PRP Records

Probable Primes Top 10000

(288949 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 ?
27512^460078-69581138498Enzo Doria12/2015
275237384^5065+5065^37384138492Hans Havermann05/2021
275334774^9585+9585^34774138456Hans Havermann05/2021
275410^138444-5001138444Robert Price12/2021
27552^459768+1531138404Lelio R Paula06/2012
2756(266*10^138328-17)/3138330Robert Price07/2020
275732963^15696+15696^32963138306Hans Havermann05/2021
27582^459343-113611138277Enzo Doria08/2014
2759(28*10^138240+113)/3138241Robert Price03/2020
27602^459199+1874393138233Enzo Doria06/2016
276133339^14002+14002^33339138230Hans Havermann05/2021
27622^459063-345307138192Enzo Doria06/2015
27632*10^138162-43138163Robert Price04/2018
27642^458927-112747138151Enzo Doria06/2014
27652^458927-69217138151Enzo Doria11/2015
276630907^29458+29458^30907138130Hans Havermann05/2021
276732882^15837+15837^32882138094Hans Havermann05/2021
276839252^3295+3295^39252138083Hans Havermann05/2021
276933789^12190+12190^33789138062Hans Havermann06/2021
2770555555*2^458524+1513138036Darren Bedwell08/2009
277130931^29002+29002^30931138028Hans Havermann05/2021
27722^458465+2^32+1138012T. D. Noe06/2007
277332206^19275+19275^32206138003Hans Havermann05/2021
27742^458321-113053137969Enzo Doria07/2014
27752^458298+79459137962Enzo Doria06/2016
27762^458248-21815137947Enzo Doria07/2013
27772^458194+1876549137931Enzo Doria07/2016
2778(318259#+325270)/(2^2*5*11*2957)137907Makoto Morimoto10/2017
2779(318259#+2625)/(3^2*5*7^5*22965193)137899Makoto Morimoto06/2019
27802^457937+57137853Lelio R Paula09/2017
2781(8*10^137845+13)/3137846Robert Price06/2018
27822^457822+105137819Donovan Johnson06/2006
27832^457754-113711137798Enzo Doria09/2014
278411^132315-360137792Enzo Doria09/2012
278532072^19689+19689^32072137725Hans Havermann06/2021
278644592^1225+1225^44592137707Hans Havermann05/2021
27872^457347-37137676Lelio R Paula09/2017
27882^457322-2786393137668Enzo Doria10/2015
2789gcd(Phi(699340,10),(10^34967+1)^3*(10^34967+1+10^17484)-(10^69934+10^34967)*(10^17484-1)+10^104901)137664Serge Batalov04/2015
279034015^11134+11134^34015137647Hans Havermann06/2021
27912^457240-59939137643Enzo Doria10/2015
2792(856*10^137633-1)/9137635Robert Price03/2020
279336232^6289+6289^36232137631Hans Havermann05/2021
27942^457120-21575137607Enzo Doria07/2013
2796(11*2^456978+1)/15137564Lelio R Paula07/2015
279530963^27722+27722^30963137564Hans Havermann04/2021
279733722^12003+12003^33722137562Hans Havermann06/2021
2798(7*25^98399+10613)/12137556Curtis Bright05/2015
279941901^1918+1918^41901137555Hans Havermann06/2021
280032930^15021+15021^32930137539Hans Havermann05/2021
280131178^25785+25785^31178137538Hans Havermann05/2021
2802419^52446+52446^419137525Norbert Schneider11/2020
28032^456796-113513137510Enzo Doria08/2014
280431788^21137+21137^31788137485Hans Havermann04/2021
2805(7*2^456655+1)/39137467Lelio R Paula07/2015
28062^456503-114361137422Enzo Doria01/2015
2807(11*2^456387+1)/19137386Lelio R Paula07/2015
280836248^6147+6147^36248137332Hans Havermann05/2021
280931986^19651+19651^31986137329Hans Havermann05/2021
281031817^20656+20656^31817137292Hans Havermann05/2021
2811(71*10^137250+1)/9137251Serge Batalov05/2010
28122^455922+76249137247Enzo Doria05/2016
281331310^24171+24171^31310137241Hans Havermann05/2021
281414^119741-119741^14137239Serge Batalov04/2016
281535014^8297+8297^35014137218Hans Havermann05/2021
2816(19*2^455760+1)/3455137196Lelio R Paula07/2015
2818124^(2^16)+57^(2^16)137195Valeryi Kuryshev02/2011
2817124^65536+57^65536137195Serge Batalov03/2018
28192^455689+72677137177Enzo Doria04/2016
2820(17948!)^2+Prime(17948)137118Robert Price08/2014
282131287^24128+24128^31287137116Hans Havermann05/2021
2822(37^87421-1)/36137093Robert Price03/2012
282336233^6070+6070^36233137077Hans Havermann05/2021
282438418^3697+3697^38418137070Hans Havermann04/2021
28252^455323-57137066Lelio R Paula09/2017
2826(56*10^137019+583)/9137020Robert Price08/2021
2827(73*17^111333-9)/16136991Curtis Bright05/2015
28282^455025-112723136977Enzo Doria06/2014
282933876^11039+11039^33876136959Hans Havermann05/2021
283035142^7873+7873^35142136919Hans Havermann05/2021
283166*10^136894+7136896Robert Price07/2020
28322^454675-1777136871Yves Minet10/2011
283331676^20931+20931^31676136866Hans Havermann05/2021
28343*10^136829+29136830Robert Price05/2018
28354*10^136813-57136814Robert Price10/2018
2836(6092*28^94536-143)/9136812Curtis Bright05/2015
283737359^4588+4588^37359136795Hans Havermann05/2021
28382^454348-53136773Lelio R Paula09/2017
283931^91680-2136729Lelio R Paula05/2017
28402^454199-113697136728Enzo Doria09/2014
284130785^27622+27622^30785136725Hans Havermann05/2021
284232973^14014+14014^32973136725Hans Havermann05/2021
28447*10^136716+69136717Robert Price07/2019
284336002^6273+6273^36002136717Hans Havermann05/2021
28456*10^136692+53136693Robert Price05/2020
2846(13*10^136687+47)/3136688Robert Price10/2018
28472^453935-2791357136649Enzo Doria01/2016
28482^453906-69131136640Enzo Doria11/2015
284933232^12915+12915^33232136620Hans Havermann05/2021
28502^453791+1873913136605Enzo Doria06/2016
285134166^9951+9951^34166136592Hans Havermann05/2021
2852(21*2^453740-1)/2735136588Lelio R Paula07/2015
285331102^24635+24635^31102136587Hans Havermann05/2021
2854580^49413+49413^580136550Norbert Schneider02/2019
28552^453503-2788297136519Enzo Doria11/2015
285634989^7958+7958^34989136486Hans Havermann12/2020
285731007^25158+25158^31007136452Hans Havermann11/2020
28582^453267-113827136447Enzo Doria09/2014
285932234^17085+17085^32234136435Hans Havermann12/2020
28602^453102+1877629136398Enzo Doria08/2016
286131016^24981+24981^31016136397Hans Havermann12/2020
2862(62*10^136384-791)/9136385Robert Price06/2019
286334171^9798+9798^34171136382Hans Havermann12/2020
2864(17*10^136354-113)/3136355Robert Price06/2021
286532756^14541+14541^32756136350Hans Havermann11/2020
286632205^17086+17086^32205136313Hans Havermann12/2020
2867(25*10^136303+161)/3136304Robert Price09/2019
286835337^7196+7196^35337136299Hans Havermann12/2020
2869(182*10^136291+1)/3136293Robert Price02/2020
287023*10^136225-7136227Robert Price02/2020
2871L(651821)136223Henri Lifchitz09/2008
28722^452460+77701136205Enzo Doria05/2016
28732^452440-114755136199Enzo Doria04/2015
287432286^16489+16489^32286136157Hans Havermann11/2020
2875(47*10^136141+493)/9136142Robert Price03/2019
287640392^2339+2339^40392136082Hans Havermann12/2020
28772*10^136057-43136058Robert Price04/2018
2878(2^451956-5)/181136051Lelio R Paula07/2015
28792^451947-22165136050Enzo Doria07/2013
28802^451787-21805136002Enzo Doria07/2013
28812^451734-112817135986Enzo Doria06/2014
2882(11*2^451714+1)/75135979Lelio R Paula07/2015
28832^451705-21879135977Enzo Doria07/2013
28842^451560-112349135934Enzo Doria06/2014
28852^451530+45135925Lelio R Paula08/2017
288631622^19875+19875^31622135922Hans Havermann11/2020
2887(25*10^135906-73)/3135907Robert Price09/2019
28882^451450-21743135900Enzo Doria07/2013
288935218^7199+7199^35218135846Hans Havermann11/2020
289035661^6446+6446^35661135844Hans Havermann11/2020
289131869^18248+18248^31869135801Hans Havermann12/2020
28922^450805+65135706Lelio R Paula08/2017
289330761^25728+25728^30761135669Hans Havermann12/2020
28942*10^135663+69135664Robert Price06/2020
289533962^9867+9867^33962135651Hans Havermann11/2020
289634474^8605+8605^34474135647Hans Havermann11/2020
289734501^8508+8508^34501135583Hans Havermann12/2020
289835487^6614+6614^35487135577Hans Havermann12/2020
2899(13725^32768+1)/131074135573Lelio R Paula03/2012
2900(313007#+121876)/(2*30469*424867)135559Makoto Morimoto08/2020
2901(5^193939+1)/6135557Paul Bourdelais12/2008
2902(844*10^135527-7)/9135529Robert Price05/2021
290340387^2260+2260^40387135463Hans Havermann12/2020
29042^449944-113247135447Enzo Doria07/2014
29052^449770-113247135395Enzo Doria07/2014
29062^449637-21471135355Enzo Doria07/2013
29072^449571-75135335Lelio R Paula08/2017
2908(14*10^135301-53)/3135302Robert Price12/2018
2909(3*2^449494+1)/61340334013135301Lelio R Paula07/2015
2910(13*10^135279+437)/9135280Robert Price04/2018
29112^449330-35135262Lelio R Paula08/2017
2912(19*2^449325+1)/9135261Lelio R Paula07/2015
2913(13*10^135184-43)/3135185Robert Price11/2018
29142^449049-115309135178Enzo Doria07/2015
2915(10^135174+191)/3135174Robert Price02/2018
29162^449030-15135172Lelio R Paula08/2017
2917(27*2^448936-1)/11135144Lelio R Paula07/2015
2918(37*10^135099+251)/9135100Robert Price09/2021
291932221^15586+15586^32221135095Hans Havermann12/2020
29202^448762-351401135091Enzo Doria07/2015
29212*10^135083-43135084Robert Price04/2018
292231357^20278+20278^31357135056Hans Havermann12/2020
292332242^15445+15445^32242135055Hans Havermann12/2020
2924k(198476)135054Robert Price07/2020
292532461^14470+14470^32461135053Hans Havermann12/2020
292631353^20288+20288^31353135045Hans Havermann12/2020
29275*10^135019+77135020Robert Price12/2018
2928(10^135011+719)/9135011Serge Batalov12/2014
2929(197*10^134978+7)/3134980Robert Price12/2020
29302^448386-2786261134978Enzo Doria03/2016
2931(73*10^134939+143)/9134940Robert Price07/2019
293233957^9392+9392^33957134903Hans Havermann12/2020
29332^448113-113949134896Enzo Doria11/2014
293430958^22755+22755^30958134887Hans Havermann12/2020
29352^447888-2786639134828Enzo Doria03/2016
29362^447870-396765134823Enzo Doria07/2013
29372^447766-21791134791Enzo Doria07/2013
2938(19*10^134786-49)/3134787Robert Price05/2019
2939Phi(202173,10)/10064306514895399941409134758Makoto Kamada05/2019
2940(23*2^447647+1)/155134755Lelio R Paula07/2015
29412^447552-1019134727Yves Minet02/2014
2942(2*10^134720-41)/3134720Robert Price02/2018
2943(25*10^134695-97)/9134696Robert Price01/2022
29442^447437-113569134692Enzo Doria08/2014
29452^447426-65134689Lelio R Paula08/2017
29462^447357-2797573134668Enzo Doria04/2016
29472^447278+93134645Lelio R Paula08/2017
294833193^11370+11370^33193134623Hans Havermann12/2020
294930736^23979+23979^30736134619Hans Havermann11/2020
29502^447094-113193134589Enzo Doria07/2014
29513^282041-9934134568Enzo Doria05/2014
29522^447019-109039134567Enzo Doria04/2014
295331376^19437+19437^31376134561Hans Havermann12/2020
29542^446990-22041134558Enzo Doria07/2013
2955123^64370+122134528Karsten Bonath04/2018
295630100^29461+29461^30100134525Hans Havermann11/2020
295731251^20158+20158^31251134519Hans Havermann11/2020
29582^446782-39701134495Enzo Doria09/2015
295931817^16858+16858^31817134485Hans Havermann12/2020
296032448^13937+13937^32448134471Hans Havermann12/2020
29612^446494-16485134409Enzo Doria04/2013
296230042^29785+29785^30042134408Hans Havermann12/2020
296329504^30069-30069^29504134405Norbert Schneider12/2014
29642^446441+65134393Lelio R Paula08/2017
2965(10^134385+719)/9134385Serge Batalov12/2014
296630043^29688+29688^30043134370Hans Havermann12/2020
2967(2*10^134364+529)/9134364Robert Price01/2018
296834657^7512+7512^34657134323Hans Havermann11/2020
2969(13*2^446187-1)/661134314Lelio R Paula07/2015
29705^192103+3^192103+2^192103+1134275Matthias Baur12/2019
297142035^1564+1564^42035134270Hans Havermann12/2020
2973(2^446022-7)/339134264Lelio R Paula07/2015
297230621^24248+24248^30621134264Hans Havermann12/2020
297430341^26562+26562^30341134237Hans Havermann11/2020
297510^134209+99867134210Patrick De Geest05/2021
297610^134209-80000001134209Robert Price04/2021
297710^134209-323283134209Patrick De Geest05/2021
297829976^29953+29953^29976134186Hans Havermann12/2020
297935038^6755+6755^35038134183Hans Havermann12/2020
298063^74568+2134174Lelio R Paula06/2017
29812^445671-22071134161Enzo Doria07/2013
2982532^49205+49205^532134129Norbert Schneider02/2019
298336453^4780+4780^36453134127Hans Havermann04/2021
2984(28*10^134122-1)/9134123Serge Batalov10/2014
29852^445515-113859134114Enzo Doria10/2014
2987(22*10^134111-37)/3134112Robert Price04/2019
298631083^20636+20636^31083134112Hans Havermann04/2021
298831622^17379+17379^31622134079Hans Havermann04/2021
29892^445328-216917134058Enzo Doria05/2014
29902^445202+1874899134020Enzo Doria06/2016
2991(13*2^445102+1)/17133989Lelio R Paula07/2015
2992(35*10^133979-593)/9133980Robert Price07/2018
29932*10^133955+51133956Robert Price05/2018
2994(49*10^133952+437)/9133953Robert Price09/2021
29952^444964-113639133948Enzo Doria08/2014
299631811^16240+16240^31811133943Hans Havermann04/2021
299710^133902+167841133903Patrick De Geest05/2021
299928118^30097-30097^28118133902Norbert Schneider01/2015
299810^133902-100001133902Robert Price07/2020
30002^444784-113859133894Enzo Doria10/2014


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 19 2022 17:15 (Time in France)

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