PRP Records

Probable Primes Top 10000

(301692 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 ?
251124452^80465+80465^124452610513Ryan Propper10/2023
25211^586020-2610277Paul Bourdelais11/2021
253(19^476929+1)/20609874Paul Bourdelais03/2015
254(7^720497-2^720497)/5608890Jon Grantham08/2023
2552^2020893-25608350Boyan Hu01/2025
2562^2019811+1867211608024Enzo Doria04/2018
257F(2904353)606974Henri Lifchitz07/2014
2582^2014720+71893606492Enzo Doria04/2018
259(5^866029-3^866029)/2605328Jon Grantham08/2023
260L(2894561)604928Ryan Propper06/2022
261(18^481147+1)/19603970Paul Bourdelais07/2011
262200^262144+119^262144603202Kellen Shenton08/2022
263(20^463511+1)/21603041Paul Bourdelais03/2025
264(70^326437-1)/69602307Paul Bourdelais02/2025
265(83467^121801-1)/(83467^349-1)597728Ryan Propper11/2023
266(61448^124609-1)/(61448^353-1)595001Ryan Propper11/2023
267(15^505117-1)/14594063Paul Bourdelais01/2015
2682^1971190+43819593388Enzo Doria04/2025
26981^310721-80^310721593007Paul Bourdelais07/2023
270(152^270217-1)/(152-1)589570Michael Stocker06/2015
2712^1951707+234041587523Enzo Doria04/2025
272Phi(177147,94259)587458Anonymous09/2022
2732^1950002+1867369587010Enzo Doria02/2018
274116265^111218+111218^116265586694Ryan Propper10/2023
2752^1940812+3584243Paul Bourdelais06/2020
2761933695^2+2^1933695582101Ryan Propper05/2023
277(5^832151-2^832151)/3581649Jon Grantham08/2023
2782^1930263+229883581068Enzo Doria01/2025
279(129810^113569-1)/(129810^337-1)578991Ryan Propper11/2023
2802^1923104+153578912Stefano Morozzi07/2021
281(48^343901-1)/47578179Paul Bourdelais03/2025
282116761^87652+87652^116761577122Ryan Propper10/2023
283116395^87994+87994^116395575510Ryan Propper10/2023
284(3^1205459+1)/4575150Paul Bourdelais08/2015
2852^1904743+42713573385Enzo Doria06/2025
2862^1900607-47727572140Stefano Morozzi07/2025
2872^1900604-7659572139Stefano Morozzi07/2025
2882^1900012-162405571961Stefano Morozzi07/2025
2892^1900005-101625571959Stefano Morozzi07/2025
2902^1900005-101713571959Stefano Morozzi07/2025
2912^1900002-24945571958Stefano Morozzi07/2025
2922^1895562+229729570622Enzo Doria02/2025
293(160972^109561-1)/(160972^331-1)568734Ryan Propper11/2023
2942^1887092+38191568072Enzo Doria01/2025
295(37015^124609-1)/(37015^353-1)567649Ryan Propper11/2023
2962^1882800+384541566780Enzo Doria12/2017
297(2^1882787-2^941394+1)/5566775Borys Jaworski11/2012
2982^1882474+71389566682Enzo Doria04/2018
299(6^727496-11)/5566102Paul Bourdelais08/2019
3002^1875552+3564598Paul Bourdelais04/2020
301(145373^109561-1)/(145373^331-1)563899Ryan Propper11/2023
302(10^563535-7)/3563535Rytis Slatkevicius02/2023
3033^1180181-2563090Jorge Coveiro05/2020
304(15063^134689-1)/(15063^367-1)561186Ryan Propper11/2023
3052^1852265+1890425557588Enzo Doria11/2017
3065^797390-2557352Paul Bourdelais03/2021
3072^1851447+38573557342Enzo Doria02/2025
308(10^556441-7^556441)/3556441Jon Grantham07/2023
3098^615997-7^615997556301Jean-Louis Charton07/2009
310(5^795829-2^795829)/3556261Jon Grantham08/2023
311Tau(773^34960)555339Nik Lygeros / Olivier Rozier09/2015
312((((((((((1361^3+6)^3+80)^3+12)^3+450)^3+894)^3+3636)^3+70756)^3+97220)^3+66768)^3+300840)^3+1623568555154Serge Batalov08/2013
3132^1835428+227221552519Enzo Doria01/2025
3142^1835205+225197552452Enzo Doria10/2024
3152^1827961+43427550272Enzo Doria05/2025
3162^1825513+32507549535Enzo Doria07/2024
3172^1823921+34937549055Enzo Doria11/2024
3182^1822728+228991548696Enzo Doria02/2025
3192^1819810+42727547818Enzo Doria03/2025
320(42^337081-1)/41547165Paul Bourdelais09/2021
321114868^57423+57423^114868546667Ryan Propper10/2023
3222^1815834+231799546621Enzo Doria05/2025
3232^1814913+37607546344Enzo Doria12/2024
324109092^100999+100999^109092545931Ryan Propper10/2023
3252^1812446+34789545601Enzo Doria02/2025
3262^1812234+31879545537Enzo Doria05/2024
327(64814^113569-1)/(64814^337-1)544835Ryan Propper11/2023
3282^1809045+225641544577Enzo Doria12/2024
3292^1806435+42683543792Enzo Doria05/2025
3302^1804650+230149543254Enzo Doria02/2025
3312^1804109+37007543091Enzo Doria11/2024
332(92170^109561-1)/(92170^331-1)542283Ryan Propper11/2023
3332^1799578+36883541727Enzo Doria03/2025
3342^1797319+29693541047Enzo Doria11/2024
335(28262^121801-1)/(28262^349-1)540608Ryan Propper11/2023
336(68^294947+1)/69540492Paul Bourdelais03/2025
3372^1792175+230543539499Enzo Doria01/2025
3382^1791569+33587539317Enzo Doria09/2024
339(2^1790743-1)/(146840927*158358984977*3835546416767873*20752172271489035681)539014Dario Alpern06/2015
34010^538640-3538640Paul Bourdelais01/2021
341(10^538508+53)/9538508Rytis Slatkevicius01/2023
3422^1787653+224687538138Enzo Doria10/2024
3432^1787167+71963537991Enzo Doria12/2018
344(7^636043-5^636043)/2537519Jon Grantham08/2023
345108309^91610+91610^108309537424Ryan Propper10/2023
3462^1777975+233603535224Enzo Doria04/2025
347(12^495953+1)/13535223Paul Bourdelais11/2018
3482^1774781+30197534263Enzo Doria08/2024
3492^1773644+72511533921Enzo Doria10/2018
350(92^271639-1)/91533440Paul Bourdelais02/2022
3512^1771408+223201533247Enzo Doria07/2024
3522^1770613+212597533008Enzo Doria10/2023
353(11559^131072+1)/2532535Serge Batalov04/2018
354(85^275881-1)/84532289Paul Bourdelais02/2022
3552^1767579+213683532095Enzo Doria10/2023
3562^1767218+25249531986Enzo Doria02/2024
3572^1762004-3530417Paul Bourdelais04/2020
3582^1761634+48019530305Enzo Doria06/2025
3592^1754760+217465528236Enzo Doria01/2024
3602^1753261+25367527785Enzo Doria11/2023
361105006^105006-133^133527258Sergey Batalov05/2024
3622^1750727+213683527022Enzo Doria10/2023
3632^1750208+218371526866Enzo Doria01/2024
3642^1743981+28997524991Enzo Doria03/2024
3652^1740587+40493523969Enzo Doria02/2025
3662^1737680+23161523094Enzo Doria01/2024
367(73^280697+1)/74523028Paul Bourdelais02/2022
3682^1737207+218153522952Enzo Doria05/2024
3692^1735354+227509522394Enzo Doria11/2024
3702^1734898+225529522257Enzo Doria09/2024
3712^1733867+231383521946Enzo Doria03/2025
372(21^394579+1)/22521719Paul Bourdelais10/2018
3732^1732919+43553521661Enzo Doria04/2025
3742^1732565+226757521555Enzo Doria12/2024
3752^1730246+384439520856Enzo Doria09/2017
3762^1729303+34313520573Enzo Doria11/2024
377(55^299087+1)/56520519Paul Bourdelais02/2022
3782^1728446+41629520315Enzo Doria02/2025
3795^744171-3^744171-1520154Jon Grantham08/2023
3802^1727856+31951520137Enzo Doria04/2024
381(18^414269-1)/17520020Paul Bourdelais12/2014
3822^1727029+228257519888Enzo Doria12/2024
3832^1726522+30859519735Enzo Doria06/2024
3842^1724695+228353519185Enzo Doria01/2025
3852^1717949+30077517155Enzo Doria08/2024
3862^1717612+31891517053Enzo Doria04/2024
387(144171^100489-1)/(144171^317-1)516776Ryan Propper11/2023
3882^1714462+217465516105Enzo Doria01/2024
3892^1714021+29777515972Enzo Doria03/2024
3902^1713855+220703515922Enzo Doria03/2024
3912^1712979+222143515659Enzo Doria05/2024
39220^396120-3515365Paul Bourdelais01/2021
3932^1709785+36557514697Enzo Doria02/2025
394(136102^100489-1)/(136102^317-1)514270Ryan Propper11/2023
3952^1708341+221897514262Enzo Doria09/2024
396(7^608347-5^608347)/2514113Jon Grantham08/2023
397(62^286483+1)/63513488Paul Bourdelais02/2022
398155630^1971+1971^155630512753Henri Lifchitz11/2024
3992^1702747+230873512578Enzo Doria01/2025
4002^1701757+47207512280Enzo Doria06/2025
401(20^393257+1)/21511638Paul Bourdelais12/2014
4022^1699164+40141511500Enzo Doria01/2025
4032^1698083+24743511174Enzo Doria11/2023
4042^1696453+219257510684Enzo Doria06/2024
405(124869^100489-1)/(124869^317-1)510523Ryan Propper11/2023
406(124292^100489-1)/(124292^317-1)510321Ryan Propper11/2023
40710^509546+3509547Paul Bourdelais01/2021
408101876^99207+99207^101876509028Gabor Levai08/2023
4092^1690434+213589508872Enzo Doria12/2023
4102^1688450+221989508275Enzo Doria07/2024
4112^1688360+233581508248Enzo Doria05/2025
4122^1688111+217313508173Enzo Doria04/2024
413(118270^100489-1)/(118270^317-1)508160Ryan Propper11/2023
4142^1687922+40849508116Enzo Doria01/2025
4152^1687521+230267507995Enzo Doria01/2025
416105196^67205+67205^105196507824Miklos Levai09/2023
4172^1686452+220681507673Enzo Doria04/2024
4182^1685708+27781507449Enzo Doria01/2024
419(72^273149-1)/71507327Paul Bourdelais02/2022
4202^1685092+227191507264Enzo Doria12/2024
421105154^66373+66373^105154507052Miklos Levai09/2023
4222^1683331+225413506734Enzo Doria09/2024
423107890^49423+49423^107890506429Miklos Levai02/2022
424(14^441697-1)/13506241Paul Bourdelais12/2014
425101645^94522+94522^101645505739Gabor Levai02/2023
4263^1059503-2^1059503505512Mike Oakes04/2012
4272^1678670+21529505331Enzo Doria11/2023
428101542^92885+92885^101542504456Gabor Levai04/2022
4292^1675306+227839504318Enzo Doria12/2024
4302^1674819+42683504171Enzo Doria04/2025
4312^1673623+42983503811Enzo Doria03/2025
432105273^60238+60238^105273503192Miklos Levai09/2023
433105098^61113+61113^105098503014Miklos Levai09/2022
4342^1670703+60293502932Enzo Doria11/2017
435(2^1669219-2^834610+1)/5502485Borys Jaworski01/2011
436101311^90816+90816^101311502317Gabor Levai12/2021
437101643^87368+87368^101643502254Gabor Levai11/2022
438(161502^96721-1)/(161502^311-1)502121Ryan Propper11/2023
439101863^84922+84922^101863502085Gabor Levai10/2022
4402^1666440+212671501649Enzo Doria09/2023
441100291^100291+172^172501582Serge Batalov04/2024
4422^1666177+226697501570Enzo Doria10/2024
443100207^99856+99856^100207500973Gabor Levai11/2021
444101839^83028+83028^101839500969Gabor Levai11/2022
445100263^98600+98600^100263500702Gabor Levai09/2021
4462^1662045+37607500326Enzo Doria11/2024
4472^1661503+43553500163Enzo Doria04/2025
448101761^82168+82168^101761500126Gabor Levai03/2022
4492^1661176+336631500064Tony Prest / Never Odd Or Even09/2019
4508603^127088-127088^8603500047Norbert Schneider06/2025
451101070^88579+88579^101070500027Gabor Levai01/2022
452(85^259159-1)/84500025Paul Bourdelais11/2021
4532^1660973+368139500003Tony Prest / Never Odd Or Even08/2020
454100000^100000+85707^85707500001Henri Lifchitz01/2025
4552^1660964-382425500000Tony Prest / Never Odd Or Even05/2020
4562^1660328+226951499809Enzo Doria04/2025
457(87^257689-1)/86499791Paul Bourdelais01/2021
458(64*10^499210+53)/9499211Serge Batalov03/2015
4592^1656126+223227498544Enzo Doria03/2025
460Tau(631^32370)498503Nik Lygeros / Olivier Rozier05/2015
46129^339887-28^339887497051Jean-Louis Charton05/2019
4622^1650975+185225496993Stefano Morozzi09/2024
4632^1650959+198513496989Stefano Morozzi09/2024
4642^1650942+181575496984Stefano Morozzi09/2024
4652^1650905+193947496972Stefano Morozzi09/2024
4662^1650877+186537496964Stefano Morozzi01/2025
4672^1650867+192615496961Stefano Morozzi09/2024
4682^1650854+188973496957Stefano Morozzi01/2025
4692^1650837+199641496952Stefano Morozzi01/2025
4702^1650819+198315496947Stefano Morozzi07/2024
4712^1650788+185823496937Stefano Morozzi09/2024
4722^1650749+185235496925Stefano Morozzi06/2024
4732^1650695+183141496909Stefano Morozzi04/2024
4742^1650640+185311496893Stefano Morozzi03/2024
4752^1650593+187871496879Stefano Morozzi03/2024
4762^1650538+196863496862Stefano Morozzi03/2024
4772^1650484+181413496846Stefano Morozzi03/2024
4782^1650473+193151496842Stefano Morozzi03/2024
4792^1650443+193613496833Stefano Morozzi01/2024
4802^1650426+183543496828Stefano Morozzi01/2024
4812^1650388+189741496817Stefano Morozzi10/2023
4822^1650267+193743496780Stefano Morozzi09/2023
4832^1650196+191835496759Stefano Morozzi07/2023
4842^1650190+185733496757Stefano Morozzi07/2023
4852^1650141+189525496742Stefano Morozzi07/2023
4862^1650103+189519496731Stefano Morozzi05/2023
4872^1648342+215029496201Enzo Doria01/2024
4882^1646078+36937495519Enzo Doria10/2024
4892^1645332+34951495295Enzo Doria12/2024
490(136688^96721-1)/(136688^311-1)495136Ryan Propper11/2023
4912^1643411+26213494717Enzo Doria03/2024
4922^1642104+227491494323Enzo Doria10/2024
4932^1640056+216241493707Enzo Doria02/2024
4942^1639019+45113493394Enzo Doria05/2025
4952^1636027+25763492494Enzo Doria01/2024
4962^1635235+227693492255Enzo Doria10/2024
4972^1632498+30397491431Enzo Doria08/2024
4982^1631030+73519490989Enzo Doria08/2023
499(2^1629469-1)/644908484660139264379223490496Gord Palameta11/2017
5002^1627834+225529490027Enzo Doria08/2024


Find by discoverer :


Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: July, 05 2025 13:49 (Time in France)

Go back
Valid XHTML 1.0!    Valid CSS!