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 ?
35012^491851+1871453148062Enzo Doria05/2016
3502(68*10^148060-257)/9148061Robert Price07/2019
3503(151*10^148020-1)/3148022Robert Price03/2020
350439153^6032+6032^39153148017Hans Havermann10/2020
350536798^10507+10507^36798147983Hans Havermann12/2020
3506(26*10^147973-23)/3147974Robert Price12/2019
35072^491521-1865323147963Enzo Doria02/2016
3508(2^491476+7)/71147948Lelio R Paula10/2015
35092*10^147928+47147929Robert Price12/2021
35102^491391-7807147924Lelio R Paula01/2013
351139736^5279+5279^39736147920Hans Havermann11/2020
35122^491370-113297147918Enzo Doria07/2014
3513(32760^32760+32759^32759)/95546586737133567708319147900Robert Price07/2016
351444368^2155+2155^44368147899Hans Havermann12/2020
3515(17*10^147890+79)/3147891Robert Price04/2019
351694*10^147871-3147873Robert Price05/2020
351710^147843+620967147844Patrick De Geest05/2021
351810^147843-50000000001147843Robert Price12/2020
351910^147843-182891147843Patrick De Geest05/2021
352035805^13346+13346^35805147709Hans Havermann11/2020
35212^490672+255255147707Paul Bourdelais10/2021
35222^490660-17147704Lelio R Paula12/2017
3523(229*10^147699-1)/3147701Robert Price07/2020
352440656^4289+4289^40656147678Hans Havermann11/2020
35252^490550+1179439147671Enzo Doria06/2016
352627249^33292-33292^27249147662Frank Doornink06/2024
3527(23*10^147649-59)/9147650Robert Price05/2018
35282^490303+2793653147596Enzo Doria03/2016
35292^490266+255255147585Paul Bourdelais10/2021
3530199^64181-2147543Lelio R Paula11/2017
353132849^30958+30958^32849147518Hans Havermann11/2020
35322^489871-286987147466Enzo Doria07/2015
35332^489864-351899147464Enzo Doria07/2015
3534175^65724-2147422Lelio R Paula11/2017
35352^489712+1874851147419Enzo Doria06/2016
353634473^18830+18830^34473147367Hans Havermann11/2020
353763^81896-2147359Lelio R Paula10/2017
353834580^18237+18237^34580147344Hans Havermann11/2020
3539(11*10^147313-107)/3147314Robert Price09/2018
3540(397*10^147310+17)/9147312Robert Price03/2022
35412^489305-59815147296Enzo Doria10/2015
3542(2^489280-7)/6381147285Lelio R Paula09/2015
35432*10^147264-61147265Robert Price10/2021
35442*10^147260+29147261Robert Price02/2021
354533556^24457+24457^33556147258Hans Havermann11/2020
35462^489125+80357147242Enzo Doria06/2016
354710^147240-40000001147240Robert Price07/2022
354832835^30452+30452^32835147220Hans Havermann12/2020
3549(19*10^147213-97)/3147214Robert Price10/2021
355027123^33190-33190^27123147143Frank Doornink01/2024
3551(148*10^147139-1)/3147141Robert Price03/2020
355234338^19255+19255^34338147123Hans Havermann11/2020
35532^488648-112799147098Enzo Doria07/2014
35542^488627-350317147092Enzo Doria06/2015
355533432^25075+25075^33432147076Hans Havermann12/2020
3556(2^488441-1)/(61543567*30051203516986199)147012Dario Alpern12/2014
35572^488280-2165146987Yves Minet07/2014
35582^488278+45146987Lelio R Paula12/2017
35592^487927-39146881Lelio R Paula12/2017
3560(7*10^146860-13)/3146861Robert Price07/2018
3561(26*10^146856-77)/3146857Robert Price11/2019
356232948^28611+28611^32948146834Hans Havermann11/2020
356342596^2799+2799^42596146829Hans Havermann12/2020
35642^487726-1863341146821Enzo Doria12/2015
356543838^2229+2229^43838146775Hans Havermann11/2020
356635005^15594+15594^35005146775Hans Havermann11/2020
3567(167*10^146764+7)/3146766Robert Price04/2021
356853^85114+85114146761Kellen Shenton05/2022
3569(59*10^146738+157)/9146739Robert Price12/2021
3570((10^73362-1)*10000/9+6701)*10^73362+(10^73362-1)/9146728Hans Havermann09/2019
357132963^28234+28234^32963146711Hans Havermann12/2020
3572(22*10^146661-19)/3146662Robert Price04/2019
357333958^20825+20825^33958146651Hans Havermann12/2020
357426289^33178-33178^26289146640Frank Doornink03/2024
35752^487121-39523146639Enzo Doria09/2015
357661063^252+252^61063146637Hans Havermann12/2020
3577(7*2^486967+1)/39146591Lelio R Paula09/2015
357834099^19900+19900^34099146587Hans Havermann11/2020
35792^486893-79146570Yves Minet09/2017
358036818^9567+9567^36818146565Hans Havermann12/2020
35812^486840+1879141146554Enzo Doria08/2016
35822^486774-87146534Lelio R Paula12/2017
358338655^6176+6176^38655146530Hans Havermann11/2020
35848*10^146522-81146523Robert Price02/2021
358532820^29059+29059^32820146485Hans Havermann12/2020
358637261^8530+8530^37261146472Hans Havermann12/2020
358766953^154+154^66953146462Hans Havermann12/2020
358896^73877-95^73877146445Robert Price10/2015
35898*10^146421+81146422Robert Price08/2019
359033153^26090+26090^33153146420Hans Havermann11/2020
35912^486275+23961146384Enzo Doria10/2023
3592(52^85259+1)/53146304Paul Bourdelais09/2017
3593179^64935+2146290Lelio R Paula10/2017
359432595^30758+30758^32595146285Hans Havermann11/2020
359534972^15157+15157^34972146205Hans Havermann12/2020
3596(16*10^146200+131)/3146201Robert Price03/2022
3597(19*10^146181-49)/3146182Robert Price05/2019
35982^485531-114621146160Enzo Doria05/2015
35992^485473-933075146142Paul Bourdelais06/2021
3600(2^485461-9)/4249146135Lelio R Paula09/2015
3601(22*10^146130-193)/9146131Robert Price07/2022
36022^485389+81887146117Enzo Doria08/2016
360332554^30773+30773^32554146108Hans Havermann11/2020
360428075^32844-32844^28075146101Frank Doornink06/2024
3605(10^146063+71)/9146063Serge Batalov07/2015
36062*10^146051-63146052Robert Price01/2022
3607(2^485119+7)/2745146032Lelio R Paula09/2015
3608(22*10^146029+257)/9146030Robert Price06/2018
36097*10^145982-53145983Robert Price06/2020
36102^484743+1872923145923Enzo Doria05/2016
361133140^25287+25287^33140145913Hans Havermann01/2021
361237875^7112+7112^37875145895Hans Havermann01/2021
361330542^32529-32529^30542145890Frank Doornink06/2024
361432862^27473+27473^32862145872Hans Havermann01/2021
361532836^27587+27587^32836145815Hans Havermann01/2021
36162^484341+1879157145802Enzo Doria08/2016
36172*10^145784-91145785Robert Price04/2020
36182^484271-51145781Lelio R Paula11/2017
3619(188*10^145750-11)/3145752Robert Price02/2022
362070^78989-69^78989145743Robert Price01/2014
362151^85334+2145714Robert Price07/2015
36222^483886-1857101145665Enzo Doria10/2015
362329312^32607-32607^29312145657Frank Doornink06/2024
362433350^23307+23307^33350145656Hans Havermann01/2021
3625(19*10^145585+131)/3145586Robert Price06/2020
362631815^32332-32332^31815145580Frank Doornink01/2024
36272^483563-1863457145567Enzo Doria12/2015
36284*10^145563-69145564Robert Price01/2022
36292^483516-1861409145553Enzo Doria11/2015
36302^483384-115019145514Enzo Doria06/2015
3631(259*10^145501-1)/3145503Robert Price12/2020
3632(19*10^145499-61)/3145500Robert Price05/2019
36332^483302-3221145489Lelio R Paula12/2012
3634(23*10^145463+61)/3145464Robert Price01/2022
363535523^12434+12434^35523145453Hans Havermann01/2021
3636(29121^32761-1)/(29121^181-1)145444Ryan Propper11/2023
36372^483046+1874029145412Enzo Doria06/2016
36382^482991-2789317145395Enzo Doria12/2015
36392^482978-2789711145391Enzo Doria12/2015
36402^482966-2789711145388Enzo Doria12/2015
36412^482817-1858843145343Enzo Doria10/2015
36422^482751-113635145323Enzo Doria08/2014
36432^482705-459763145309Enzo Doria05/2015
3644(4^241306+11)/3145281Robert Price03/2017
3645(238*10^145276-1)/3145278Robert Price04/2020
3646(19*2^482534+1)/7145258Lelio R Paula09/2015
364753^84239-52^84239145252Robert Price01/2013
36482^482386+212419145213Enzo Doria08/2023
364947952^1067+1067^47952145207Hans Havermann01/2021
3650(2^482333+5)/9287145193Lelio R Paula09/2015
36512^482087+72623145123Enzo Doria04/2016
36522^482016-286565145102Enzo Doria07/2015
3653(19*10^145093+101)/3145094Robert Price09/2019
36542^481956+121145084Stefano Morozzi04/2021
365527535^32676-32676^27535145078Frank Doornink06/2024
36562^481840+15145049Robert Price09/2015
3657(23*10^145040+7)/3145041Robert Price05/2023
36582^481801-481801145037Henri Lifchitz03/2005
36592^481775+1869083145029Enzo Doria05/2016
366029^99167+2145022Ray Chandler08/2011
36612^481663+1875653144996Enzo Doria07/2016
36628*10^144977+27144978Robert Price09/2021
366329840^32393-32393^29840144953Frank Doornink06/2024
366436486^9379+9379^36486144929Hans Havermann12/2020
366531580^32209-32209^31580144922Frank Doornink01/2024
366635111^13378+13378^35111144882Hans Havermann01/2021
36672^481149-459073144841Enzo Doria05/2015
36682^481113+181419144830Boyan Hu04/2024
366934619^15246+15246^34619144817Hans Havermann01/2021
36702^481045-113215144809Enzo Doria07/2014
3671(64*10^144797+287)/9144798Robert Price04/2019
367227320^32629-32629^27320144758Frank Doornink06/2024
36732^480859-113695144753Enzo Doria09/2014
3674(106*10^144744+17)/3144746Robert Price04/2021
36757*10^144742-27144743Robert Price11/2022
36762^480766-2787191144725Enzo Doria11/2015
3677(21*27^101106-151)/26144720Curtis Bright05/2015
367828915^32438-32438^28915144710Frank Doornink06/2024
36792^480678+1874239144699Enzo Doria06/2016
3680(8*10^144683+1)/9144683Serge Batalov05/2010
3681L(692147)144651Henri Lifchitz10/2008
3682(76*10^144648+77)/9144649Robert Price10/2019
368332672^26721+26721^32672144635Hans Havermann01/2021
368431478^32153-32153^31478144625Frank Doornink01/2024
36852^480417+35144620Robert Price11/2015
36862^480296-59879144584Enzo Doria10/2015
368733157^22878+22878^33157144546Hans Havermann12/2020
368827520^32541-32541^27520144471Frank Doornink06/2024
368945494^1497+1497^45494144454Hans Havermann12/2020
36902^479844+3144448Donovan Johnson06/2006
369133442^20803+20803^33442144407Hans Havermann01/2021
3692(441*33^95095-3833)/32144405Eric Chen12/2023
369331892^32061-32061^31892144393Norbert Schneider01/2023
3694(27*2^479642+1)/733144386Lelio R Paula08/2015
3695(56*10^144380+169)/9144381Robert Price03/2022
369644917^1638+1638^44917144378Hans Havermann12/2020
3697(21*2^479605-1)/11144376Lelio R Paula09/2015
3698(56*10^144336+583)/9144337Robert Price08/2021
36995*2^479430-3144324Jon Grantham07/2023
37002^479348-2792219144299Enzo Doria02/2016
370131134^32111-32111^31134144283Frank Doornink01/2024
37023^302389-6242144277Enzo Doria05/2014
370331665^32056-32056^31665144271Frank Doornink01/2024
370433778^18641+18641^33778144248Hans Havermann01/2021
370529083^32312-32312^29083144230Frank Doornink06/2024
37062*10^144220-3144221Robert Price07/2015
370725313^32750-32750^25313144210Frank Doornink01/2024
37082^478904-109109144165Enzo Doria04/2014
370943698^1987+1987^43698144125Hans Havermann12/2020
371079^75948+75948144121Kellen Shenton06/2023
371126941^32522-32522^26941144086Frank Doornink06/2024
371236128^9723+9723^36128144072Hans Havermann01/2021
371332817^24518+24518^32817144050Hans Havermann12/2020
3714(772*10^144036-7)/9144038Robert Price06/2022
371534295^15828+15828^34295144020Hans Havermann01/2021
37162^478337-115333143994Enzo Doria07/2015
3717(7*2^478330-1)/3143993Lelio R Paula08/2015
371888^74047-87^74047143984Robert Price05/2015
371933242^21441+21441^33242143980Hans Havermann01/2021
3720(19*10^143963+467)/9143964Robert Price02/2018
3721(71^77761+1)/72143954Paul Bourdelais09/2017
372233490^19859+19859^33490143939Hans Havermann01/2021
3723(853*10^143931-7)/9143933Robert Price07/2021
37242^478088+27143919Robert Price11/2015
3725(8*10^143898-137)/3143899Robert Price03/2022
37267*10^143857-93143858Robert Price08/2020
37273*10^143844+61143845Robert Price09/2020
372841358^3005+3005^41358143837Hans Havermann01/2021
37292^477475-22071143735Enzo Doria07/2013
37302^477417-22123143717Enzo Doria07/2013
37312^477359-3577143700Yves Minet03/2017
373239435^4402+4402^39435143688Hans Havermann01/2021
3733(14*10^143662-71)/3143663Robert Price12/2018
37346^184614+5143658Paul Bourdelais01/2021
373546371^1252+1252^46371143640Hans Havermann12/2020
373634975^12748+12748^34975143588Hans Havermann01/2021
37372^476936-396765143573Enzo Doria07/2013
37382^476888-2791229143558Enzo Doria01/2016
37392^476868-1859939143552Enzo Doria11/2015
374040807^3294+3294^40807143548Hans Havermann12/2020
3741755^49878+49878^755143547Norbert Schneider04/2019
3742(19^112247-4^112247)/15143536Robert Price03/2021
374335561^10872+10872^35561143536Hans Havermann06/2021
374437637^6492+6492^37637143487Hans Havermann05/2021
374561567^214+214^61567143477Hans Havermann05/2021
374625933^32504-32504^25933143468Frank Doornink03/2024
37472^476558-113627143459Enzo Doria08/2014
37482^476478-45143435Lelio R Paula11/2017
374936380^8757+8757^36380143423Hans Havermann06/2021
375032510^25707+25707^32510143371Hans Havermann05/2021


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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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