PRP Records

Probable Primes Top 10000

(291192 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 ?
300134015^11134+11134^34015137647Hans Havermann06/2021
30022^457240-59939137643Enzo Doria10/2015
3003(856*10^137633-1)/9137635Robert Price03/2020
300436232^6289+6289^36232137631Hans Havermann05/2021
30052^457120-21575137607Enzo Doria07/2013
3007(11*2^456978+1)/15137564Lelio R Paula07/2015
300630963^27722+27722^30963137564Hans Havermann04/2021
300833722^12003+12003^33722137562Hans Havermann06/2021
3009(7*25^98399+10613)/12137556Curtis Bright05/2015
301041901^1918+1918^41901137555Hans Havermann06/2021
3011(7*10^137551-1)/3137552Robert Price08/2022
301232930^15021+15021^32930137539Hans Havermann05/2021
301331178^25785+25785^31178137538Hans Havermann05/2021
3014419^52446+52446^419137525Norbert Schneider11/2020
30152^456796-113513137510Enzo Doria08/2014
301631788^21137+21137^31788137485Hans Havermann04/2021
3017(7*2^456655+1)/39137467Lelio R Paula07/2015
30182^456503-114361137422Enzo Doria01/2015
3019(11*2^456387+1)/19137386Lelio R Paula07/2015
302036248^6147+6147^36248137332Hans Havermann05/2021
302131986^19651+19651^31986137329Hans Havermann05/2021
302231817^20656+20656^31817137292Hans Havermann05/2021
3023(71*10^137250+1)/9137251Serge Batalov05/2010
30242^455922+76249137247Enzo Doria05/2016
302531310^24171+24171^31310137241Hans Havermann05/2021
302614^119741-119741^14137239Serge Batalov04/2016
302735014^8297+8297^35014137218Hans Havermann05/2021
3028(19*2^455760+1)/3455137196Lelio R Paula07/2015
3030124^(2^16)+57^(2^16)137195Valeryi Kuryshev02/2011
3029124^65536+57^65536137195Serge Batalov03/2018
30312^455689+72677137177Enzo Doria04/2016
3032(17948!)^2+Prime(17948)137118Robert Price08/2014
303331287^24128+24128^31287137116Hans Havermann05/2021
3034(37^87421-1)/36137093Robert Price03/2012
303536233^6070+6070^36233137077Hans Havermann05/2021
303638418^3697+3697^38418137070Hans Havermann04/2021
30372^455323-57137066Lelio R Paula09/2017
3038(56*10^137019+583)/9137020Robert Price08/2021
3039(73*17^111333-9)/16136991Curtis Bright05/2015
30402^455025-112723136977Enzo Doria06/2014
304133876^11039+11039^33876136959Hans Havermann05/2021
304235142^7873+7873^35142136919Hans Havermann05/2021
304366*10^136894+7136896Robert Price07/2020
30442^454675-1777136871Yves Minet10/2011
304531676^20931+20931^31676136866Hans Havermann05/2021
30463*10^136829+29136830Robert Price05/2018
30474*10^136813-57136814Robert Price10/2018
3048(6092*28^94536-143)/9136812Curtis Bright05/2015
304937359^4588+4588^37359136795Hans Havermann05/2021
30502^454348-53136773Lelio R Paula09/2017
305131^91680-2136729Lelio R Paula05/2017
30522^454199-113697136728Enzo Doria09/2014
305330785^27622+27622^30785136725Hans Havermann05/2021
305432973^14014+14014^32973136725Hans Havermann05/2021
30567*10^136716+69136717Robert Price07/2019
305536002^6273+6273^36002136717Hans Havermann05/2021
30576*10^136692+53136693Robert Price05/2020
3058(13*10^136687+47)/3136688Robert Price10/2018
30592^453935-2791357136649Enzo Doria01/2016
30602^453906-69131136640Enzo Doria11/2015
306133232^12915+12915^33232136620Hans Havermann05/2021
30622^453791+1873913136605Enzo Doria06/2016
306334166^9951+9951^34166136592Hans Havermann05/2021
3064(21*2^453740-1)/2735136588Lelio R Paula07/2015
306531102^24635+24635^31102136587Hans Havermann05/2021
3066580^49413+49413^580136550Norbert Schneider02/2019
30672^453503-2788297136519Enzo Doria11/2015
306834989^7958+7958^34989136486Hans Havermann12/2020
3069(2*10^136484+187)/9136484Robert Price06/2022
307031007^25158+25158^31007136452Hans Havermann11/2020
30712^453267-113827136447Enzo Doria09/2014
307232234^17085+17085^32234136435Hans Havermann12/2020
30732^453102+1877629136398Enzo Doria08/2016
307431016^24981+24981^31016136397Hans Havermann12/2020
3075(62*10^136384-791)/9136385Robert Price06/2019
307634171^9798+9798^34171136382Hans Havermann12/2020
3077(17*10^136354-113)/3136355Robert Price06/2021
307832756^14541+14541^32756136350Hans Havermann11/2020
307932205^17086+17086^32205136313Hans Havermann12/2020
3080(25*10^136303+161)/3136304Robert Price09/2019
308135337^7196+7196^35337136299Hans Havermann12/2020
3082(182*10^136291+1)/3136293Robert Price02/2020
3083(88*10^136234+83)/9136235Robert Price03/2022
308423*10^136225-7136227Robert Price02/2020
3085L(651821)136223Henri Lifchitz09/2008
30862^452460+77701136205Enzo Doria05/2016
30872^452440-114755136199Enzo Doria04/2015
308832286^16489+16489^32286136157Hans Havermann11/2020
3089(47*10^136141+493)/9136142Robert Price03/2019
309040392^2339+2339^40392136082Hans Havermann12/2020
30912*10^136057-43136058Robert Price04/2018
3092(2^451956-5)/181136051Lelio R Paula07/2015
30932^451947-22165136050Enzo Doria07/2013
30942^451787-21805136002Enzo Doria07/2013
30952^451734-112817135986Enzo Doria06/2014
3096(11*2^451714+1)/75135979Lelio R Paula07/2015
30972^451705-21879135977Enzo Doria07/2013
30982^451560-112349135934Enzo Doria06/2014
30992^451530+45135925Lelio R Paula08/2017
310031622^19875+19875^31622135922Hans Havermann11/2020
3101(25*10^135906-73)/3135907Robert Price09/2019
31022^451450-21743135900Enzo Doria07/2013
310335218^7199+7199^35218135846Hans Havermann11/2020
310435661^6446+6446^35661135844Hans Havermann11/2020
310531869^18248+18248^31869135801Hans Havermann12/2020
3106(77*10^135789+157)/9135790Robert Price05/2022
31072^450805+65135706Lelio R Paula08/2017
310830761^25728+25728^30761135669Hans Havermann12/2020
31092*10^135663+69135664Robert Price06/2020
311033962^9867+9867^33962135651Hans Havermann11/2020
311134474^8605+8605^34474135647Hans Havermann11/2020
311234501^8508+8508^34501135583Hans Havermann12/2020
311335487^6614+6614^35487135577Hans Havermann12/2020
3114(13725^32768+1)/131074135573Lelio R Paula03/2012
3115(313007#+121876)/(2*30469*424867)135559Makoto Morimoto08/2020
3116(5^193939+1)/6135557Paul Bourdelais12/2008
3117(76*10^135553-49)/9135554Robert Price07/2022
3118(844*10^135527-7)/9135529Robert Price05/2021
311940387^2260+2260^40387135463Hans Havermann12/2020
31202^449944-113247135447Enzo Doria07/2014
31212^449770-113247135395Enzo Doria07/2014
31222^449637-21471135355Enzo Doria07/2013
31232^449571-75135335Lelio R Paula08/2017
3124(14*10^135301-53)/3135302Robert Price12/2018
3125(3*2^449494+1)/61340334013135301Lelio R Paula07/2015
3126(13*10^135279+437)/9135280Robert Price04/2018
31272^449330-35135262Lelio R Paula08/2017
3128(19*2^449325+1)/9135261Lelio R Paula07/2015
3129(13*10^135184-43)/3135185Robert Price11/2018
31302^449049-115309135178Enzo Doria07/2015
3131(10^135174+191)/3135174Robert Price02/2018
31322^449030-15135172Lelio R Paula08/2017
3133(157*10^135151-1)/3135153Robert Price01/2022
3134(2^448966+100280245065)135153Paul Bourdelais05/2022
3135(27*2^448936-1)/11135144Lelio R Paula07/2015
3136(37*10^135099+251)/9135100Robert Price09/2021
313732221^15586+15586^32221135095Hans Havermann12/2020
31382^448762-351401135091Enzo Doria07/2015
31392*10^135083-43135084Robert Price04/2018
314031357^20278+20278^31357135056Hans Havermann12/2020
314132242^15445+15445^32242135055Hans Havermann12/2020
3142k(198476)135054Robert Price07/2020
314332461^14470+14470^32461135053Hans Havermann12/2020
314431353^20288+20288^31353135045Hans Havermann12/2020
31455*10^135019+77135020Robert Price12/2018
3146(10^135011+719)/9135011Serge Batalov12/2014
3147(197*10^134978+7)/3134980Robert Price12/2020
31482^448386-2786261134978Enzo Doria03/2016
3149(73*10^134939+143)/9134940Robert Price07/2019
315033957^9392+9392^33957134903Hans Havermann12/2020
31512^448113-113949134896Enzo Doria11/2014
315230958^22755+22755^30958134887Hans Havermann12/2020
31532^447888-2786639134828Enzo Doria03/2016
31542^447870-396765134823Enzo Doria07/2013
31552^447766-21791134791Enzo Doria07/2013
3156(19*10^134786-49)/3134787Robert Price05/2019
3157Phi(202173,10)/10064306514895399941409134758Makoto Kamada05/2019
3158(23*2^447647+1)/155134755Lelio R Paula07/2015
31592^447552-1019134727Yves Minet02/2014
3160(2*10^134720-41)/3134720Robert Price02/2018
3161(25*10^134695-97)/9134696Robert Price01/2022
31622^447437-113569134692Enzo Doria08/2014
31632^447426-65134689Lelio R Paula08/2017
31642^447357-2797573134668Enzo Doria04/2016
31652^447278+93134645Lelio R Paula08/2017
316633193^11370+11370^33193134623Hans Havermann12/2020
316730736^23979+23979^30736134619Hans Havermann11/2020
31682^447094-113193134589Enzo Doria07/2014
31693^282041-9934134568Enzo Doria05/2014
31702^447019-109039134567Enzo Doria04/2014
317131376^19437+19437^31376134561Hans Havermann12/2020
31722^446990-22041134558Enzo Doria07/2013
3173123^64370+122134528Karsten Bonath04/2018
317430100^29461+29461^30100134525Hans Havermann11/2020
317531251^20158+20158^31251134519Hans Havermann11/2020
31762^446782-39701134495Enzo Doria09/2015
317731817^16858+16858^31817134485Hans Havermann12/2020
317832448^13937+13937^32448134471Hans Havermann12/2020
31792^446494-16485134409Enzo Doria04/2013
318030042^29785+29785^30042134408Hans Havermann12/2020
318129504^30069-30069^29504134405Norbert Schneider12/2014
31822^446441+65134393Lelio R Paula08/2017
3183(10^134385+719)/9134385Serge Batalov12/2014
318430043^29688+29688^30043134370Hans Havermann12/2020
3185(2*10^134364+529)/9134364Robert Price01/2018
318634657^7512+7512^34657134323Hans Havermann11/2020
3187(13*2^446187-1)/661134314Lelio R Paula07/2015
31885^192103+3^192103+2^192103+1134275Matthias Baur12/2019
318942035^1564+1564^42035134270Hans Havermann12/2020
3191(2^446022-7)/339134264Lelio R Paula07/2015
319030621^24248+24248^30621134264Hans Havermann12/2020
319230341^26562+26562^30341134237Hans Havermann11/2020
319310^134209+99867134210Patrick De Geest05/2021
319410^134209-80000001134209Robert Price04/2021
319510^134209-323283134209Patrick De Geest05/2021
319629976^29953+29953^29976134186Hans Havermann12/2020
319735038^6755+6755^35038134183Hans Havermann12/2020
319863^74568+2134174Lelio R Paula06/2017
31992^445671-22071134161Enzo Doria07/2013
3200532^49205+49205^532134129Norbert Schneider02/2019
320136453^4780+4780^36453134127Hans Havermann04/2021
3202(28*10^134122-1)/9134123Serge Batalov10/2014
32032^445515-113859134114Enzo Doria10/2014
3205(22*10^134111-37)/3134112Robert Price04/2019
320431083^20636+20636^31083134112Hans Havermann04/2021
320631622^17379+17379^31622134079Hans Havermann04/2021
3207(277*10^134059-7)/9134061Robert Price02/2022
32082^445328-216917134058Enzo Doria05/2014
32092^445202+1874899134020Enzo Doria06/2016
3210(35*10^134003-89)/9134004Robert Price02/2022
3211(13*2^445102+1)/17133989Lelio R Paula07/2015
3212(35*10^133979-593)/9133980Robert Price07/2018
32132*10^133955+51133956Robert Price05/2018
3214(49*10^133952+437)/9133953Robert Price09/2021
32152^444964-113639133948Enzo Doria08/2014
321631811^16240+16240^31811133943Hans Havermann04/2021
321710^133902+167841133903Patrick De Geest05/2021
321928118^30097-30097^28118133902Norbert Schneider01/2015
321810^133902-100001133902Robert Price07/2020
32202^444784-113859133894Enzo Doria10/2014
322132303^13914+13914^32303133846Hans Havermann04/2021
322230739^22458+22458^30739133757Hans Havermann04/2021
322334942^6721+6721^34942133739Hans Havermann04/2021
3224(2^444046+100280245065)133672Paul Bourdelais05/2022
322534792^6935+6935^34792133638Hans Havermann04/2021
3226(266*10^133603+1)/3133605Robert Price04/2020
322732261^13842+13842^32261133600Hans Havermann04/2021
3228(89*10^133580+1)/9133581Serge Batalov05/2010
3229(134*10^133573-11)/3133575Robert Price01/2022
323062^74521-61^74521133571Robert Price05/2013
3231(182*10^133543+1)/3133545Robert Price02/2020
3232(103*10^133535+11)/3133537Robert Price01/2021
323332589^12520+12520^32589133537Hans Havermann03/2021
323434516^7373+7373^34516133496Hans Havermann04/2021
32358*10^133487-37133488Robert Price03/2022
323630135^26882+26882^30135133482Hans Havermann04/2021
32372^443198-1867301133416Enzo Doria03/2016
3238(19*10^133390+101)/3133391Robert Price09/2019
3239(71^72043-1)/70133369Paul Bourdelais09/2017
324036117^4910+4910^36117133311Hans Havermann04/2021
32412^442799+1874633133296Enzo Doria06/2016
3242L(637751)133283Henri Lifchitz09/2008
3243109^65410-2133269Lelio R Paula10/2017
32442^442688-113489133263Enzo Doria08/2014
3245(7*2^442640-1)/783133246Lelio R Paula07/2015
3246(9*2^442463+1)/17441133192Lelio R Paula07/2015
32472^442437-1849993133187Enzo Doria08/2015
32482^442430-2791721133185Enzo Doria03/2016
3249(13*2^442428-1)/309133183Lelio R Paula07/2015
325029959^27870+27870^29959133172Hans Havermann03/2021


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 22 2022 18:03 (Time in France)

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