PRP Records

Probable Primes Top 10000

(297738 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 ?
37512^485389+81887146117Enzo Doria08/2016
375232554^30773+30773^32554146108Hans Havermann11/2020
375328075^32844-32844^28075146101Frank Doornink06/2024
3754(10^146063+71)/9146063Serge Batalov07/2015
37552*10^146051-63146052Robert Price01/2022
3756(2^485119+7)/2745146032Lelio R Paula09/2015
3757(22*10^146029+257)/9146030Robert Price06/2018
37587*10^145982-53145983Robert Price06/2020
37592^484743+1872923145923Enzo Doria05/2016
376033140^25287+25287^33140145913Hans Havermann01/2021
376137875^7112+7112^37875145895Hans Havermann01/2021
376230542^32529-32529^30542145890Frank Doornink06/2024
376332862^27473+27473^32862145872Hans Havermann01/2021
3764V(1046652)/2093303145817Serge Batalov07/2024
376532836^27587+27587^32836145815Hans Havermann01/2021
37662^484341+1879157145802Enzo Doria08/2016
37672*10^145784-91145785Robert Price04/2020
37682^484271-51145781Lelio R Paula11/2017
3769(188*10^145750-11)/3145752Robert Price02/2022
377070^78989-69^78989145743Robert Price01/2014
377151^85334+2145714Robert Price07/2015
37722^483886-1857101145665Enzo Doria10/2015
377329312^32607-32607^29312145657Frank Doornink06/2024
377433350^23307+23307^33350145656Hans Havermann01/2021
3775(19*10^145585+131)/3145586Robert Price06/2020
377631815^32332-32332^31815145580Frank Doornink01/2024
37772^483563-1863457145567Enzo Doria12/2015
37784*10^145563-69145564Robert Price01/2022
37792^483516-1861409145553Enzo Doria11/2015
37802^483384-115019145514Enzo Doria06/2015
3781(259*10^145501-1)/3145503Robert Price12/2020
3782(19*10^145499-61)/3145500Robert Price05/2019
37832^483302-3221145489Lelio R Paula12/2012
3784(23*10^145463+61)/3145464Robert Price01/2022
378535523^12434+12434^35523145453Hans Havermann01/2021
3786(29121^32761-1)/(29121^181-1)145444Ryan Propper11/2023
37872^483046+1874029145412Enzo Doria06/2016
37882^482991-2789317145395Enzo Doria12/2015
37892^482978-2789711145391Enzo Doria12/2015
37902^482966-2789711145388Enzo Doria12/2015
37912^482817-1858843145343Enzo Doria10/2015
37922^482751-113635145323Enzo Doria08/2014
37932^482705-459763145309Enzo Doria05/2015
3794(4^241306+11)/3145281Robert Price03/2017
3795(238*10^145276-1)/3145278Robert Price04/2020
3796(19*2^482534+1)/7145258Lelio R Paula09/2015
379753^84239-52^84239145252Robert Price01/2013
3798U(1042497)145243Serge Batalov07/2024
37992^482386+212419145213Enzo Doria08/2023
380047952^1067+1067^47952145207Hans Havermann01/2021
3801(2^482333+5)/9287145193Lelio R Paula09/2015
38022^482087+72623145123Enzo Doria04/2016
38032^482016-286565145102Enzo Doria07/2015
3804(19*10^145093+101)/3145094Robert Price09/2019
38052^481956+121145084Stefano Morozzi04/2021
380627535^32676-32676^27535145078Frank Doornink06/2024
38072^481840+15145049Robert Price09/2015
3808(23*10^145040+7)/3145041Robert Price05/2023
38092^481801-481801145037Henri Lifchitz03/2005
38102^481775+1869083145029Enzo Doria05/2016
381129^99167+2145022Ray Chandler08/2011
38122^481663+1875653144996Enzo Doria07/2016
38138*10^144977+27144978Robert Price09/2021
381429840^32393-32393^29840144953Frank Doornink06/2024
381536486^9379+9379^36486144929Hans Havermann12/2020
381631580^32209-32209^31580144922Frank Doornink01/2024
381735111^13378+13378^35111144882Hans Havermann01/2021
38182^481149-459073144841Enzo Doria05/2015
38192^481113+181419144830Boyan Hu04/2024
382034619^15246+15246^34619144817Hans Havermann01/2021
38212^481045-113215144809Enzo Doria07/2014
3822(64*10^144797+287)/9144798Robert Price04/2019
382327320^32629-32629^27320144758Frank Doornink06/2024
38242^480859-113695144753Enzo Doria09/2014
3825(106*10^144744+17)/3144746Robert Price04/2021
38267*10^144742-27144743Robert Price11/2022
38272^480766-2787191144725Enzo Doria11/2015
3828(21*27^101106-151)/26144720Curtis Bright05/2015
382928915^32438-32438^28915144710Frank Doornink06/2024
38302^480678+1874239144699Enzo Doria06/2016
3831(8*10^144683+1)/9144683Serge Batalov05/2010
3832L(692147)144651Henri Lifchitz10/2008
3833(76*10^144648+77)/9144649Robert Price10/2019
383432672^26721+26721^32672144635Hans Havermann01/2021
383531478^32153-32153^31478144625Frank Doornink01/2024
38362^480417+35144620Robert Price11/2015
38372^480296-59879144584Enzo Doria10/2015
383833157^22878+22878^33157144546Hans Havermann12/2020
383927520^32541-32541^27520144471Frank Doornink06/2024
384045494^1497+1497^45494144454Hans Havermann12/2020
38412^479844+3144448Donovan Johnson06/2006
384233442^20803+20803^33442144407Hans Havermann01/2021
3843(441*33^95095-3833)/32144405Eric Chen12/2023
384431892^32061-32061^31892144393Norbert Schneider01/2023
3845(27*2^479642+1)/733144386Lelio R Paula08/2015
3846(56*10^144380+169)/9144381Robert Price03/2022
384744917^1638+1638^44917144378Hans Havermann12/2020
3848(21*2^479605-1)/11144376Lelio R Paula09/2015
3849(56*10^144336+583)/9144337Robert Price08/2021
38505*2^479430-3144324Jon Grantham07/2023
38512^479348-2792219144299Enzo Doria02/2016
385231134^32111-32111^31134144283Frank Doornink01/2024
38533^302389-6242144277Enzo Doria05/2014
385431665^32056-32056^31665144271Frank Doornink01/2024
385533778^18641+18641^33778144248Hans Havermann01/2021
385629083^32312-32312^29083144230Frank Doornink06/2024
38572*10^144220-3144221Robert Price07/2015
385825313^32750-32750^25313144210Frank Doornink01/2024
38592^478904-109109144165Enzo Doria04/2014
386043698^1987+1987^43698144125Hans Havermann12/2020
386179^75948+75948144121Kellen Shenton06/2023
386226941^32522-32522^26941144086Frank Doornink06/2024
386336128^9723+9723^36128144072Hans Havermann01/2021
386432817^24518+24518^32817144050Hans Havermann12/2020
3865(772*10^144036-7)/9144038Robert Price06/2022
386634295^15828+15828^34295144020Hans Havermann01/2021
38672^478337-115333143994Enzo Doria07/2015
3868(7*2^478330-1)/3143993Lelio R Paula08/2015
386988^74047-87^74047143984Robert Price05/2015
387033242^21441+21441^33242143980Hans Havermann01/2021
3871(19*10^143963+467)/9143964Robert Price02/2018
3872(71^77761+1)/72143954Paul Bourdelais09/2017
387333490^19859+19859^33490143939Hans Havermann01/2021
3874(853*10^143931-7)/9143933Robert Price07/2021
38752^478088+27143919Robert Price11/2015
3876(8*10^143898-137)/3143899Robert Price03/2022
38777*10^143857-93143858Robert Price08/2020
38783*10^143844+61143845Robert Price09/2020
387941358^3005+3005^41358143837Hans Havermann01/2021
38802^477475-22071143735Enzo Doria07/2013
38812^477417-22123143717Enzo Doria07/2013
38822^477359-3577143700Yves Minet03/2017
388339435^4402+4402^39435143688Hans Havermann01/2021
3884(14*10^143662-71)/3143663Robert Price12/2018
38856^184614+5143658Paul Bourdelais01/2021
388646371^1252+1252^46371143640Hans Havermann12/2020
388734975^12748+12748^34975143588Hans Havermann01/2021
38882^476936-396765143573Enzo Doria07/2013
38892^476888-2791229143558Enzo Doria01/2016
38902^476868-1859939143552Enzo Doria11/2015
389140807^3294+3294^40807143548Hans Havermann12/2020
3892755^49878+49878^755143547Norbert Schneider04/2019
3893(19^112247-4^112247)/15143536Robert Price03/2021
389435561^10872+10872^35561143536Hans Havermann06/2021
389537637^6492+6492^37637143487Hans Havermann05/2021
389661567^214+214^61567143477Hans Havermann05/2021
389725933^32504-32504^25933143468Frank Doornink03/2024
38982^476558-113627143459Enzo Doria08/2014
38992^476478-45143435Lelio R Paula11/2017
390036380^8757+8757^36380143423Hans Havermann06/2021
390132510^25707+25707^32510143371Hans Havermann05/2021
39028*10^143361+17143362Robert Price07/2021
3903(2^475854+9)/73143245Lelio R Paula08/2015
39042^475813-113239143234Enzo Doria07/2014
3905(19*10^143212+137)/3143213Robert Price03/2022
390632218^27849+27849^32218143203Hans Havermann04/2021
3907580*33^94296+19143193Eric Chen12/2023
39082^475624-114059143178Enzo Doria11/2014
3909(11*2^475553-7)/15143156Renaud Lifchitz03/2011
39102^475480-2786129143134Enzo Doria10/2015
391133912^16621+16621^33912143131Hans Havermann05/2021
3912(19*10^143129-43)/3143130Robert Price05/2019
391331830^31373+31373^31830143126Hans Havermann05/2021
39146*10^143105-53143106Robert Price05/2021
3915(14*10^143097+73)/3143098Robert Price12/2018
39162^475299-111937143080Enzo Doria05/2014
391735488^10753+10753^35488143071Hans Havermann04/2021
391829695^31986-31986^29695143064Frank Doornink06/2024
39192^475160-2797859143038Enzo Doria04/2016
3920(2^475069+3)/395143008Lelio R Paula08/2015
39212^475027-461437142998Enzo Doria07/2015
3922(2^474958+78557)/3142977Lelio R Paula07/2015
3923(8*10^142932+43)/3142933Robert Price06/2018
392435055^11942+11942^35055142922Hans Havermann05/2021
392537650^6239+6239^37650142887Hans Havermann05/2021
3926(54^82471-1)/53142871Paul Bourdelais09/2017
392731205^31784-31784^31205142845Frank Doornink01/2024
3928(11*2^474432-1)/95142818Lelio R Paula09/2015
39292^474417-59923142814Enzo Doria10/2015
39304*10^142810-21142811Robert Price09/2018
393132287^26494+26494^32287142811Hans Havermann06/2021
393237162^6965+6965^37162142811Hans Havermann06/2021
3933(34*10^142805-601)/9142806Robert Price07/2022
393437456^6493+6493^37456142799Hans Havermann05/2021
393535141^11572+11572^35141142793Hans Havermann05/2021
393632231^26908+26908^32231142780Hans Havermann05/2021
3937(3*2^474166+1)/7142738Lelio R Paula08/2015
39382^474053+2897142705Lelio R Paula08/2012
3939(10^142699+359)/9142699Serge Batalov12/2014
394026073^32312-32312^26073142696Frank Doornink03/2024
3941898^48311-897^48311142676Jean-Louis Charton12/2012
39422^473740-1856639142610Enzo Doria09/2015
3943(25*10^142573-403)/9142574Robert Price12/2020
39442^473617-114223142573Enzo Doria12/2014
394536115^8856+8856^36115142555Hans Havermann05/2021
3946fibonacci(682007)+4142531Jon Grantham08/2023
39472^473257+1873217142465Enzo Doria06/2016
3948(19*2^473242+1)/11142461Lelio R Paula09/2015
394932750^22371+22371^32750142453Hans Havermann06/2021
3950(61*10^142446-1)/3142448Robert Price01/2020
3951(14*10^142440+61)/3142441Robert Price12/2018
3952(10^142425+359)/9142425Serge Batalov12/2014
39532^473101+773027142418Enzo Doria05/2016
3954(13*2^472838-1)/3142340Lelio R Paula09/2015
3955(17*2^472789-1)/187347142320Lelio R Paula09/2015
395636915^7162+7162^36915142309Hans Havermann05/2021
39572^472634-109511142278Enzo Doria04/2014
395831870^28997+28997^31870142216Hans Havermann06/2021
3959(48^84589+1)/49142213Robert Price01/2014
39607*10^142189+87142190Robert Price07/2019
39612^472258+7142164Lelio R Paula08/2015
396240135^3484+3484^40135142162Hans Havermann05/2021
39639*33^93598+26142131Eric Chen12/2023
3964(23*10^142105+91)/3142106Robert Price08/2019
3965tau(317^10330)142098Nik Lygeros / Olivier Rozier / LR team10/2013
3966(11*2^471913-1)/21142060Lelio R Paula09/2015
3967(16*10^142058+197)/3142059Robert Price04/2019
39689*10^142037+91142038Robert Price10/2020
3969(4*10^142034+17)/3142035Tyler Busby01/2023
39702^471792+1880881142024Enzo Doria11/2016
3971(509*10^142018+31)/9142020Robert Price08/2022
3972(31*2^471580-1)/135141960Lelio R Paula08/2015
3973(4*10^141926-79)/3141927Robert Price02/2018
39742^471464-111546435141925Paul Bourdelais10/2021
3975(904*19^110984-1)/3141924Curtis Bright05/2015
3976(14*10^141853+37)/3141854Robert Price12/2018
3977(41*10^141836-59)/9141837Robert Price10/2018
39784*5^202913-9141831Lelio R Paula04/2015
39792*7^167812-3141818Lelio R Paula12/2014
39802^471043+35141799Robert Price11/2015
3981(11*2^470956-1)/7945141770Lelio R Paula08/2015
398243636^1773+1773^43636141761Hans Havermann05/2021
3983(2*10^141751-17)/3141751Serge Batalov11/2022
3984(53*10^141722-611)/9141723Robert Price02/2022
3985(11*10^141718-131)/3141719Robert Price09/2018
3986(61*10^141716+47)/9141717Robert Price07/2022
398726057^32088-32088^26057141699Frank Doornink03/2024
39882^470692+76771141693Enzo Doria05/2016
398950160^667+667^50160141659Hans Havermann05/2021
399031522^31181+31181^31522141657Hans Havermann05/2021
399129487^31690-31690^29487141643Frank Doornink06/2024
399233076^19135+19135^33076141626Hans Havermann04/2021
399328237^31818-31818^28237141617Frank Doornink06/2024
3994(91*10^141610+71)/9141612Robert Price01/2022
3995(21*2^470391+1)/533141601Lelio R Paula09/2015
3996(5*10^141594-23)/9141594Serge Batalov11/2022
399731932^27155+27155^31932141582Hans Havermann05/2021
399836449^7660+7660^36449141577Hans Havermann05/2021
39992^470305-459373141576Enzo Doria05/2015
400032195^24936+24936^32195141556Hans Havermann05/2021


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: November, 12 2024 22:37 (Time in France)

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