PRP Records

Probable Primes Top 10000

(294627 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 ?
3751(16*10^140091+167)/3140092Robert Price06/2019
3752(8*10^140087-137)/3140088Robert Price03/2022
37536^179964+179964^6-1140040Robert Price04/2014
3754(89*10^140008-179)/9140009Robert Price12/2019
3755(29*2^465077-1)/9140003Lelio R Paula08/2015
37562^465072-344789140001Enzo Doria07/2015
375734742^10683+10683^34742139965Hans Havermann05/2021
37585*10^139945+81139946Robert Price03/2019
375932648^19335+19335^32648139941Hans Havermann05/2021
37602^464864-17139939Lelio R Paula09/2017
37618*10^139920+51139921Robert Price08/2019
3762(85*10^139913-1)/3139915Robert Price02/2020
376331203^30436+30436^31203139896Hans Havermann04/2021
37642^464642+22189139872Enzo Doria09/2023
3765(16^116139+619)/5139845Anonymous08/2022
3766(2^464556+619)/5139845Eric Chen10/2023
37674*10^139839-27139840Robert Price08/2021
376833582^14573+14573^33582139821Hans Havermann05/2021
3769(17^113621+1)/18139804Paul Bourdelais09/2011
37712*10^139800-21139801Robert Price09/2020
377032628^19261+19261^32628139801Hans Havermann04/2021
3772(13*10^139782+191)/3139783Robert Price11/2018
3773(64*10^139776+791)/9139777Robert Price01/2022
3774(695*10^139772+7)/9139774Robert Price12/2021
3775(19*2^464312-1)/3139773Lelio R Paula08/2015
3776(74*10^139723+133)/9139724Robert Price06/2019
37773*10^139722+13139723Robert Price07/2018
377831577^26592+26592^31577139721Hans Havermann05/2021
377977*10^139692+3139694Robert Price06/2020
3780(31*2^463970+1)/5139670Lelio R Paula08/2015
3781(18203^(2^15)+(18201)^(2^15))/2139597Robert Price05/2018
378239640^3321+3321^39640139584Hans Havermann05/2021
378336663^6410+6410^36663139571Hans Havermann05/2021
37842^463633-2788423139568Enzo Doria11/2015
378533659^13978+13978^33659139532Hans Havermann05/2021
378631811^24318+24318^31811139521Hans Havermann04/2021
378734149^12172+12172^34149139512Hans Havermann04/2021
3788(29*10^139476+313)/9139477Robert Price04/2021
378931721^24940+24940^31721139474Hans Havermann05/2021
379032833^17698+17698^32833139473Hans Havermann05/2021
37912^463271-109501139459Enzo Doria04/2014
3792(5*10^139457+79)/3139458Robert Price03/2018
37932^463237-99139449Lelio R Paula09/2017
3794(49*10^139442+383)/9139443Robert Price04/2019
379531155^29902+29902^31155139441Hans Havermann05/2021
3796(7*10^139417-547)/9139417Robert Price01/2018
3797(10^139398+191)/3139398Robert Price02/2018
379823*10^139386-3139388Robert Price10/2021
37992^463019+79463139383Enzo Doria06/2016
38003^292129-112756139381Enzo Doria07/2014
3801(15*2^462951+1)/527139361Lelio R Paula08/2015
380231922^23205+23205^31922139359Hans Havermann05/2021
3803(19*10^139336+503)/9139337Alfred Reich11/2023
38052^462855-1865707139334Enzo Doria02/2016
380431237^28876+28876^31237139334Hans Havermann05/2021
3806(86*10^139315+121)/9139316Robert Price08/2019
38072^462786-292043139313Enzo Doria08/2015
380838915^3798+3798^38915139299Hans Havermann05/2021
3810(26*10^139289+1)/9139290Serge Batalov05/2010
3809(17*10^139289+7)/3139290Robert Price06/2023
381134065^12248+12248^34065139260Hans Havermann05/2021
381236425^6654+6654^36425139256Hans Havermann05/2021
381339252^3527+3527^39252139243Hans Havermann05/2021
3814(17*10^139239+67)/3139240Robert Price01/2019
381531887^23248+23248^31887139231Hans Havermann05/2021
3816(25*10^139210-97)/9139211Robert Price01/2022
38172^462238-935139148Yves Minet02/2014
3818(29*10^139134-119)/9139135Robert Price12/2021
3819(109*10^139100-7)/3139102Robert Price03/2021
382038744^3885+3885^38744139068Hans Havermann05/2021
382131112^29499+29499^31112139065Hans Havermann05/2021
38222*10^139043-63139044Robert Price01/2022
382336390^6613+6613^36390139025Hans Havermann04/2021
38242*10^138975+33138976Robert Price11/2021
382542437^1882+1882^42437138966Hans Havermann05/2021
382632151^20990+20990^32151138958Hans Havermann05/2021
382732154^20933+20933^32154138933Hans Havermann04/2021
382831082^29499+29499^31082138931Hans Havermann04/2021
38292^461228+1870441138844Enzo Doria05/2016
38302^461204-113675138837Enzo Doria08/2014
3831(2^461139-7)/47138815Lelio R Paula08/2015
3832(17*10^138812-521)/9138813Robert Price04/2018
38333*10^138811-11138812Robert Price07/2018
3834(28*10^138768+173)/3138769Robert Price12/2019
3835(17*2^460963+1)/124051613138757Lelio R Paula08/2015
3836(379*10^138737-1)/9138739Robert Price02/2020
3837(43*10^138648+101)/9138649Robert Price11/2018
38382^460567-113541138645Enzo Doria08/2014
3839(10^138622+161)/9138622Robert Price09/2021
38407*10^138604+3138605Robert Price08/2015
3841(133*10^138600+17)/3138602Robert Price11/2021
384233912^12203+12203^33912138581Hans Havermann05/2021
38432^460330+69138574Lelio R Paula09/2017
3844(17*10^138569-77)/3138570Robert Price08/2019
384531186^27725+27725^31186138556Hans Havermann05/2021
3846(16*10^138545+89)/3138546Robert Price03/2021
384739753^3056+3056^39753138546Hans Havermann05/2021
384831282^26847+26847^31282138545Hans Havermann05/2021
38496*10^138520-37138521Robert Price02/2021
38512^460078-69581138498Enzo Doria12/2015
385031830^22447+22447^31830138498Hans Havermann05/2021
385237384^5065+5065^37384138492Hans Havermann05/2021
385334774^9585+9585^34774138456Hans Havermann05/2021
385410^138444-5001138444Robert Price12/2021
38552^459768+1531138404Lelio R Paula06/2012
3856(266*10^138328-17)/3138330Robert Price07/2020
385727200^31193-31193^27200138328Frank Doornink01/2024
385832963^15696+15696^32963138306Hans Havermann05/2021
38592^459343-113611138277Enzo Doria08/2014
3860(28*10^138240+113)/3138241Robert Price03/2020
38612^459199+1874393138233Enzo Doria06/2016
386233339^14002+14002^33339138230Hans Havermann05/2021
38632^459063-345307138192Enzo Doria06/2015
38642*10^138162-43138163Robert Price04/2018
38652^458927-112747138151Enzo Doria06/2014
38662^458927-69217138151Enzo Doria11/2015
386730907^29458+29458^30907138130Hans Havermann05/2021
386832882^15837+15837^32882138094Hans Havermann05/2021
386939252^3295+3295^39252138083Hans Havermann05/2021
387033789^12190+12190^33789138062Hans Havermann06/2021
3871555555*2^458524+1513138036Darren Bedwell08/2009
387230931^29002+29002^30931138028Hans Havermann05/2021
38732^458465+2^32+1138012T. D. Noe06/2007
387432206^19275+19275^32206138003Hans Havermann05/2021
38752^458321-113053137969Enzo Doria07/2014
38766^177298+323137965Riley Fisher03/2023
38772^458298+79459137962Enzo Doria06/2016
38782^458248-21815137947Enzo Doria07/2013
38792^458194+1876549137931Enzo Doria07/2016
3880(318259#+325270)/(2^2*5*11*2957)137907Makoto Morimoto10/2017
3881(318259#+2625)/(3^2*5*7^5*22965193)137899Makoto Morimoto06/2019
3882(793*10^137887+53)/9137889Robert Price01/2022
38832^457937+57137853Lelio R Paula09/2017
3884(8*10^137845+13)/3137846Robert Price06/2018
38852^457822+105137819Donovan Johnson06/2006
38862^457754-113711137798Enzo Doria09/2014
388711^132315-360137792Enzo Doria09/2012
388832072^19689+19689^32072137725Hans Havermann06/2021
388944592^1225+1225^44592137707Hans Havermann05/2021
38902^457347-37137676Lelio R Paula09/2017
38912^457322-2786393137668Enzo Doria10/2015
3892gcd(Phi(699340,10),(10^34967+1)^3*(10^34967+1+10^17484)-(10^69934+10^34967)*(10^17484-1)+10^104901)137664Serge Batalov04/2015
389334015^11134+11134^34015137647Hans Havermann06/2021
38942^457240-59939137643Enzo Doria10/2015
3895(856*10^137633-1)/9137635Robert Price03/2020
389636232^6289+6289^36232137631Hans Havermann05/2021
38972^457120-21575137607Enzo Doria07/2013
3898(11*2^456978+1)/15137564Lelio R Paula07/2015
389930963^27722+27722^30963137564Hans Havermann04/2021
390033722^12003+12003^33722137562Hans Havermann06/2021
3901(7*25^98399+10613)/12137556Curtis Bright05/2015
390241901^1918+1918^41901137555Hans Havermann06/2021
3903(7*10^137551-1)/3137552Robert Price08/2022
390432930^15021+15021^32930137539Hans Havermann05/2021
390531178^25785+25785^31178137538Hans Havermann05/2021
3906419^52446+52446^419137525Norbert Schneider11/2020
39072^456813+214175137515Enzo Doria10/2023
39082^456796-113513137510Enzo Doria08/2014
390931788^21137+21137^31788137485Hans Havermann04/2021
3910(7*2^456655+1)/39137467Lelio R Paula07/2015
391127151^31004-31004^27151137466Frank Doornink01/2024
39122^456503-114361137422Enzo Doria01/2015
3913(11*2^456387+1)/19137386Lelio R Paula07/2015
391436248^6147+6147^36248137332Hans Havermann05/2021
391531986^19651+19651^31986137329Hans Havermann05/2021
39162^456167+22313137320Enzo Doria09/2023
391731817^20656+20656^31817137292Hans Havermann05/2021
3918(71*10^137250+1)/9137251Serge Batalov05/2010
39192^455922+76249137247Enzo Doria05/2016
392031310^24171+24171^31310137241Hans Havermann05/2021
392114^119741-119741^14137239Serge Batalov04/2016
392235014^8297+8297^35014137218Hans Havermann05/2021
3923(19*2^455760+1)/3455137196Lelio R Paula07/2015
3925124^(2^16)+57^(2^16)137195Valeryi Kuryshev02/2011
3924124^65536+57^65536137195Serge Batalov03/2018
39262^455689+72677137177Enzo Doria04/2016
3927(17948!)^2+Prime(17948)137118Robert Price08/2014
392831287^24128+24128^31287137116Hans Havermann05/2021
3929(37^87421-1)/36137093Robert Price03/2012
393036233^6070+6070^36233137077Hans Havermann05/2021
3931(8*10^137073-17)/9137073Serge Batalov11/2022
393238418^3697+3697^38418137070Hans Havermann04/2021
39332^455323-57137066Lelio R Paula09/2017
3934(56*10^137019+583)/9137020Robert Price08/2021
393525017^31148-31148^25017136997Frank Doornink12/2023
3936(73*17^111333-9)/16136991Curtis Bright05/2015
39372^455025-112723136977Enzo Doria06/2014
393833876^11039+11039^33876136959Hans Havermann05/2021
3939(19860^32041-1)/(19860^179-1)136943Ryan Propper11/2023
394035142^7873+7873^35142136919Hans Havermann05/2021
394166*10^136894+7136896Robert Price07/2020
39422^454675-1777136871Yves Minet10/2011
394331676^20931+20931^31676136866Hans Havermann05/2021
39443*10^136829+29136830Robert Price05/2018
39454*10^136813-57136814Robert Price10/2018
3946(6092*28^94536-143)/9136812Curtis Bright05/2015
3947fibonacci(654572)-2136798Jon Grantham08/2023
394837359^4588+4588^37359136795Hans Havermann05/2021
39492^454348-53136773Lelio R Paula09/2017
395031^91680-2136729Lelio R Paula05/2017
39512^454199-113697136728Enzo Doria09/2014
395230785^27622+27622^30785136725Hans Havermann05/2021
395332973^14014+14014^32973136725Hans Havermann05/2021
39557*10^136716+69136717Robert Price07/2019
395436002^6273+6273^36002136717Hans Havermann05/2021
39566*10^136692+53136693Robert Price05/2020
3957(13*10^136687+47)/3136688Robert Price10/2018
39582^453935-2791357136649Enzo Doria01/2016
39592^453906-69131136640Enzo Doria11/2015
396033232^12915+12915^33232136620Hans Havermann05/2021
39612^453791+1873913136605Enzo Doria06/2016
396234166^9951+9951^34166136592Hans Havermann05/2021
3963(21*2^453740-1)/2735136588Lelio R Paula07/2015
396431102^24635+24635^31102136587Hans Havermann05/2021
3965580^49413+49413^580136550Norbert Schneider02/2019
39662^453503-2788297136519Enzo Doria11/2015
396734989^7958+7958^34989136486Hans Havermann12/2020
3968(2*10^136484+187)/9136484Robert Price06/2022
396931007^25158+25158^31007136452Hans Havermann11/2020
39702^453267-113827136447Enzo Doria09/2014
397132234^17085+17085^32234136435Hans Havermann12/2020
39722^453102+1877629136398Enzo Doria08/2016
397331016^24981+24981^31016136397Hans Havermann12/2020
3974(62*10^136384-791)/9136385Robert Price06/2019
397534171^9798+9798^34171136382Hans Havermann12/2020
3976(17*10^136354-113)/3136355Robert Price06/2021
397732756^14541+14541^32756136350Hans Havermann11/2020
397832205^17086+17086^32205136313Hans Havermann12/2020
3979(25*10^136303+161)/3136304Robert Price09/2019
398035337^7196+7196^35337136299Hans Havermann12/2020
3981(182*10^136291+1)/3136293Robert Price02/2020
3982(88*10^136234+83)/9136235Robert Price03/2022
398323*10^136225-7136227Robert Price02/2020
3984L(651821)136223Henri Lifchitz09/2008
398525519^30908-30908^25519136208Frank Doornink02/2024
39862^452460+77701136205Enzo Doria05/2016
39872^452440-114755136199Enzo Doria04/2015
398832286^16489+16489^32286136157Hans Havermann11/2020
3989(47*10^136141+493)/9136142Robert Price03/2019
399027140^30699-30699^27140136108Frank Doornink01/2024
399140392^2339+2339^40392136082Hans Havermann12/2020
39922*10^136057-43136058Robert Price04/2018
39932^451971+21563136057Enzo Doria08/2023
3994(2^451956-5)/181136051Lelio R Paula07/2015
39952^451947-22165136050Enzo Doria07/2013
39962^451787-21805136002Enzo Doria07/2013
39972^451734-112817135986Enzo Doria06/2014
3998(11*2^451714+1)/75135979Lelio R Paula07/2015
39992^451705-21879135977Enzo Doria07/2013
4000(4666^37249-1)/(4666^193-1)135957Ryan Propper11/2023


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: March, 12 2024 13:37 (Time in France)

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