PRP Records

Probable Primes Top 10000

(295461 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 ?
37518*10^143361+17143362Robert Price07/2021
3752(2^475854+9)/73143245Lelio R Paula08/2015
37532^475813-113239143234Enzo Doria07/2014
3754(19*10^143212+137)/3143213Robert Price03/2022
375532218^27849+27849^32218143203Hans Havermann04/2021
3756580*33^94296+19143193Eric Chen12/2023
37572^475624-114059143178Enzo Doria11/2014
3758(11*2^475553-7)/15143156Renaud Lifchitz03/2011
37592^475480-2786129143134Enzo Doria10/2015
376033912^16621+16621^33912143131Hans Havermann05/2021
3761(19*10^143129-43)/3143130Robert Price05/2019
376231830^31373+31373^31830143126Hans Havermann05/2021
37636*10^143105-53143106Robert Price05/2021
3764(14*10^143097+73)/3143098Robert Price12/2018
37652^475299-111937143080Enzo Doria05/2014
376635488^10753+10753^35488143071Hans Havermann04/2021
376729695^31986-31986^29695143064Frank Doornink06/2024
37682^475160-2797859143038Enzo Doria04/2016
3769(2^475069+3)/395143008Lelio R Paula08/2015
37702^475027-461437142998Enzo Doria07/2015
3771(2^474958+78557)/3142977Lelio R Paula07/2015
3772(8*10^142932+43)/3142933Robert Price06/2018
377335055^11942+11942^35055142922Hans Havermann05/2021
377437650^6239+6239^37650142887Hans Havermann05/2021
3775(54^82471-1)/53142871Paul Bourdelais09/2017
377631205^31784-31784^31205142845Frank Doornink01/2024
3777(11*2^474432-1)/95142818Lelio R Paula09/2015
37782^474417-59923142814Enzo Doria10/2015
37794*10^142810-21142811Robert Price09/2018
378032287^26494+26494^32287142811Hans Havermann06/2021
378137162^6965+6965^37162142811Hans Havermann06/2021
3782(34*10^142805-601)/9142806Robert Price07/2022
378337456^6493+6493^37456142799Hans Havermann05/2021
378435141^11572+11572^35141142793Hans Havermann05/2021
378532231^26908+26908^32231142780Hans Havermann05/2021
3786(3*2^474166+1)/7142738Lelio R Paula08/2015
37872^474053+2897142705Lelio R Paula08/2012
3788(10^142699+359)/9142699Serge Batalov12/2014
378926073^32312-32312^26073142696Frank Doornink03/2024
3790898^48311-897^48311142676Jean-Louis Charton12/2012
37912^473740-1856639142610Enzo Doria09/2015
3792(25*10^142573-403)/9142574Robert Price12/2020
37932^473617-114223142573Enzo Doria12/2014
379436115^8856+8856^36115142555Hans Havermann05/2021
3795fibonacci(682007)+4142531Jon Grantham08/2023
37962^473257+1873217142465Enzo Doria06/2016
3797(19*2^473242+1)/11142461Lelio R Paula09/2015
379832750^22371+22371^32750142453Hans Havermann06/2021
3799(61*10^142446-1)/3142448Robert Price01/2020
3800(14*10^142440+61)/3142441Robert Price12/2018
3801(10^142425+359)/9142425Serge Batalov12/2014
38022^473101+773027142418Enzo Doria05/2016
3803(13*2^472838-1)/3142340Lelio R Paula09/2015
3804(17*2^472789-1)/187347142320Lelio R Paula09/2015
380536915^7162+7162^36915142309Hans Havermann05/2021
38062^472634-109511142278Enzo Doria04/2014
380731870^28997+28997^31870142216Hans Havermann06/2021
3808(48^84589+1)/49142213Robert Price01/2014
38097*10^142189+87142190Robert Price07/2019
38102^472258+7142164Lelio R Paula08/2015
381140135^3484+3484^40135142162Hans Havermann05/2021
38129*33^93598+26142131Eric Chen12/2023
3813(23*10^142105+91)/3142106Robert Price08/2019
3814tau(317^10330)142098Nik Lygeros / Olivier Rozier / LR team10/2013
3815(11*2^471913-1)/21142060Lelio R Paula09/2015
3816(16*10^142058+197)/3142059Robert Price04/2019
38179*10^142037+91142038Robert Price10/2020
3818(4*10^142034+17)/3142035Tyler Busby01/2023
38192^471792+1880881142024Enzo Doria11/2016
3820(509*10^142018+31)/9142020Robert Price08/2022
3821(31*2^471580-1)/135141960Lelio R Paula08/2015
3822(4*10^141926-79)/3141927Robert Price02/2018
38232^471464-111546435141925Paul Bourdelais10/2021
3824(904*19^110984-1)/3141924Curtis Bright05/2015
3825(14*10^141853+37)/3141854Robert Price12/2018
3826(41*10^141836-59)/9141837Robert Price10/2018
38274*5^202913-9141831Lelio R Paula04/2015
38282*7^167812-3141818Lelio R Paula12/2014
38292^471043+35141799Robert Price11/2015
3830(11*2^470956-1)/7945141770Lelio R Paula08/2015
383143636^1773+1773^43636141761Hans Havermann05/2021
3832(2*10^141751-17)/3141751Serge Batalov11/2022
3833(53*10^141722-611)/9141723Robert Price02/2022
3834(11*10^141718-131)/3141719Robert Price09/2018
3835(61*10^141716+47)/9141717Robert Price07/2022
383626057^32088-32088^26057141699Frank Doornink03/2024
38372^470692+76771141693Enzo Doria05/2016
383850160^667+667^50160141659Hans Havermann05/2021
383931522^31181+31181^31522141657Hans Havermann05/2021
384029487^31690-31690^29487141643Frank Doornink06/2024
384133076^19135+19135^33076141626Hans Havermann04/2021
384228237^31818-31818^28237141617Frank Doornink06/2024
3843(91*10^141610+71)/9141612Robert Price01/2022
3844(21*2^470391+1)/533141601Lelio R Paula09/2015
3845(5*10^141594-23)/9141594Serge Batalov11/2022
384631932^27155+27155^31932141582Hans Havermann05/2021
384736449^7660+7660^36449141577Hans Havermann05/2021
38482^470305-459373141576Enzo Doria05/2015
384932195^24936+24936^32195141556Hans Havermann05/2021
38502^470183+72623141540Enzo Doria04/2016
38512^470173-16465141537Enzo Doria04/2013
385237297^6234+6234^37297141534Hans Havermann05/2021
3853(509*10^141479+13)/9141481Robert Price05/2022
385444*10^141476+9141478Robert Price10/2020
38552^469974-1841141477Enzo Doria05/2014
3856(23*2^469939+1)/25141466Lelio R Paula08/2015
3857312*33^93158+23141465Eric Chen12/2023
38582*10^141448+63141449Robert Price05/2018
38592^469824+43141432Lelio R Paula09/2017
38602*10^141407-27141408Robert Price05/2018
3861(214*10^141385-1)/3141387Robert Price01/2021
38622^469630-59711141373Enzo Doria10/2015
386335277^10172+10172^35277141370Hans Havermann04/2021
386433397^17100+17100^33397141370Hans Havermann04/2021
3865(25*10^141366-331)/9141367Robert Price08/2018
386636986^6639+6639^36986141365Hans Havermann06/2021
386734572^12271+12271^34572141361Hans Havermann06/2021
386837179^6338+6338^37179141353Hans Havermann05/2021
3869(2^469564-3)/611141351Lelio R Paula08/2015
3870197^61601+2141342Lelio R Paula08/2017
387133420^16951+16951^33420141340Hans Havermann05/2021
387231623^29458+29458^31623141330Hans Havermann05/2021
387348112^865+865^48112141306Hans Havermann05/2021
38742^469372-112949141296Enzo Doria07/2014
38755*10^141294-63141295Robert Price04/2021
38763^296115+4141283Tyler NeSmith01/2021
3877(64*10^141256+161)/9141257Robert Price08/2022
3879143^(2^16)+106^(2^16)141253Valeryi Kuryshev02/2011
3878143^65536+106^65536141253Serge Batalov03/2018
3880(11*10^141243-23)/3141244Robert Price09/2021
38822^469198+782569141243Enzo Doria10/2016
388138129^5062+5062^38129141243Hans Havermann05/2021
38832^469076-2786939141206Enzo Doria11/2015
388438630^4521+4521^38630141202Hans Havermann05/2021
388531755^27836+27836^31755141139Hans Havermann05/2021
388635554^9325+9325^35554141137Hans Havermann05/2021
38872^468804+1874941141125Enzo Doria06/2016
38882^468787+81353141119Enzo Doria08/2016
388930204^31493-31493^30204141091Frank Doornink06/2024
38902^468595-350407141062Enzo Doria06/2015
38912^468564+87855141052Lelio R Paula01/2016
38922^468551-21987141048Enzo Doria07/2013
38932^468523-7141040Lelio R Paula08/2015
3894(25*10^141019-13)/3141020Robert Price09/2019
38952^468405+87855141004Lelio R Paula01/2016
389639338^3831+3831^39338140961Hans Havermann05/2021
389731458^30239+30239^31458140950Hans Havermann05/2021
38988*10^140932+29140933Robert Price11/2021
389933166^17691+17691^33166140881Hans Havermann06/2021
39002^467978-113051140876Enzo Doria07/2014
39012^467780-344429140816Enzo Doria07/2015
39029*10^140802-89140803Robert Price04/2020
39032^467605-1855603140764Enzo Doria09/2015
3904(9^147503-5^147503)/4140754Jon Grantham07/2023
39055*10^140744-7140745Robert Price09/2015
3906(5^201359-1)/4140744Paul Bourdelais12/2008
39072^467401-1850023140702Enzo Doria08/2015
3908(14*10^140693+13)/9140694Tyler Busby02/2023
3909(266*10^140681-17)/3140683Robert Price07/2020
3910(2^467270+78557)/23247140658Lelio R Paula07/2015
391132138^23781+23781^32138140644Hans Havermann05/2021
391231654^27735+27735^31654140640Hans Havermann05/2021
3913(29*2^467205+1)/2780517107140635Lelio R Paula08/2015
39142^467166-1854941140631Enzo Doria09/2015
3915(203*10^140615-11)/3140617Robert Price12/2020
3916(85*10^140609+473)/9140610Robert Price01/2020
391739231^3836+3836^39231140600Hans Havermann06/2021
39185*3^294676+2^294676140597Jon Grantham08/2023
39192^466866-1840571140541Enzo Doria06/2015
39202^466829-459523140530Enzo Doria05/2015
39212^466692-113213140489Enzo Doria07/2014
392223*10^140464-3140466Robert Price10/2021
3923(2*10^140461-17)/3140461Serge Batalov11/2022
392431335^30364+30364^31335140455Hans Havermann05/2021
392528511^31524-31524^28511140440Frank Doornink06/2024
392632795^19126+19126^32795140416Hans Havermann05/2021
3927(44*10^140410-503)/9140411Robert Price12/2018
392828332^31535-31535^28332140403Frank Doornink06/2024
3929153^64265-2140400Lelio R Paula11/2017
393030323^31322-31322^30323140379Frank Doornink06/2024
3931(112*10^140357-1)/3140359Serge Batalov12/2014
3932(29*10^140337-17)/3140338Robert Price09/2019
39332^466181-112735140335Enzo Doria07/2014
3934(16*10^140290-37)/3140291Robert Price05/2021
3935(5*10^140281-119)/3140282Robert Price03/2018
393634568^11415+11415^34568140259Hans Havermann05/2021
3937(27*2^465872+1)/691140241Lelio R Paula08/2015
393833632^14781+14781^33632140236Hans Havermann05/2021
393931803^25670+25670^31803140233Hans Havermann05/2021
39402^465803-114817140221Enzo Doria05/2015
3941floor(Pi*10^140344)%10^140165140165Serge Batalov08/2012
39422^465503-112735140131Enzo Doria07/2014
3943(16*10^140091+167)/3140092Robert Price06/2019
3944(8*10^140087-137)/3140088Robert Price03/2022
39456^179964+179964^6-1140040Robert Price04/2014
3946(89*10^140008-179)/9140009Robert Price12/2019
3947(29*2^465077-1)/9140003Lelio R Paula08/2015
39482^465072-344789140001Enzo Doria07/2015
394934742^10683+10683^34742139965Hans Havermann05/2021
39505*10^139945+81139946Robert Price03/2019
395132648^19335+19335^32648139941Hans Havermann05/2021
39522^464864-17139939Lelio R Paula09/2017
39538*10^139920+51139921Robert Price08/2019
3954(85*10^139913-1)/3139915Robert Price02/2020
395531203^30436+30436^31203139896Hans Havermann04/2021
39562^464642+22189139872Enzo Doria09/2023
395726138^31663-31663^26138139865Frank Doornink03/2024
3958(16^116139+619)/5139845Anonymous08/2022
3959(2^464556+619)/5139845Eric Chen10/2023
39604*10^139839-27139840Robert Price08/2021
396133582^14573+14573^33582139821Hans Havermann05/2021
3962(17^113621+1)/18139804Paul Bourdelais09/2011
39642*10^139800-21139801Robert Price09/2020
396332628^19261+19261^32628139801Hans Havermann04/2021
3965(13*10^139782+191)/3139783Robert Price11/2018
3966(64*10^139776+791)/9139777Robert Price01/2022
3967(695*10^139772+7)/9139774Robert Price12/2021
3968(19*2^464312-1)/3139773Lelio R Paula08/2015
3969(74*10^139723+133)/9139724Robert Price06/2019
39703*10^139722+13139723Robert Price07/2018
397131577^26592+26592^31577139721Hans Havermann05/2021
397277*10^139692+3139694Robert Price06/2020
3973(31*2^463970+1)/5139670Lelio R Paula08/2015
3974(18203^(2^15)+(18201)^(2^15))/2139597Robert Price05/2018
397539640^3321+3321^39640139584Hans Havermann05/2021
397636663^6410+6410^36663139571Hans Havermann05/2021
39772^463633-2788423139568Enzo Doria11/2015
397833659^13978+13978^33659139532Hans Havermann05/2021
397931811^24318+24318^31811139521Hans Havermann04/2021
398034149^12172+12172^34149139512Hans Havermann04/2021
3981(29*10^139476+313)/9139477Robert Price04/2021
398231721^24940+24940^31721139474Hans Havermann05/2021
398332833^17698+17698^32833139473Hans Havermann05/2021
39842^463271-109501139459Enzo Doria04/2014
3985(5*10^139457+79)/3139458Robert Price03/2018
39862^463237-99139449Lelio R Paula09/2017
3987(49*10^139442+383)/9139443Robert Price04/2019
398831155^29902+29902^31155139441Hans Havermann05/2021
3989(7*10^139417-547)/9139417Robert Price01/2018
399029636^31175-31175^29636139409Frank Doornink05/2024
3991(10^139398+191)/3139398Robert Price02/2018
399223*10^139386-3139388Robert Price10/2021
39932^463019+79463139383Enzo Doria06/2016
39943^292129-112756139381Enzo Doria07/2014
3995(15*2^462951+1)/527139361Lelio R Paula08/2015
399631922^23205+23205^31922139359Hans Havermann05/2021
3997(19*10^139336+503)/9139337Alfred Reich11/2023
39992^462855-1865707139334Enzo Doria02/2016
399831237^28876+28876^31237139334Hans Havermann05/2021
4000(86*10^139315+121)/9139316Robert Price08/2019


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 19 2024 15:29 (Time in France)

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