PRP Records

Probable Primes Top 10000

(293016 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 ?
325114^119741-119741^14137239Serge Batalov04/2016
325235014^8297+8297^35014137218Hans Havermann05/2021
3253(19*2^455760+1)/3455137196Lelio R Paula07/2015
3255124^(2^16)+57^(2^16)137195Valeryi Kuryshev02/2011
3254124^65536+57^65536137195Serge Batalov03/2018
32562^455689+72677137177Enzo Doria04/2016
3257(17948!)^2+Prime(17948)137118Robert Price08/2014
325831287^24128+24128^31287137116Hans Havermann05/2021
3259(37^87421-1)/36137093Robert Price03/2012
326036233^6070+6070^36233137077Hans Havermann05/2021
3261(8*10^137073-17)/9137073Serge Batalov11/2022
326238418^3697+3697^38418137070Hans Havermann04/2021
32632^455323-57137066Lelio R Paula09/2017
3264(56*10^137019+583)/9137020Robert Price08/2021
3265(73*17^111333-9)/16136991Curtis Bright05/2015
32662^455025-112723136977Enzo Doria06/2014
326733876^11039+11039^33876136959Hans Havermann05/2021
326835142^7873+7873^35142136919Hans Havermann05/2021
326966*10^136894+7136896Robert Price07/2020
32702^454675-1777136871Yves Minet10/2011
327131676^20931+20931^31676136866Hans Havermann05/2021
32723*10^136829+29136830Robert Price05/2018
32734*10^136813-57136814Robert Price10/2018
3274(6092*28^94536-143)/9136812Curtis Bright05/2015
327537359^4588+4588^37359136795Hans Havermann05/2021
32762^454348-53136773Lelio R Paula09/2017
327731^91680-2136729Lelio R Paula05/2017
32782^454199-113697136728Enzo Doria09/2014
327930785^27622+27622^30785136725Hans Havermann05/2021
328032973^14014+14014^32973136725Hans Havermann05/2021
32827*10^136716+69136717Robert Price07/2019
328136002^6273+6273^36002136717Hans Havermann05/2021
32836*10^136692+53136693Robert Price05/2020
3284(13*10^136687+47)/3136688Robert Price10/2018
32852^453935-2791357136649Enzo Doria01/2016
32862^453906-69131136640Enzo Doria11/2015
328733232^12915+12915^33232136620Hans Havermann05/2021
32882^453791+1873913136605Enzo Doria06/2016
328934166^9951+9951^34166136592Hans Havermann05/2021
3290(21*2^453740-1)/2735136588Lelio R Paula07/2015
329131102^24635+24635^31102136587Hans Havermann05/2021
3292580^49413+49413^580136550Norbert Schneider02/2019
32932^453503-2788297136519Enzo Doria11/2015
329434989^7958+7958^34989136486Hans Havermann12/2020
3295(2*10^136484+187)/9136484Robert Price06/2022
329631007^25158+25158^31007136452Hans Havermann11/2020
32972^453267-113827136447Enzo Doria09/2014
329832234^17085+17085^32234136435Hans Havermann12/2020
32992^453102+1877629136398Enzo Doria08/2016
330031016^24981+24981^31016136397Hans Havermann12/2020
3301(62*10^136384-791)/9136385Robert Price06/2019
330234171^9798+9798^34171136382Hans Havermann12/2020
3303(17*10^136354-113)/3136355Robert Price06/2021
330432756^14541+14541^32756136350Hans Havermann11/2020
330532205^17086+17086^32205136313Hans Havermann12/2020
3306(25*10^136303+161)/3136304Robert Price09/2019
330735337^7196+7196^35337136299Hans Havermann12/2020
3308(182*10^136291+1)/3136293Robert Price02/2020
3309(88*10^136234+83)/9136235Robert Price03/2022
331023*10^136225-7136227Robert Price02/2020
3311L(651821)136223Henri Lifchitz09/2008
33122^452460+77701136205Enzo Doria05/2016
33132^452440-114755136199Enzo Doria04/2015
331432286^16489+16489^32286136157Hans Havermann11/2020
3315(47*10^136141+493)/9136142Robert Price03/2019
331640392^2339+2339^40392136082Hans Havermann12/2020
33172*10^136057-43136058Robert Price04/2018
3318(2^451956-5)/181136051Lelio R Paula07/2015
33192^451947-22165136050Enzo Doria07/2013
33202^451787-21805136002Enzo Doria07/2013
33212^451734-112817135986Enzo Doria06/2014
3322(11*2^451714+1)/75135979Lelio R Paula07/2015
33232^451705-21879135977Enzo Doria07/2013
33242^451560-112349135934Enzo Doria06/2014
33252^451530+45135925Lelio R Paula08/2017
332631622^19875+19875^31622135922Hans Havermann11/2020
3327(25*10^135906-73)/3135907Robert Price09/2019
33282^451450-21743135900Enzo Doria07/2013
3329(7*10^135879+11)/9135879Tyler Busby01/2023
333035218^7199+7199^35218135846Hans Havermann11/2020
333135661^6446+6446^35661135844Hans Havermann11/2020
333231869^18248+18248^31869135801Hans Havermann12/2020
3333(77*10^135789+157)/9135790Robert Price05/2022
33342^450805+65135706Lelio R Paula08/2017
333530761^25728+25728^30761135669Hans Havermann12/2020
33362*10^135663+69135664Robert Price06/2020
333733962^9867+9867^33962135651Hans Havermann11/2020
333834474^8605+8605^34474135647Hans Havermann11/2020
333934501^8508+8508^34501135583Hans Havermann12/2020
334035487^6614+6614^35487135577Hans Havermann12/2020
3341(13725^32768+1)/131074135573Lelio R Paula03/2012
3342(313007#+121876)/(2*30469*424867)135559Makoto Morimoto08/2020
3343(5^193939+1)/6135557Paul Bourdelais12/2008
3344(76*10^135553-49)/9135554Robert Price07/2022
3345(844*10^135527-7)/9135529Robert Price05/2021
334640387^2260+2260^40387135463Hans Havermann12/2020
33472^449944-113247135447Enzo Doria07/2014
33482^449770-113247135395Enzo Doria07/2014
33492^449637-21471135355Enzo Doria07/2013
33502^449571-75135335Lelio R Paula08/2017
3351(14*10^135301-53)/3135302Robert Price12/2018
3352(3*2^449494+1)/61340334013135301Lelio R Paula07/2015
3353(13*10^135279+437)/9135280Robert Price04/2018
33542^449330-35135262Lelio R Paula08/2017
3355(19*2^449325+1)/9135261Lelio R Paula07/2015
3356(13*10^135184-43)/3135185Robert Price11/2018
33572^449049-115309135178Enzo Doria07/2015
3358(10^135174+191)/3135174Robert Price02/2018
33592^449030-15135172Lelio R Paula08/2017
3360(157*10^135151-1)/3135153Robert Price01/2022
3361(2^448966+100280245065)135153Paul Bourdelais05/2022
3362(27*2^448936-1)/11135144Lelio R Paula07/2015
3363(37*10^135099+251)/9135100Robert Price09/2021
336432221^15586+15586^32221135095Hans Havermann12/2020
33652^448762-351401135091Enzo Doria07/2015
33662*10^135083-43135084Robert Price04/2018
336731357^20278+20278^31357135056Hans Havermann12/2020
336832242^15445+15445^32242135055Hans Havermann12/2020
3369k(198476)135054Robert Price07/2020
337032461^14470+14470^32461135053Hans Havermann12/2020
337131353^20288+20288^31353135045Hans Havermann12/2020
33725*10^135019+77135020Robert Price12/2018
3373(10^135011+719)/9135011Serge Batalov12/2014
3374(197*10^134978+7)/3134980Robert Price12/2020
33752^448386-2786261134978Enzo Doria03/2016
3376(73*10^134939+143)/9134940Robert Price07/2019
337733957^9392+9392^33957134903Hans Havermann12/2020
33782^448113-113949134896Enzo Doria11/2014
337930958^22755+22755^30958134887Hans Havermann12/2020
33802^447888-2786639134828Enzo Doria03/2016
33812^447870-396765134823Enzo Doria07/2013
33822^447766-21791134791Enzo Doria07/2013
3383(19*10^134786-49)/3134787Robert Price05/2019
3384Phi(202173,10)/10064306514895399941409134758Makoto Kamada05/2019
3385(23*2^447647+1)/155134755Lelio R Paula07/2015
33862^447552-1019134727Yves Minet02/2014
3387(2*10^134720-41)/3134720Robert Price02/2018
3388(25*10^134695-97)/9134696Robert Price01/2022
33892^447437-113569134692Enzo Doria08/2014
33902^447426-65134689Lelio R Paula08/2017
33912^447357-2797573134668Enzo Doria04/2016
33922^447278+93134645Lelio R Paula08/2017
339333193^11370+11370^33193134623Hans Havermann12/2020
339430736^23979+23979^30736134619Hans Havermann11/2020
33952^447094-113193134589Enzo Doria07/2014
33963^282041-9934134568Enzo Doria05/2014
33972^447019-109039134567Enzo Doria04/2014
339831376^19437+19437^31376134561Hans Havermann12/2020
33992^446990-22041134558Enzo Doria07/2013
3400123^64370+122134528Karsten Bonath04/2018
340130100^29461+29461^30100134525Hans Havermann11/2020
340231251^20158+20158^31251134519Hans Havermann11/2020
34032^446782-39701134495Enzo Doria09/2015
340431817^16858+16858^31817134485Hans Havermann12/2020
340532448^13937+13937^32448134471Hans Havermann12/2020
34062^446494-16485134409Enzo Doria04/2013
340730042^29785+29785^30042134408Hans Havermann12/2020
340829504^30069-30069^29504134405Norbert Schneider12/2014
34092^446441+65134393Lelio R Paula08/2017
3410(10^134385+719)/9134385Serge Batalov12/2014
341130043^29688+29688^30043134370Hans Havermann12/2020
3412(2*10^134364+529)/9134364Robert Price01/2018
341334657^7512+7512^34657134323Hans Havermann11/2020
3414(13*2^446187-1)/661134314Lelio R Paula07/2015
34155^192103+3^192103+2^192103+1134275Matthias Baur12/2019
341642035^1564+1564^42035134270Hans Havermann12/2020
3418(2^446022-7)/339134264Lelio R Paula07/2015
341730621^24248+24248^30621134264Hans Havermann12/2020
341930341^26562+26562^30341134237Hans Havermann11/2020
342010^134209+99867134210Patrick De Geest05/2021
342110^134209-80000001134209Robert Price04/2021
342210^134209-323283134209Patrick De Geest05/2021
342329976^29953+29953^29976134186Hans Havermann12/2020
342435038^6755+6755^35038134183Hans Havermann12/2020
342563^74568+2134174Lelio R Paula06/2017
34262^445671-22071134161Enzo Doria07/2013
3427532^49205+49205^532134129Norbert Schneider02/2019
342836453^4780+4780^36453134127Hans Havermann04/2021
3429(28*10^134122-1)/9134123Serge Batalov10/2014
34302^445515-113859134114Enzo Doria10/2014
3432(22*10^134111-37)/3134112Robert Price04/2019
343131083^20636+20636^31083134112Hans Havermann04/2021
343331622^17379+17379^31622134079Hans Havermann04/2021
3434(277*10^134059-7)/9134061Robert Price02/2022
34352^445328-216917134058Enzo Doria05/2014
34362^445202+1874899134020Enzo Doria06/2016
3437(35*10^134003-89)/9134004Robert Price02/2022
3438(13*2^445102+1)/17133989Lelio R Paula07/2015
3439(35*10^133979-593)/9133980Robert Price07/2018
34402*10^133955+51133956Robert Price05/2018
3441(49*10^133952+437)/9133953Robert Price09/2021
34422^444964-113639133948Enzo Doria08/2014
344331811^16240+16240^31811133943Hans Havermann04/2021
344410^133902+167841133903Patrick De Geest05/2021
344628118^30097-30097^28118133902Norbert Schneider01/2015
344510^133902-100001133902Robert Price07/2020
34472^444784-113859133894Enzo Doria10/2014
344832303^13914+13914^32303133846Hans Havermann04/2021
3449(2276213*2^444444+1)/3133797Alex_soldier11/2022
3450(1403559*2^444444+1)/5133797Alex_soldier11/2022
3451(1209887*2^444444+1)/9133797Alex_soldier11/2022
3452(608239*2^444444+1)/25133796Alex_soldier11/2022
3453(1824587*2^444444+1)/27133796Alex_soldier11/2022
3454(40795*2^444444+1)/7133795Alex_soldier11/2022
345530739^22458+22458^30739133757Hans Havermann04/2021
345634942^6721+6721^34942133739Hans Havermann04/2021
3457(2^444046+100280245065)133672Paul Bourdelais05/2022
345834792^6935+6935^34792133638Hans Havermann04/2021
3459(266*10^133603+1)/3133605Robert Price04/2020
346032261^13842+13842^32261133600Hans Havermann04/2021
3461(89*10^133580+1)/9133581Serge Batalov05/2010
3462(134*10^133573-11)/3133575Robert Price01/2022
346362^74521-61^74521133571Robert Price05/2013
3464(182*10^133543+1)/3133545Robert Price02/2020
3465(103*10^133535+11)/3133537Robert Price01/2021
346632589^12520+12520^32589133537Hans Havermann03/2021
346734516^7373+7373^34516133496Hans Havermann04/2021
34688*10^133487-37133488Robert Price03/2022
346930135^26882+26882^30135133482Hans Havermann04/2021
34702^443198-1867301133416Enzo Doria03/2016
3471(19*10^133390+101)/3133391Robert Price09/2019
3472(71^72043-1)/70133369Paul Bourdelais09/2017
347336117^4910+4910^36117133311Hans Havermann04/2021
34742^442799+1874633133296Enzo Doria06/2016
3475L(637751)133283Henri Lifchitz09/2008
3476109^65410-2133269Lelio R Paula10/2017
34772^442688-113489133263Enzo Doria08/2014
3478(7*2^442640-1)/783133246Lelio R Paula07/2015
3479(9*2^442463+1)/17441133192Lelio R Paula07/2015
34802^442437-1849993133187Enzo Doria08/2015
34812^442430-2791721133185Enzo Doria03/2016
3482(13*2^442428-1)/309133183Lelio R Paula07/2015
348329959^27870+27870^29959133172Hans Havermann03/2021
3484(25*2^442379-1)/71133169Lelio R Paula07/2015
348534240^7737+7737^34240133145Hans Havermann03/2021
3486452^50145+50145^452133142Norbert Schneider09/2020
348730659^21796+21796^30659133011Hans Havermann04/2021
348833276^9935+9935^33276133010Hans Havermann04/2021
348930111^26122+26122^30111133001Hans Havermann04/2021
349030790^20869+20869^30790132998Hans Havermann04/2021
3492(2^441799+78557)/5132995Lelio R Paula07/2015
34918*10^132994-27132995Robert Price10/2021
3493(109*10^132992+11)/3132994Robert Price06/2022
34942^441781-2787883132990Enzo Doria03/2016
3495(3*2^441685+1)/749132959Lelio R Paula07/2015
34962^441618+37132941Lelio R Paula08/2017
349734857^6514+6514^34857132940Hans Havermann04/2021
349834065^7988+7988^34065132937Hans Havermann04/2021
349935571^5452+5452^35571132914Hans Havermann04/2021
35002^441521-113575132912Enzo Doria08/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: June, 04 2023 08:38 (Time in France)

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