert Price08/2019
2226tau(317^10330)142098Nik Lygeros / Olivier Rozier / LR team10/2013
2227(11*2^471913-1)/21142060Lelio R Paula09/2015
2228(16*10^142058+197)/3142059Robert Price04/2019
22299*10^142037+91142038Robert Price10/2020
22302^471792+1880881142024Enzo Doria11/2016
2231(31*2^471580-1)/135141960Lelio R Paula08/2015
2232(4*10^141926-79)/3141927Robert Price02/2018
2233(904*19^110984-1)/3141924Curtis Bright05/2015
2234(14*10^141853+37)/3141854Robert Price12/2018
2235(41*10^141836-59)/9141837Robert Price10/2018
22364*5^202913-9141831Lelio R Paula04/2015
22372*7^167812-3141818Lelio R Paula12/2014
22382^471043+35141799Robert Price11/2015
2239(11*2^470956-1)/7945141770Lelio R Paula08/2015
2240(11*10^141718-131)/3141719Robert Price09/2018
22412^470692+76771141693Enzo Doria05/2016
2242(21*2^470391+1)/533141601Lelio R Paula09/2015
22432^470305-459373141576Enzo Doria05/2015
22442^470183+72623141540Enzo Doria04/2016
22452^470173-16465141537Enzo Doria04/2013
224644*10^141476+9141478Robert Price10/2020
22472^469974-1841141477Enzo Doria05/2014
2248(23*2^469939+1)/25141466Lelio R Paula08/2015
22492*10^141448+63141449Robert Price05/2018
22502^469824+43141432Lelio R Paula09/2017


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: April, 13 2021 12:02 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!