PRP Records

Probable Primes Top 10000

(295503 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) !!!


Submit your PRPs


See the Top discoverers
See the Latest PRPs
Search by form



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 ?
350136303^12016+12016^36303148108Hans Havermann10/2020
3502(77*10^148089-149)/9148090Robert Price03/2022
3503(16*10^148071+41)/3148072Robert Price03/2019
3504187^65175-2148068Lelio R Paula11/2017
35052^491851+1871453148062Enzo Doria05/2016
3506(68*10^148060-257)/9148061Robert Price07/2019
3507(151*10^148020-1)/3148022Robert Price03/2020
350839153^6032+6032^39153148017Hans Havermann10/2020
350936798^10507+10507^36798147983Hans Havermann12/2020
3510(26*10^147973-23)/3147974Robert Price12/2019
35112^491521-1865323147963Enzo Doria02/2016
3512(2^491476+7)/71147948Lelio R Paula10/2015
35132*10^147928+47147929Robert Price12/2021
35142^491391-7807147924Lelio R Paula01/2013
351539736^5279+5279^39736147920Hans Havermann11/2020
35162^491370-113297147918Enzo Doria07/2014
3517(32760^32760+32759^32759)/95546586737133567708319147900Robert Price07/2016
351844368^2155+2155^44368147899Hans Havermann12/2020
3519(17*10^147890+79)/3147891Robert Price04/2019
352094*10^147871-3147873Robert Price05/2020
352110^147843+620967147844Patrick De Geest05/2021
352210^147843-50000000001147843Robert Price12/2020
352310^147843-182891147843Patrick De Geest05/2021
352435805^13346+13346^35805147709Hans Havermann11/2020
35252^490672+255255147707Paul Bourdelais10/2021
35262^490660-17147704Lelio R Paula12/2017
3527(229*10^147699-1)/3147701Robert Price07/2020
352840656^4289+4289^40656147678Hans Havermann11/2020
35292^490550+1179439147671Enzo Doria06/2016
353027249^33292-33292^27249147662Frank Doornink06/2024
3531(23*10^147649-59)/9147650Robert Price05/2018
35322^490303+2793653147596Enzo Doria03/2016
35332^490266+255255147585Paul Bourdelais10/2021
3534199^64181-2147543Lelio R Paula11/2017
353532849^30958+30958^32849147518Hans Havermann11/2020
35362^489871-286987147466Enzo Doria07/2015
35372^489864-351899147464Enzo Doria07/2015
3538175^65724-2147422Lelio R Paula11/2017
35392^489712+1874851147419Enzo Doria06/2016
354034473^18830+18830^34473147367Hans Havermann11/2020
354163^81896-2147359Lelio R Paula10/2017
354234580^18237+18237^34580147344Hans Havermann11/2020
3543(11*10^147313-107)/3147314Robert Price09/2018
3544(397*10^147310+17)/9147312Robert Price03/2022
35452^489305-59815147296Enzo Doria10/2015
3546(2^489280-7)/6381147285Lelio R Paula09/2015
35472*10^147264-61147265Robert Price10/2021
35482*10^147260+29147261Robert Price02/2021
354933556^24457+24457^33556147258Hans Havermann11/2020
35502^489125+80357147242Enzo Doria06/2016
355110^147240-40000001147240Robert Price07/2022
355232835^30452+30452^32835147220Hans Havermann12/2020
3553(19*10^147213-97)/3147214Robert Price10/2021
355427123^33190-33190^27123147143Frank Doornink01/2024
3555(148*10^147139-1)/3147141Robert Price03/2020
355634338^19255+19255^34338147123Hans Havermann11/2020
35572^488648-112799147098Enzo Doria07/2014
35582^488627-350317147092Enzo Doria06/2015
355933432^25075+25075^33432147076Hans Havermann12/2020
3560(2^488441-1)/(61543567*30051203516986199)147012Dario Alpern12/2014
35612^488280-2165146987Yves Minet07/2014
35622^488278+45146987Lelio R Paula12/2017
35632^487927-39146881Lelio R Paula12/2017
3564(7*10^146860-13)/3146861Robert Price07/2018
3565(26*10^146856-77)/3146857Robert Price11/2019
356632948^28611+28611^32948146834Hans Havermann11/2020
356742596^2799+2799^42596146829Hans Havermann12/2020
35682^487726-1863341146821Enzo Doria12/2015
356943838^2229+2229^43838146775Hans Havermann11/2020
357035005^15594+15594^35005146775Hans Havermann11/2020
3571(167*10^146764+7)/3146766Robert Price04/2021
357253^85114+85114146761Kellen Shenton05/2022
3573(59*10^146738+157)/9146739Robert Price12/2021
3574((10^73362-1)*10000/9+6701)*10^73362+(10^73362-1)/9146728Hans Havermann09/2019
357532963^28234+28234^32963146711Hans Havermann12/2020
3576(22*10^146661-19)/3146662Robert Price04/2019
357733958^20825+20825^33958146651Hans Havermann12/2020
357826289^33178-33178^26289146640Frank Doornink03/2024
35792^487121-39523146639Enzo Doria09/2015
358061063^252+252^61063146637Hans Havermann12/2020
3581(7*2^486967+1)/39146591Lelio R Paula09/2015
358234099^19900+19900^34099146587Hans Havermann11/2020
35832^486893-79146570Yves Minet09/2017
358436818^9567+9567^36818146565Hans Havermann12/2020
35852^486840+1879141146554Enzo Doria08/2016
35862^486774-87146534Lelio R Paula12/2017
358738655^6176+6176^38655146530Hans Havermann11/2020
35888*10^146522-81146523Robert Price02/2021
358932820^29059+29059^32820146485Hans Havermann12/2020
359037261^8530+8530^37261146472Hans Havermann12/2020
359166953^154+154^66953146462Hans Havermann12/2020
359296^73877-95^73877146445Robert Price10/2015
35938*10^146421+81146422Robert Price08/2019
359433153^26090+26090^33153146420Hans Havermann11/2020
35952^486275+23961146384Enzo Doria10/2023
3596(52^85259+1)/53146304Paul Bourdelais09/2017
3597179^64935+2146290Lelio R Paula10/2017
359832595^30758+30758^32595146285Hans Havermann11/2020
359934972^15157+15157^34972146205Hans Havermann12/2020
3600(16*10^146200+131)/3146201Robert Price03/2022
3601(19*10^146181-49)/3146182Robert Price05/2019
36022^485531-114621146160Enzo Doria05/2015
36032^485473-933075146142Paul Bourdelais06/2021
3604(2^485461-9)/4249146135Lelio R Paula09/2015
3605(22*10^146130-193)/9146131Robert Price07/2022
36062^485389+81887146117Enzo Doria08/2016
360732554^30773+30773^32554146108Hans Havermann11/2020
360828075^32844-32844^28075146101Frank Doornink06/2024
3609(10^146063+71)/9146063Serge Batalov07/2015
36102*10^146051-63146052Robert Price01/2022
3611(2^485119+7)/2745146032Lelio R Paula09/2015
3612(22*10^146029+257)/9146030Robert Price06/2018
36137*10^145982-53145983Robert Price06/2020
36142^484743+1872923145923Enzo Doria05/2016
361533140^25287+25287^33140145913Hans Havermann01/2021
361637875^7112+7112^37875145895Hans Havermann01/2021
361730542^32529-32529^30542145890Frank Doornink06/2024
361832862^27473+27473^32862145872Hans Havermann01/2021
361932836^27587+27587^32836145815Hans Havermann01/2021
36202^484341+1879157145802Enzo Doria08/2016
36212*10^145784-91145785Robert Price04/2020
36222^484271-51145781Lelio R Paula11/2017
3623(188*10^145750-11)/3145752Robert Price02/2022
362470^78989-69^78989145743Robert Price01/2014
362551^85334+2145714Robert Price07/2015
36262^483886-1857101145665Enzo Doria10/2015
362729312^32607-32607^29312145657Frank Doornink06/2024
362833350^23307+23307^33350145656Hans Havermann01/2021
3629(19*10^145585+131)/3145586Robert Price06/2020
363031815^32332-32332^31815145580Frank Doornink01/2024
36312^483563-1863457145567Enzo Doria12/2015
36324*10^145563-69145564Robert Price01/2022
36332^483516-1861409145553Enzo Doria11/2015
36342^483384-115019145514Enzo Doria06/2015
3635(259*10^145501-1)/3145503Robert Price12/2020
3636(19*10^145499-61)/3145500Robert Price05/2019
36372^483302-3221145489Lelio R Paula12/2012
3638(23*10^145463+61)/3145464Robert Price01/2022
363935523^12434+12434^35523145453Hans Havermann01/2021
3640(29121^32761-1)/(29121^181-1)145444Ryan Propper11/2023
36412^483046+1874029145412Enzo Doria06/2016
36422^482991-2789317145395Enzo Doria12/2015
36432^482978-2789711145391Enzo Doria12/2015
36442^482966-2789711145388Enzo Doria12/2015
36452^482817-1858843145343Enzo Doria10/2015
36462^482751-113635145323Enzo Doria08/2014
36472^482705-459763145309Enzo Doria05/2015
3648(4^241306+11)/3145281Robert Price03/2017
3649(238*10^145276-1)/3145278Robert Price04/2020
3650(19*2^482534+1)/7145258Lelio R Paula09/2015
365153^84239-52^84239145252Robert Price01/2013
36522^482386+212419145213Enzo Doria08/2023
365347952^1067+1067^47952145207Hans Havermann01/2021
3654(2^482333+5)/9287145193Lelio R Paula09/2015
36552^482087+72623145123Enzo Doria04/2016
36562^482016-286565145102Enzo Doria07/2015
3657(19*10^145093+101)/3145094Robert Price09/2019
36582^481956+121145084Stefano Morozzi04/2021
365927535^32676-32676^27535145078Frank Doornink06/2024
36602^481840+15145049Robert Price09/2015
3661(23*10^145040+7)/3145041Robert Price05/2023
36622^481801-481801145037Henri Lifchitz03/2005
36632^481775+1869083145029Enzo Doria05/2016
366429^99167+2145022Ray Chandler08/2011
36652^481663+1875653144996Enzo Doria07/2016
36668*10^144977+27144978Robert Price09/2021
366729840^32393-32393^29840144953Frank Doornink06/2024
366836486^9379+9379^36486144929Hans Havermann12/2020
366931580^32209-32209^31580144922Frank Doornink01/2024
367035111^13378+13378^35111144882Hans Havermann01/2021
36712^481149-459073144841Enzo Doria05/2015
36722^481113+181419144830Boyan Hu04/2024
367334619^15246+15246^34619144817Hans Havermann01/2021
36742^481045-113215144809Enzo Doria07/2014
3675(64*10^144797+287)/9144798Robert Price04/2019
367627320^32629-32629^27320144758Frank Doornink06/2024
36772^480859-113695144753Enzo Doria09/2014
3678(106*10^144744+17)/3144746Robert Price04/2021
36797*10^144742-27144743Robert Price11/2022
36802^480766-2787191144725Enzo Doria11/2015
3681(21*27^101106-151)/26144720Curtis Bright05/2015
368228915^32438-32438^28915144710Frank Doornink06/2024
36832^480678+1874239144699Enzo Doria06/2016
3684(8*10^144683+1)/9144683Serge Batalov05/2010
3685L(692147)144651Henri Lifchitz10/2008
3686(76*10^144648+77)/9144649Robert Price10/2019
368732672^26721+26721^32672144635Hans Havermann01/2021
368831478^32153-32153^31478144625Frank Doornink01/2024
36892^480417+35144620Robert Price11/2015
36902^480296-59879144584Enzo Doria10/2015
369133157^22878+22878^33157144546Hans Havermann12/2020
369227520^32541-32541^27520144471Frank Doornink06/2024
369345494^1497+1497^45494144454Hans Havermann12/2020
36942^479844+3144448Donovan Johnson06/2006
369533442^20803+20803^33442144407Hans Havermann01/2021
3696(441*33^95095-3833)/32144405Eric Chen12/2023
369731892^32061-32061^31892144393Norbert Schneider01/2023
3698(27*2^479642+1)/733144386Lelio R Paula08/2015
3699(56*10^144380+169)/9144381Robert Price03/2022
370044917^1638+1638^44917144378Hans Havermann12/2020
3701(21*2^479605-1)/11144376Lelio R Paula09/2015
3702(56*10^144336+583)/9144337Robert Price08/2021
37035*2^479430-3144324Jon Grantham07/2023
37042^479348-2792219144299Enzo Doria02/2016
370531134^32111-32111^31134144283Frank Doornink01/2024
37063^302389-6242144277Enzo Doria05/2014
370731665^32056-32056^31665144271Frank Doornink01/2024
370833778^18641+18641^33778144248Hans Havermann01/2021
370929083^32312-32312^29083144230Frank Doornink06/2024
37102*10^144220-3144221Robert Price07/2015
371125313^32750-32750^25313144210Frank Doornink01/2024
37122^478904-109109144165Enzo Doria04/2014
371343698^1987+1987^43698144125Hans Havermann12/2020
371479^75948+75948144121Kellen Shenton06/2023
371526941^32522-32522^26941144086Frank Doornink06/2024
371636128^9723+9723^36128144072Hans Havermann01/2021
371732817^24518+24518^32817144050Hans Havermann12/2020
3718(772*10^144036-7)/9144038Robert Price06/2022
371934295^15828+15828^34295144020Hans Havermann01/2021
37202^478337-115333143994Enzo Doria07/2015
3721(7*2^478330-1)/3143993Lelio R Paula08/2015
372288^74047-87^74047143984Robert Price05/2015
372333242^21441+21441^33242143980Hans Havermann01/2021
3724(19*10^143963+467)/9143964Robert Price02/2018
3725(71^77761+1)/72143954Paul Bourdelais09/2017
372633490^19859+19859^33490143939Hans Havermann01/2021
3727(853*10^143931-7)/9143933Robert Price07/2021
37282^478088+27143919Robert Price11/2015
3729(8*10^143898-137)/3143899Robert Price03/2022
37307*10^143857-93143858Robert Price08/2020
37313*10^143844+61143845Robert Price09/2020
373241358^3005+3005^41358143837Hans Havermann01/2021
37332^477475-22071143735Enzo Doria07/2013
37342^477417-22123143717Enzo Doria07/2013
37352^477359-3577143700Yves Minet03/2017
373639435^4402+4402^39435143688Hans Havermann01/2021
3737(14*10^143662-71)/3143663Robert Price12/2018
37386^184614+5143658Paul Bourdelais01/2021
373946371^1252+1252^46371143640Hans Havermann12/2020
374034975^12748+12748^34975143588Hans Havermann01/2021
37412^476936-396765143573Enzo Doria07/2013
37422^476888-2791229143558Enzo Doria01/2016
37432^476868-1859939143552Enzo Doria11/2015
374440807^3294+3294^40807143548Hans Havermann12/2020
3745755^49878+49878^755143547Norbert Schneider04/2019
3746(19^112247-4^112247)/15143536Robert Price03/2021
374735561^10872+10872^35561143536Hans Havermann06/2021
374837637^6492+6492^37637143487Hans Havermann05/2021
374961567^214+214^61567143477Hans Havermann05/2021
375025933^32504-32504^25933143468Frank Doornink03/2024


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 22 2024 13:34 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!