PRP Records

Probable Primes Top 10000

(295148 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 ?
2512^1882800+384541566780Enzo Doria12/2017
252(2^1882787-2^941394+1)/5566775Borys Jaworski11/2012
2532^1882474+71389566682Enzo Doria04/2018
254(6^727496-11)/5566102Paul Bourdelais08/2019
2552^1875552+3564598Paul Bourdelais04/2020
256(145373^109561-1)/(145373^331-1)563899Ryan Propper11/2023
257(10^563535-7)/3563535Rytis Slatkevicius02/2023
2583^1180181-2563090Jorge Coveiro05/2020
259(15063^134689-1)/(15063^367-1)561186Ryan Propper11/2023
2602^1852265+1890425557588Enzo Doria11/2017
2615^797390-2557352Paul Bourdelais03/2021
262(10^556441-7^556441)/3556441Jon Grantham07/2023
2638^615997-7^615997556301Jean-Louis Charton07/2009
264(5^795829-2^795829)/3556261Jon Grantham08/2023
265Tau(773^34960)555339Nik Lygeros / Olivier Rozier09/2015
266((((((((((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
267(42^337081-1)/41547165Paul Bourdelais09/2021
268114868^57423+57423^114868546667Ryan Propper10/2023
269109092^100999+100999^109092545931Ryan Propper10/2023
2702^1812234+31879545537Enzo Doria05/2024
271(64814^113569-1)/(64814^337-1)544835Ryan Propper11/2023
272(92170^109561-1)/(92170^331-1)542283Ryan Propper11/2023
273(28262^121801-1)/(28262^349-1)540608Ryan Propper11/2023
274(2^1790743-1)/(146840927*158358984977*3835546416767873*20752172271489035681)539014Dario Alpern06/2015
27510^538640-3538640Paul Bourdelais01/2021
276(10^538508+53)/9538508Rytis Slatkevicius01/2023
2772^1787167+71963537991Enzo Doria12/2018
278(7^636043-5^636043)/2537519Jon Grantham08/2023
279108309^91610+91610^108309537424Ryan Propper10/2023
280(12^495953+1)/13535223Paul Bourdelais11/2018
2812^1773644+72511533921Enzo Doria10/2018
282(92^271639-1)/91533440Paul Bourdelais02/2022
2832^1770613+212597533008Enzo Doria10/2023
284(11559^131072+1)/2532535Serge Batalov04/2018
285(85^275881-1)/84532289Paul Bourdelais02/2022
2862^1767579+213683532095Enzo Doria10/2023
2872^1767218+25249531986Enzo Doria02/2024
2882^1762004-3530417Paul Bourdelais04/2020
2892^1754760+217465528236Enzo Doria01/2024
2902^1753261+25367527785Enzo Doria11/2023
291105006^105006-133^133527258Sergey Batalov05/2024
2922^1750727+213683527022Enzo Doria10/2023
2932^1750208+218371526866Enzo Doria01/2024
2942^1743981+28997524991Enzo Doria03/2024
2952^1737680+23161523094Enzo Doria01/2024
296(73^280697+1)/74523028Paul Bourdelais02/2022
297(21^394579+1)/22521719Paul Bourdelais10/2018
2982^1730246+384439520856Enzo Doria09/2017
299(55^299087+1)/56520519Paul Bourdelais02/2022
3005^744171-3^744171-1520154Jon Grantham08/2023
3012^1727856+31951520137Enzo Doria04/2024
302(18^414269-1)/17520020Paul Bourdelais12/2014
3032^1717612+31891517053Enzo Doria04/2024
304(144171^100489-1)/(144171^317-1)516776Ryan Propper11/2023
3052^1714462+217465516105Enzo Doria01/2024
3062^1714021+29777515972Enzo Doria03/2024
3072^1713855+220703515922Enzo Doria03/2024
3082^1712979+222143515659Enzo Doria05/2024
30920^396120-3515365Paul Bourdelais01/2021
310(136102^100489-1)/(136102^317-1)514270Ryan Propper11/2023
311(7^608347-5^608347)/2514113Jon Grantham08/2023
312(62^286483+1)/63513488Paul Bourdelais02/2022
313(20^393257+1)/21511638Paul Bourdelais12/2014
3142^1698083+24743511174Enzo Doria11/2023
315(124869^100489-1)/(124869^317-1)510523Ryan Propper11/2023
316(124292^100489-1)/(124292^317-1)510321Ryan Propper11/2023
31710^509546+3509547Paul Bourdelais01/2021
318101876^99207+99207^101876509028Gabor Levai08/2023
3192^1690434+213589508872Enzo Doria12/2023
3202^1688111+217313508173Enzo Doria04/2024
321(118270^100489-1)/(118270^317-1)508160Ryan Propper11/2023
322105196^67205+67205^105196507824Miklos Levai09/2023
3232^1686452+220681507673Enzo Doria04/2024
3242^1685708+27781507449Enzo Doria01/2024
325(72^273149-1)/71507327Paul Bourdelais02/2022
326105154^66373+66373^105154507052Miklos Levai09/2023
327107890^49423+49423^107890506429Miklos Levai02/2022
328(14^441697-1)/13506241Paul Bourdelais12/2014
329101645^94522+94522^101645505739Gabor Levai02/2023
3303^1059503-2^1059503505512Mike Oakes04/2012
3312^1678670+21529505331Enzo Doria11/2023
332101542^92885+92885^101542504456Gabor Levai04/2022
333105273^60238+60238^105273503192Miklos Levai09/2023
334105098^61113+61113^105098503014Miklos Levai09/2022
3352^1670703+60293502932Enzo Doria11/2017
336(2^1669219-2^834610+1)/5502485Borys Jaworski01/2011
337101311^90816+90816^101311502317Gabor Levai12/2021
338101643^87368+87368^101643502254Gabor Levai11/2022
339(161502^96721-1)/(161502^311-1)502121Ryan Propper11/2023
340101863^84922+84922^101863502085Gabor Levai10/2022
3412^1666440+212671501649Enzo Doria09/2023
342100291^100291+172^172501582Serge Batalov04/2024
343100207^99856+99856^100207500973Gabor Levai11/2021
344101839^83028+83028^101839500969Gabor Levai11/2022
345100263^98600+98600^100263500702Gabor Levai09/2021
346101761^82168+82168^101761500126Gabor Levai03/2022
3472^1661176+336631500064Tony Prest / Never Odd Or Even09/2019
348101070^88579+88579^101070500027Gabor Levai01/2022
349(85^259159-1)/84500025Paul Bourdelais11/2021
3502^1660973+368139500003Tony Prest / Never Odd Or Even08/2020
3512^1660964-382425500000Tony Prest / Never Odd Or Even05/2020
352(87^257689-1)/86499791Paul Bourdelais01/2021
353(64*10^499210+53)/9499211Serge Batalov03/2015
354Tau(631^32370)498503Nik Lygeros / Olivier Rozier05/2015
35529^339887-28^339887497051Jean-Louis Charton05/2019
3562^1650695+183141496909Stefano Morozzi04/2024
3572^1650640+185311496893Stefano Morozzi03/2024
3582^1650593+187871496879Stefano Morozzi03/2024
3592^1650538+196863496862Stefano Morozzi03/2024
3602^1650484+181413496846Stefano Morozzi03/2024
3612^1650473+193151496842Stefano Morozzi03/2024
3622^1650443+193613496833Stefano Morozzi01/2024
3632^1650426+183543496828Stefano Morozzi01/2024
3642^1650388+189741496817Stefano Morozzi10/2023
3652^1650267+193743496780Stefano Morozzi09/2023
3662^1650196+191835496759Stefano Morozzi07/2023
3672^1650190+185733496757Stefano Morozzi07/2023
3682^1650141+189525496742Stefano Morozzi07/2023
3692^1650103+189519496731Stefano Morozzi05/2023
3702^1648342+215029496201Enzo Doria01/2024
371(136688^96721-1)/(136688^311-1)495136Ryan Propper11/2023
3722^1643411+26213494717Enzo Doria03/2024
3732^1640056+216241493707Enzo Doria02/2024
3742^1636027+25763492494Enzo Doria01/2024
3752^1631030+73519490989Enzo Doria08/2023
376(2^1629469-1)/644908484660139264379223490496Gord Palameta11/2017
3772^1619885+28229487634Enzo Doria04/2024
37810^487291+7487292Alfred Reich06/2021
3792^1617579+1889543486940Enzo Doria09/2017
3802^1613632+215011485752Enzo Doria11/2023
3812^1612600+27331485441Enzo Doria03/2024
3822^1610146+24739484703Enzo Doria11/2023
383L(2316773)484177Serge Batalov06/2017
384(57^275669-1)/56484039Paul Bourdelais04/2021
3852^1601964+215491482240Enzo Doria11/2023
3862^1599624+20011481535Enzo Doria07/2023
3872^1599205+27047481409Enzo Doria03/2024
3882^1599120-5481384Stefano Morozzi12/2022
38910^480684-3480684Paul Bourdelais01/2021
3902^1595483+184133480289Enzo Doria07/2017
3912^1594947+3480127Paul Bourdelais07/2019
3922^1594129+22697479881Enzo Doria11/2023
3932^1593922+213289479819Enzo Doria10/2023
3942^1592234+26809479311Enzo Doria03/2024
395(94^241993-1)/93477482Paul Bourdelais09/2020
3962^1585195+1888373477192Enzo Doria08/2017
397(33^313553+1)/34476134Paul Bourdelais02/2021
3982^1581306+220309476021Enzo Doria03/2024
3992^1578654+215029475223Enzo Doria01/2024
400(84615^96721-1)/(84615^311-1)475056Ryan Propper11/2023
4013^994536+16474515Robert Price10/2020
4022^1575391+71483474240Enzo Doria04/2018
403(2^1572882+5)/3473485Serge Batalov08/2015
404(6^608099-1)/5473193Paul Bourdelais05/2010
4052^1569708+20371472530Enzo Doria09/2023
4062^1569375+29153472429Enzo Doria05/2024
4073^989124+16471933Robert Price10/2020
4082^1567006+1888099471716Enzo Doria05/2017
4092^1563067+1889813470531Enzo Doria08/2017
4102^1562428+215851470338Enzo Doria02/2024
4112^1551415+215813467023Enzo Doria02/2024
4122^1551411+212933467022Enzo Doria09/2023
4132^1549797+60197466536Enzo Doria02/2018
4142^1549030+1887619466305Enzo Doria05/2017
415416^177481-415^177481464840Jean-Louis Charton12/2016
416(78^245183-1)/77463908Paul Bourdelais02/2021
4172^1540117+31907463622Enzo Doria04/2024
4182^1534770+20809462012Enzo Doria08/2023
4192^1531286+24799460964Enzo Doria11/2023
42010^459480-11459480Mischa Rodermond04/2023
421(5^656657-2^656657)/3458984Jon Grantham08/2023
4222^1522569+71657458339Enzo Doria04/2018
423(55814^96721-1)/(55814^311-1)457634Ryan Propper11/2023
4242^1518191+75353457022Ben Maloney / Five or Bust01/2009
4256^584279-5454658Paul Bourdelais02/2021
4262^1509037-13454266Stefano Morozzi12/2022
427(52^264697-1)/51454220Paul Bourdelais10/2021
4282^1507169+29027453704Enzo Doria05/2024
4292^1506029+1890167453360Enzo Doria02/2018
4302^1504232+26101452819Enzo Doria01/2024
4312^1498015+219113450948Enzo Doria03/2024
4322^1497532+220471450803Enzo Doria04/2024
4332^1497369+216977450753Enzo Doria01/2024
434(34^294277+1)/35450678Paul Bourdelais06/2018
4352^1495434+1890439450171Enzo Doria12/2017
4362^1494634+7449930Stefano Morozzi10/2022
4372^1493170+784129449489Enzo Doria08/2017
4382^1489873+1888277448497Enzo Doria06/2017
4392^1485203+71663447091Enzo Doria09/2023
4402^1484671+1888463446931Enzo Doria06/2017
4412^1483112+23961446462Enzo Doria12/2023
4422^1482867+1886783446388Enzo Doria04/2017
4432^1482148+284011446172Enzo Doria04/2017
4442^1481363+215843445935Enzo Doria12/2023
4452^1480415+217643445650Enzo Doria02/2024
4462^1479356+1888291445331Enzo Doria06/2017
447(157742^85849-1)/(157742^293-1)444716Ryan Propper11/2023
4482^1476810+23299444565Enzo Doria12/2023
4492^1473184+212671443473Enzo Doria09/2023
4502^1466432+20371441441Enzo Doria08/2023
45114^384558+3440753Paul Bourdelais01/2021
4522^1463913+219047440682Enzo Doria04/2024
4532^1461244+784531439879Enzo Doria10/2017
4542^1459599+215813439384Enzo Doria01/2024
4552^1457449+25757438736Enzo Doria12/2023
4563^919094+5*2^919094438520Jon Grantham08/2023
4572^1456277+28229438384Enzo Doria03/2024
4582^1455129+218027438038Enzo Doria01/2024
4592^1454061+216977437716Enzo Doria01/2024
4602^1453419+26783437523Enzo Doria01/2024
461(67^239053+1)/68436527Paul Bourdelais09/2021
4622^1448122+74209435929Enzo Doria08/2023
4632^1446263+74333435369Enzo Doria08/2023
4642^1444386+221029434804Enzo Doria03/2024
465(80^228419+1)/81434701Paul Bourdelais02/2021
4662^1443089+60227434414Enzo Doria10/2017
467(21^328129-1)/20433858Paul Bourdelais06/2014
468(35^280979+1)/36433850Paul Bourdelais09/2021
4692^1438663+214175433081Enzo Doria11/2023
4702^1434519+215813431834Enzo Doria01/2024
4712^1434400+3431798Paul Bourdelais06/2019
4722^1434097+215207431707Enzo Doria11/2023
4732^1433033+212987431386Enzo Doria10/2023
4742^1432308+1888801431168Enzo Doria10/2017
475(2^1430131+1)/(3*356468732537*36519993971459)430487Gord Palameta12/2018
476(7^508867-2^508867)/5430042Jon Grantham08/2023
4772^1428489+25097430019Enzo Doria11/2023
4782^1425483+1886813429114Enzo Doria04/2017
479(63^238481+1)/64429107Paul Bourdelais12/2020
480(17^348259+1)/18428514Paul Bourdelais05/2014
4812^1422688+24391428272Enzo Doria12/2023
482(10^427912+89)/9427912Serge Batalov12/2014
4832^1421089+1890167427791Enzo Doria09/2017
4842^1418388+25771426978Enzo Doria12/2023
4852^1416724+214981426477Enzo Doria11/2023
486(96228^85849-1)/(96228^293-1)426352Ryan Propper11/2023
48720^326600+3424917Paul Bourdelais01/2021
488(10^424861-7)/3424861Leonid Durman01/2012
48910^424821-11424821Mischa Rodermond04/2023
490(2^1411200+13)/7424813Stefano Morozzi09/2022
4912^1410894+219859424722Enzo Doria03/2024
4922^1410310+30409424546Enzo Doria05/2024
4932^1410233+218447424523Enzo Doria03/2024
4941+3^605376+5^605376423140Jon Grantham08/2023
4952^1405367+213413423058Enzo Doria10/2023
4962^1404213+184217422711Enzo Doria09/2017
4972^1401872+1884385422006Enzo Doria04/2017
4982^1401257+6077421821Enzo Doria09/2017
499138^196873-137^196873421285Jean-Louis Charton12/2009
5002^1398726+7421059Stefano Morozzi10/2022


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: May, 20 2024 09:22 (Time in France)

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