PRP Records

Probable Primes Top 10000

(294613 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 ?
37512^464642+22189139872Enzo Doria09/2023
3752(16^116139+619)/5139845Anonymous08/2022
3753(2^464556+619)/5139845Eric Chen10/2023
37544*10^139839-27139840Robert Price08/2021
375533582^14573+14573^33582139821Hans Havermann05/2021
3756(17^113621+1)/18139804Paul Bourdelais09/2011
37582*10^139800-21139801Robert Price09/2020
375732628^19261+19261^32628139801Hans Havermann04/2021
3759(13*10^139782+191)/3139783Robert Price11/2018
3760(64*10^139776+791)/9139777Robert Price01/2022
3761(695*10^139772+7)/9139774Robert Price12/2021
3762(19*2^464312-1)/3139773Lelio R Paula08/2015
3763(74*10^139723+133)/9139724Robert Price06/2019
37643*10^139722+13139723Robert Price07/2018
376531577^26592+26592^31577139721Hans Havermann05/2021
376677*10^139692+3139694Robert Price06/2020
3767(31*2^463970+1)/5139670Lelio R Paula08/2015
3768(18203^(2^15)+(18201)^(2^15))/2139597Robert Price05/2018
376939640^3321+3321^39640139584Hans Havermann05/2021
377036663^6410+6410^36663139571Hans Havermann05/2021
37712^463633-2788423139568Enzo Doria11/2015
377233659^13978+13978^33659139532Hans Havermann05/2021
377331811^24318+24318^31811139521Hans Havermann04/2021
377434149^12172+12172^34149139512Hans Havermann04/2021
3775(29*10^139476+313)/9139477Robert Price04/2021
377631721^24940+24940^31721139474Hans Havermann05/2021
377732833^17698+17698^32833139473Hans Havermann05/2021
37782^463271-109501139459Enzo Doria04/2014
3779(5*10^139457+79)/3139458Robert Price03/2018
37802^463237-99139449Lelio R Paula09/2017
3781(49*10^139442+383)/9139443Robert Price04/2019
378231155^29902+29902^31155139441Hans Havermann05/2021
3783(7*10^139417-547)/9139417Robert Price01/2018
3784(10^139398+191)/3139398Robert Price02/2018
378523*10^139386-3139388Robert Price10/2021
37862^463019+79463139383Enzo Doria06/2016
37873^292129-112756139381Enzo Doria07/2014
3788(15*2^462951+1)/527139361Lelio R Paula08/2015
378931922^23205+23205^31922139359Hans Havermann05/2021
3790(19*10^139336+503)/9139337Alfred Reich11/2023
37922^462855-1865707139334Enzo Doria02/2016
379131237^28876+28876^31237139334Hans Havermann05/2021
3793(86*10^139315+121)/9139316Robert Price08/2019
37942^462786-292043139313Enzo Doria08/2015
379538915^3798+3798^38915139299Hans Havermann05/2021
3797(26*10^139289+1)/9139290Serge Batalov05/2010
3796(17*10^139289+7)/3139290Robert Price06/2023
379834065^12248+12248^34065139260Hans Havermann05/2021
379936425^6654+6654^36425139256Hans Havermann05/2021
380039252^3527+3527^39252139243Hans Havermann05/2021
3801(17*10^139239+67)/3139240Robert Price01/2019
380231887^23248+23248^31887139231Hans Havermann05/2021
3803(25*10^139210-97)/9139211Robert Price01/2022
38042^462238-935139148Yves Minet02/2014
3805(29*10^139134-119)/9139135Robert Price12/2021
3806(109*10^139100-7)/3139102Robert Price03/2021
380738744^3885+3885^38744139068Hans Havermann05/2021
380831112^29499+29499^31112139065Hans Havermann05/2021
38092*10^139043-63139044Robert Price01/2022
381036390^6613+6613^36390139025Hans Havermann04/2021
38112*10^138975+33138976Robert Price11/2021
381242437^1882+1882^42437138966Hans Havermann05/2021
381332151^20990+20990^32151138958Hans Havermann05/2021
381432154^20933+20933^32154138933Hans Havermann04/2021
381531082^29499+29499^31082138931Hans Havermann04/2021
38162^461228+1870441138844Enzo Doria05/2016
38172^461204-113675138837Enzo Doria08/2014
3818(2^461139-7)/47138815Lelio R Paula08/2015
3819(17*10^138812-521)/9138813Robert Price04/2018
38203*10^138811-11138812Robert Price07/2018
3821(28*10^138768+173)/3138769Robert Price12/2019
3822(17*2^460963+1)/124051613138757Lelio R Paula08/2015
3823(379*10^138737-1)/9138739Robert Price02/2020
3824(43*10^138648+101)/9138649Robert Price11/2018
38252^460567-113541138645Enzo Doria08/2014
3826(10^138622+161)/9138622Robert Price09/2021
38277*10^138604+3138605Robert Price08/2015
3828(133*10^138600+17)/3138602Robert Price11/2021
382933912^12203+12203^33912138581Hans Havermann05/2021
38302^460330+69138574Lelio R Paula09/2017
3831(17*10^138569-77)/3138570Robert Price08/2019
383231186^27725+27725^31186138556Hans Havermann05/2021
3833(16*10^138545+89)/3138546Robert Price03/2021
383439753^3056+3056^39753138546Hans Havermann05/2021
383531282^26847+26847^31282138545Hans Havermann05/2021
38366*10^138520-37138521Robert Price02/2021
38382^460078-69581138498Enzo Doria12/2015
383731830^22447+22447^31830138498Hans Havermann05/2021
383937384^5065+5065^37384138492Hans Havermann05/2021
384034774^9585+9585^34774138456Hans Havermann05/2021
384110^138444-5001138444Robert Price12/2021
38422^459768+1531138404Lelio R Paula06/2012
3843(266*10^138328-17)/3138330Robert Price07/2020
384427200^31193-31193^27200138328Frank Doornink01/2024
384532963^15696+15696^32963138306Hans Havermann05/2021
38462^459343-113611138277Enzo Doria08/2014
3847(28*10^138240+113)/3138241Robert Price03/2020
38482^459199+1874393138233Enzo Doria06/2016
384933339^14002+14002^33339138230Hans Havermann05/2021
38502^459063-345307138192Enzo Doria06/2015
38512*10^138162-43138163Robert Price04/2018
38522^458927-112747138151Enzo Doria06/2014
38532^458927-69217138151Enzo Doria11/2015
385430907^29458+29458^30907138130Hans Havermann05/2021
385532882^15837+15837^32882138094Hans Havermann05/2021
385639252^3295+3295^39252138083Hans Havermann05/2021
385733789^12190+12190^33789138062Hans Havermann06/2021
3858555555*2^458524+1513138036Darren Bedwell08/2009
385930931^29002+29002^30931138028Hans Havermann05/2021
38602^458465+2^32+1138012T. D. Noe06/2007
386132206^19275+19275^32206138003Hans Havermann05/2021
38622^458321-113053137969Enzo Doria07/2014
38636^177298+323137965Riley Fisher03/2023
38642^458298+79459137962Enzo Doria06/2016
38652^458248-21815137947Enzo Doria07/2013
38662^458194+1876549137931Enzo Doria07/2016
3867(318259#+325270)/(2^2*5*11*2957)137907Makoto Morimoto10/2017
3868(318259#+2625)/(3^2*5*7^5*22965193)137899Makoto Morimoto06/2019
3869(793*10^137887+53)/9137889Robert Price01/2022
38702^457937+57137853Lelio R Paula09/2017
3871(8*10^137845+13)/3137846Robert Price06/2018
38722^457822+105137819Donovan Johnson06/2006
38732^457754-113711137798Enzo Doria09/2014
387411^132315-360137792Enzo Doria09/2012
387532072^19689+19689^32072137725Hans Havermann06/2021
387644592^1225+1225^44592137707Hans Havermann05/2021
38772^457347-37137676Lelio R Paula09/2017
38782^457322-2786393137668Enzo Doria10/2015
3879gcd(Phi(699340,10),(10^34967+1)^3*(10^34967+1+10^17484)-(10^69934+10^34967)*(10^17484-1)+10^104901)137664Serge Batalov04/2015
388034015^11134+11134^34015137647Hans Havermann06/2021
38812^457240-59939137643Enzo Doria10/2015
3882(856*10^137633-1)/9137635Robert Price03/2020
388336232^6289+6289^36232137631Hans Havermann05/2021
38842^457120-21575137607Enzo Doria07/2013
3885(11*2^456978+1)/15137564Lelio R Paula07/2015
388630963^27722+27722^30963137564Hans Havermann04/2021
388733722^12003+12003^33722137562Hans Havermann06/2021
3888(7*25^98399+10613)/12137556Curtis Bright05/2015
388941901^1918+1918^41901137555Hans Havermann06/2021
3890(7*10^137551-1)/3137552Robert Price08/2022
389132930^15021+15021^32930137539Hans Havermann05/2021
389231178^25785+25785^31178137538Hans Havermann05/2021
3893419^52446+52446^419137525Norbert Schneider11/2020
38942^456813+214175137515Enzo Doria10/2023
38952^456796-113513137510Enzo Doria08/2014
389631788^21137+21137^31788137485Hans Havermann04/2021
3897(7*2^456655+1)/39137467Lelio R Paula07/2015
389827151^31004-31004^27151137466Frank Doornink01/2024
38992^456503-114361137422Enzo Doria01/2015
3900(11*2^456387+1)/19137386Lelio R Paula07/2015
390136248^6147+6147^36248137332Hans Havermann05/2021
390231986^19651+19651^31986137329Hans Havermann05/2021
39032^456167+22313137320Enzo Doria09/2023
390431817^20656+20656^31817137292Hans Havermann05/2021
3905(71*10^137250+1)/9137251Serge Batalov05/2010
39062^455922+76249137247Enzo Doria05/2016
390731310^24171+24171^31310137241Hans Havermann05/2021
390814^119741-119741^14137239Serge Batalov04/2016
390935014^8297+8297^35014137218Hans Havermann05/2021
3910(19*2^455760+1)/3455137196Lelio R Paula07/2015
3912124^(2^16)+57^(2^16)137195Valeryi Kuryshev02/2011
3911124^65536+57^65536137195Serge Batalov03/2018
39132^455689+72677137177Enzo Doria04/2016
3914(17948!)^2+Prime(17948)137118Robert Price08/2014
391531287^24128+24128^31287137116Hans Havermann05/2021
3916(37^87421-1)/36137093Robert Price03/2012
391736233^6070+6070^36233137077Hans Havermann05/2021
3918(8*10^137073-17)/9137073Serge Batalov11/2022
391938418^3697+3697^38418137070Hans Havermann04/2021
39202^455323-57137066Lelio R Paula09/2017
3921(56*10^137019+583)/9137020Robert Price08/2021
392225017^31148-31148^25017136997Frank Doornink12/2023
3923(73*17^111333-9)/16136991Curtis Bright05/2015
39242^455025-112723136977Enzo Doria06/2014
392533876^11039+11039^33876136959Hans Havermann05/2021
3926(19860^32041-1)/(19860^179-1)136943Ryan Propper11/2023
392735142^7873+7873^35142136919Hans Havermann05/2021
392866*10^136894+7136896Robert Price07/2020
39292^454675-1777136871Yves Minet10/2011
393031676^20931+20931^31676136866Hans Havermann05/2021
39313*10^136829+29136830Robert Price05/2018
39324*10^136813-57136814Robert Price10/2018
3933(6092*28^94536-143)/9136812Curtis Bright05/2015
3934fibonacci(654572)-2136798Jon Grantham08/2023
393537359^4588+4588^37359136795Hans Havermann05/2021
39362^454348-53136773Lelio R Paula09/2017
393731^91680-2136729Lelio R Paula05/2017
39382^454199-113697136728Enzo Doria09/2014
393930785^27622+27622^30785136725Hans Havermann05/2021
394032973^14014+14014^32973136725Hans Havermann05/2021
39427*10^136716+69136717Robert Price07/2019
394136002^6273+6273^36002136717Hans Havermann05/2021
39436*10^136692+53136693Robert Price05/2020
3944(13*10^136687+47)/3136688Robert Price10/2018
39452^453935-2791357136649Enzo Doria01/2016
39462^453906-69131136640Enzo Doria11/2015
394733232^12915+12915^33232136620Hans Havermann05/2021
39482^453791+1873913136605Enzo Doria06/2016
394934166^9951+9951^34166136592Hans Havermann05/2021
3950(21*2^453740-1)/2735136588Lelio R Paula07/2015
395131102^24635+24635^31102136587Hans Havermann05/2021
3952580^49413+49413^580136550Norbert Schneider02/2019
39532^453503-2788297136519Enzo Doria11/2015
395434989^7958+7958^34989136486Hans Havermann12/2020
3955(2*10^136484+187)/9136484Robert Price06/2022
395631007^25158+25158^31007136452Hans Havermann11/2020
39572^453267-113827136447Enzo Doria09/2014
395832234^17085+17085^32234136435Hans Havermann12/2020
39592^453102+1877629136398Enzo Doria08/2016
396031016^24981+24981^31016136397Hans Havermann12/2020
3961(62*10^136384-791)/9136385Robert Price06/2019
396234171^9798+9798^34171136382Hans Havermann12/2020
3963(17*10^136354-113)/3136355Robert Price06/2021
396432756^14541+14541^32756136350Hans Havermann11/2020
396532205^17086+17086^32205136313Hans Havermann12/2020
3966(25*10^136303+161)/3136304Robert Price09/2019
396735337^7196+7196^35337136299Hans Havermann12/2020
3968(182*10^136291+1)/3136293Robert Price02/2020
3969(88*10^136234+83)/9136235Robert Price03/2022
397023*10^136225-7136227Robert Price02/2020
3971L(651821)136223Henri Lifchitz09/2008
397225519^30908-30908^25519136208Frank Doornink02/2024
39732^452460+77701136205Enzo Doria05/2016
39742^452440-114755136199Enzo Doria04/2015
397532286^16489+16489^32286136157Hans Havermann11/2020
3976(47*10^136141+493)/9136142Robert Price03/2019
397727140^30699-30699^27140136108Frank Doornink01/2024
397840392^2339+2339^40392136082Hans Havermann12/2020
39792*10^136057-43136058Robert Price04/2018
39802^451971+21563136057Enzo Doria08/2023
3981(2^451956-5)/181136051Lelio R Paula07/2015
39822^451947-22165136050Enzo Doria07/2013
39832^451787-21805136002Enzo Doria07/2013
39842^451734-112817135986Enzo Doria06/2014
3985(11*2^451714+1)/75135979Lelio R Paula07/2015
39862^451705-21879135977Enzo Doria07/2013
3987(4666^37249-1)/(4666^193-1)135957Ryan Propper11/2023
39882^451560-112349135934Enzo Doria06/2014
39892^451530+45135925Lelio R Paula08/2017
399031622^19875+19875^31622135922Hans Havermann11/2020
3991(25*10^135906-73)/3135907Robert Price09/2019
39922^451450-21743135900Enzo Doria07/2013
3993(7*10^135879+11)/9135879Tyler Busby01/2023
399435218^7199+7199^35218135846Hans Havermann11/2020
399535661^6446+6446^35661135844Hans Havermann11/2020
3996(7*33^89453-4743239)/32135835Eric Chen12/2023
399731869^18248+18248^31869135801Hans Havermann12/2020
3998(77*10^135789+157)/9135790Robert Price05/2022
39992^450958+60529135752Enzo Doria08/2023
40002^450805+65135706Lelio R Paula08/2017


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 04 2024 15:31 (Time in France)

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