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 ?
2251(10^139398+191)/3139398Robert Price02/2018
22522^463019+79463139383Enzo Doria06/2016
22533^292129-112756139381Enzo Doria07/2014
2254(15*2^462951+1)/527139361Lelio R Paula08/2015
22552^462855-1865707139334Enzo Doria02/2016
2256(86*10^139315+121)/9139316Robert Price08/2019
22572^462786-292043139313Enzo Doria08/2015
2258(26*10^139289+1)/9139290Serge Batalov05/2010
2259(17*10^139239+67)/3139240Robert Price01/2019
22602^462238-935139148Yves Minet02/2014
22612^461228+1870441138844Enzo Doria05/2016
22622^461204-113675138837Enzo Doria08/2014
2263(2^461139-7)/47138815Lelio R Paula08/2015
2264(17*10^138812-521)/9138813Robert Price04/2018
22653*10^138811-11138812Robert Price07/2018
2266(28*10^138768+173)/3138769Robert Price12/2019
2267(17*2^460963+1)/124051613138757Lelio R Paula08/2015
2268(379*10^138737-1)/9138739Robert Price02/2020
2269(43*10^138648+101)/9138649Robert Price11/2018
22702^460567-113541138645Enzo Doria08/2014
22717*10^138604+3138605Robert Price08/2015
22722^460330+69138574Lelio R Paula09/2017
2273(17*10^138569-77)/3138570Robert Price08/2019
22742^460078-69581138498Enzo Doria12/2015
22752^459768+1531138404Lelio R Paula06/2012
2276(266*10^138328-17)/3138330Robert Price07/2020
22772^459343-113611138277Enzo Doria08/2014
2278(28*10^138240+113)/3138241Robert Price03/2020
22792^459199+1874393138233Enzo Doria06/2016
22802^459063-345307138192Enzo Doria06/2015
22812*10^138162-43138163Robert Price04/2018
22822^458927-112747138151Enzo Doria06/2014
22832^458927-69217138151Enzo Doria11/2015
2284555555*2^458524+1513138036Darren Bedwell08/2009
22852^458465+2^32+1138012T. D. Noe06/2007
22862^458321-113053137969Enzo Doria07/2014
22872^458298+79459137962Enzo Doria06/2016
22882^458248-21815137947Enzo Doria07/2013
22892^458194+1876549137931Enzo Doria07/2016
2290(318259#+325270)/(2^2*5*11*2957)137907Makoto Morimoto10/2017
2291(318259#+2625)/(3^2*5*7^5*22965193)137899Makoto Morimoto06/2019
22922^457937+57137853Lelio R Paula09/2017
2293(8*10^137845+13)/3137846Robert Price06/2018
22942^457822+105137819Donovan Johnson06/2006
22952^457754-113711137798Enzo Doria09/2014
229611^132315-360137792Enzo Doria09/2012
22972^457347-37137676Lelio R Paula09/2017
22982^457322-2786393137668Enzo Doria10/2015
2299gcd(Phi(699340,10),(10^34967+1)^3*(10^34967+1+10^17484)-(10^69934+10^34967)*(10^17484-1)+10^104901)137664Serge Batalov04/2015
23002^457240-59939137643Enzo Doria10/2015
2301(856*10^137633-1)/9137635Robert Price03/2020
23022^457120-21575137607Enzo Doria07/2013
2303(11*2^456978+1)/15137564Lelio R Paula07/2015
2304(7*25^98399+10613)/12137556Curtis Bright05/2015
2305419^52446+52446^419137525Norbert Schneider11/2020
23062^456796-113513137510Enzo Doria08/2014
2307(7*2^456655+1)/39137467Lelio R Paula07/2015
23082^456503-114361137422Enzo Doria01/2015
2309(11*2^456387+1)/19137386Lelio R Paula07/2015
2310(71*10^137250+1)/9137251Serge Batalov05/2010
23112^455922+76249137247Enzo Doria05/2016
231214^119741-119741^14137239Serge Batalov04/2016
2313(19*2^455760+1)/3455137196Lelio R Paula07/2015
2315124^(2^16)+57^(2^16)137195Valeryi Kuryshev02/2011
2314124^65536+57^65536137195Serge Batalov03/2018
23162^455689+72677137177Enzo Doria04/2016
2317(17948!)^2+Prime(17948)137118Robert Price08/2014
2318(37^87421-1)/36137093Robert Price03/2012
23192^455323-57137066Lelio R Paula09/2017
2320(73*17^111333-9)/16136991Curtis Bright05/2015
23212^455025-112723136977Enzo Doria06/2014
232266*10^136894+7136896Robert Price07/2020
23232^454675-1777136871Yves Minet10/2011
23243*10^136829+29136830Robert Price05/2018
23254*10^136813-57136814Robert Price10/2018
2326(6092*28^94536-143)/9136812Curtis Bright05/2015
23272^454348-53136773Lelio R Paula09/2017
232831^91680-2136729Lelio R Paula05/2017
23292^454199-113697136728Enzo Doria09/2014
23307*10^136716+69136717Robert Price07/2019
23316*10^136692+53136693Robert Price05/2020
2332(13*10^136687+47)/3136688Robert Price10/2018
23332^453935-2791357136649Enzo Doria01/2016
23342^453906-69131136640Enzo Doria11/2015
23352^453791+1873913136605Enzo Doria06/2016
2336(21*2^453740-1)/2735136588Lelio R Paula07/2015
2337580^49413+49413^580136550Norbert Schneider02/2019
23382^453503-2788297136519Enzo Doria11/2015
233934989^7958+7958^34989136486Hans Havermann12/2020
234031007^25158+25158^31007136452Hans Havermann11/2020
23412^453267-113827136447Enzo Doria09/2014
234232234^17085+17085^32234136435Hans Havermann12/2020
23432^453102+1877629136398Enzo Doria08/2016
234431016^24981+24981^31016136397Hans Havermann12/2020
2345(62*10^136384-791)/9136385Robert Price06/2019
234634171^9798+9798^34171136382Hans Havermann12/2020
234732756^14541+14541^32756136350Hans Havermann11/2020
234832205^17086+17086^32205136313Hans Havermann12/2020
2349(25*10^136303+161)/3136304Robert Price09/2019
235035337^7196+7196^35337136299Hans Havermann12/2020
2351(182*10^136291+1)/3136293Robert Price02/2020
235223*10^136225-7136227Robert Price02/2020
2353L(651821)136223Henri Lifchitz09/2008
23542^452460+77701136205Enzo Doria05/2016
23552^452440-114755136199Enzo Doria04/2015
235632286^16489+16489^32286136157Hans Havermann11/2020
2357(47*10^136141+493)/9136142Robert Price03/2019
235840392^2339+2339^40392136082Hans Havermann12/2020
23592*10^136057-43136058Robert Price04/2018
2360(2^451956-5)/181136051Lelio R Paula07/2015
23612^451947-22165136050Enzo Doria07/2013
23622^451787-21805136002Enzo Doria07/2013
23632^451734-112817135986Enzo Doria06/2014
2364(11*2^451714+1)/75135979Lelio R Paula07/2015
23652^451705-21879135977Enzo Doria07/2013
23662^451560-112349135934Enzo Doria06/2014
23672^451530+45135925Lelio R Paula08/2017
236831622^19875+19875^31622135922Hans Havermann11/2020
2369(25*10^135906-73)/3135907Robert Price09/2019
23702^451450-21743135900Enzo Doria07/2013
237135218^7199+7199^35218135846Hans Havermann11/2020
237235661^6446+6446^35661135844Hans Havermann11/2020
237331869^18248+18248^31869135801Hans Havermann12/2020
23742^450805+65135706Lelio R Paula08/2017
237530761^25728+25728^30761135669Hans Havermann12/2020
23762*10^135663+69135664Robert Price06/2020
237733962^9867+9867^33962135651Hans Havermann11/2020
237834474^8605+8605^34474135647Hans Havermann11/2020
237934501^8508+8508^34501135583Hans Havermann12/2020
238035487^6614+6614^35487135577Hans Havermann12/2020
2381(13725^32768+1)/131074135573Lelio R Paula03/2012
2382(313007#+121876)/(2*30469*424867)135559Makoto Morimoto08/2020
2383(5^193939+1)/6135557Paul Bourdelais12/2008
238440387^2260+2260^40387135463Hans Havermann12/2020
23852^449944-113247135447Enzo Doria07/2014
23862^449770-113247135395Enzo Doria07/2014
23872^449637-21471135355Enzo Doria07/2013
23882^449571-75135335Lelio R Paula08/2017
2389(14*10^135301-53)/3135302Robert Price12/2018
2390(3*2^449494+1)/61340334013135301Lelio R Paula07/2015
2391(13*10^135279+437)/9135280Robert Price04/2018
23922^449330-35135262Lelio R Paula08/2017
2393(19*2^449325+1)/9135261Lelio R Paula07/2015
2394(13*10^135184-43)/3135185Robert Price11/2018
23952^449049-115309135178Enzo Doria07/2015
2396(10^135174+191)/3135174Robert Price02/2018
23972^449030-15135172Lelio R Paula08/2017
2398(27*2^448936-1)/11135144Lelio R Paula07/2015
239932221^15586+15586^32221135095Hans Havermann12/2020
24002^448762-351401135091Enzo Doria07/2015
24012*10^135083-43135084Robert Price04/2018
240231357^20278+20278^31357135056Hans Havermann12/2020
240332242^15445+15445^32242135055Hans Havermann12/2020
2404k(198476)135054Robert Price07/2020
240532461^14470+14470^32461135053Hans Havermann12/2020
240631353^20288+20288^31353135045Hans Havermann12/2020
24075*10^135019+77135020Robert Price12/2018
2408(10^135011+719)/9135011Serge Batalov12/2014
2409(197*10^134978+7)/3134980Robert Price12/2020
24102^448386-2786261134978Enzo Doria03/2016
2411(73*10^134939+143)/9134940Robert Price07/2019
241233957^9392+9392^33957134903Hans Havermann12/2020
24132^448113-113949134896Enzo Doria11/2014
241430958^22755+22755^30958134887Hans Havermann12/2020
24152^447888-2786639134828Enzo Doria03/2016
24162^447870-396765134823Enzo Doria07/2013
24172^447766-21791134791Enzo Doria07/2013
2418(19*10^134786-49)/3134787Robert Price05/2019
2419Phi(202173,10)/10064306514895399941409134758Makoto Kamada05/2019
2420(23*2^447647+1)/155134755Lelio R Paula07/2015
24212^447552-1019134727Yves Minet02/2014
2422(2*10^134720-41)/3134720Robert Price02/2018
24232^447437-113569134692Enzo Doria08/2014
24242^447426-65134689Lelio R Paula08/2017
24252^447357-2797573134668Enzo Doria04/2016
24262^447278+93134645Lelio R Paula08/2017
242733193^11370+11370^33193134623Hans Havermann12/2020
242830736^23979+23979^30736134619Hans Havermann11/2020
24292^447094-113193134589Enzo Doria07/2014
24303^282041-9934134568Enzo Doria05/2014
24312^447019-109039134567Enzo Doria04/2014
243231376^19437+19437^31376134561Hans Havermann12/2020
24332^446990-22041134558Enzo Doria07/2013
2434123^64370+122134528Karsten Bonath04/2018
243530100^29461+29461^30100134525Hans Havermann11/2020
243631251^20158+20158^31251134519Hans Havermann11/2020
24372^446782-39701134495Enzo Doria09/2015
243831817^16858+16858^31817134485Hans Havermann12/2020
243932448^13937+13937^32448134471Hans Havermann12/2020
24402^446494-16485134409Enzo Doria04/2013
244130042^29785+29785^30042134408Hans Havermann12/2020
244229504^30069-30069^29504134405Norbert Schneider12/2014
24432^446441+65134393Lelio R Paula08/2017
2444(10^134385+719)/9134385Serge Batalov12/2014
244530043^29688+29688^30043134370Hans Havermann12/2020
2446(2*10^134364+529)/9134364Robert Price01/2018
244734657^7512+7512^34657134323Hans Havermann11/2020
2448(13*2^446187-1)/661134314Lelio R Paula07/2015
24495^192103+3^192103+2^192103+1134275Matthias Baur12/2019
245042035^1564+1564^42035134270Hans Havermann12/2020
2452(2^446022-7)/339134264Lelio R Paula07/2015
245130621^24248+24248^30621134264Hans Havermann12/2020
245330341^26562+26562^30341134237Hans Havermann11/2020
245429976^29953+29953^29976134186Hans Havermann12/2020
245535038^6755+6755^35038134183Hans Havermann12/2020
245663^74568+2134174Lelio R Paula06/2017
24572^445671-22071134161Enzo Doria07/2013
2458532^49205+49205^532134129Norbert Schneider02/2019
2459(28*10^134122-1)/9134123Serge Batalov10/2014
24602^445515-113859134114Enzo Doria10/2014
2461(22*10^134111-37)/3134112Robert Price04/2019
24622^445328-216917134058Enzo Doria05/2014
24632^445202+1874899134020Enzo Doria06/2016
2464(13*2^445102+1)/17133989Lelio R Paula07/2015
2465(35*10^133979-593)/9133980Robert Price07/2018
24662*10^133955+51133956Robert Price05/2018
24672^444964-113639133948Enzo Doria08/2014
246828118^30097-30097^28118133902Norbert Schneider01/2015
246910^133902-100001133902Robert Price07/2020
24702^444784-113859133894Enzo Doria10/2014
2471(266*10^133603+1)/3133605Robert Price04/2020
2472(89*10^133580+1)/9133581Serge Batalov05/2010
247362^74521-61^74521133571Robert Price05/2013
2474(182*10^133543+1)/3133545Robert Price02/2020
2475(103*10^133535+11)/3133537Robert Price01/2021
24762^443198-1867301133416Enzo Doria03/2016
2477(19*10^133390+101)/3133391Robert Price09/2019
2478(71^72043-1)/70133369Paul Bourdelais09/2017
24792^442799+1874633133296Enzo Doria06/2016
2480L(637751)133283Henri Lifchitz09/2008
2481109^65410-2133269Lelio R Paula10/2017
24822^442688-113489133263Enzo Doria08/2014
2483(7*2^442640-1)/783133246Lelio R Paula07/2015
2484(9*2^442463+1)/17441133192Lelio R Paula07/2015
24852^442437-1849993133187Enzo Doria08/2015
24862^442430-2791721133185Enzo Doria03/2016
2487(13*2^442428-1)/309133183Lelio R Paula07/2015
2488(25*2^442379-1)/71133169Lelio R Paula07/2015
2489452^50145+50145^452133142Norbert Schneider09/2020
2490(2^441799+78557)/5132995Lelio R Paula07/2015
24912^441781-2787883132990Enzo Doria03/2016
2492(3*2^441685+1)/749132959Lelio R Paula07/2015
24932^441618+37132941Lelio R Paula08/2017
24942^441521-113575132912Enzo Doria08/2014
24957*10^132884-99132885Robert Price06/2019
2496(103*10^132879+17)/3132881Robert Price08/2020
24972^441396-65132874Lelio R Paula08/2017
24982^441330+1871959132854Enzo Doria05/2016
24992^441063+383132774Lelio R Paula06/2012
2500(22*10^132746+53)/3132747Robert Price07/2019


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!