PRP Records

Probable Primes Top 10000

(293510 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 ?
251(14^441697-1)/13506241Paul Bourdelais12/2014
252101645^94522+94522^101645505739Gabor Levai02/2023
2533^1059503-2^1059503505512Mike Oakes04/2012
254101542^92885+92885^101542504465Gabor Levai04/2022
255105273^60238+60238^105273503192Miklos Levai09/2023
256105098^61113+61113^105098503014Miklos Levai09/2022
2572^1670703+60293502932Enzo Doria11/2017
258(2^1669219-2^834610+1)/5502485Borys Jaworski01/2011
259101311^90816+90816^101311502317Gabor Levai12/2021
260101643^87368+87368^101643502254Gabor Levai11/2022
261101863^84922+84922^101863502085Gabor Levai10/2022
2622^1666440+212671501649Enzo Doria09/2023
263100207^99856+99856^100207500973Gabor Levai11/2021
264101839^83028+83028^101839500969Gabor Levai11/2022
265100263^98600+98600^100263500702Gabor Levai09/2021
266101761^82168+82168^101761500126Gabor Levai03/2022
2672^1661176+336631500064Tony Prest / Never Odd Or Even09/2019
268101070^88579+88579^101070500027Gabor Levai01/2022
269(85^259159-1)/84500025Paul Bourdelais11/2021
2702^1660973+368139500003Tony Prest / Never Odd Or Even08/2020
2712^1660964-382425500000Tony Prest / Never Odd Or Even05/2020
272(87^257689-1)/86499791Paul Bourdelais01/2021
273(64*10^499210+53)/9499211Serge Batalov03/2015
274Tau(631^32370)498503Nik Lygeros / Olivier Rozier05/2015
27529^339887-28^339887497051Jean-Louis Charton05/2019
2762^1650267+193743496780Stefano Morozzi09/2023
2772^1650196+191835496759Stefano Morozzi07/2023
2782^1650190+185733496757Stefano Morozzi07/2023
2792^1650141+189525496742Stefano Morozzi07/2023
2802^1650103+189519496731Stefano Morozzi05/2023
2812^1631030+73519490989Enzo Doria08/2023
282(2^1629469-1)/644908484660139264379223490496Gord Palameta11/2017
28310^487291+7487292Alfred Reich06/2021
2842^1617579+1889543486940Enzo Doria09/2017
285L(2316773)484177Serge Batalov06/2017
286(57^275669-1)/56484039Paul Bourdelais04/2021
2872^1599624+20011481535Enzo Doria07/2023
2882^1599120-5481384Stefano Morozzi12/2022
28910^480684-3480684Paul Bourdelais01/2021
2902^1595483+184133480289Enzo Doria07/2017
2912^1594947+3480127Paul Bourdelais07/2019
292(94^241993-1)/93477482Paul Bourdelais09/2020
2932^1585195+1888373477192Enzo Doria08/2017
294(33^313553+1)/34476134Paul Bourdelais02/2021
2953^994536+16474515Robert Price10/2020
2962^1575391+71483474240Enzo Doria04/2018
297(2^1572882+5)/3473485Serge Batalov08/2015
298(6^608099-1)/5473193Paul Bourdelais05/2010
2992^1569708+20371472530Enzo Doria09/2023
3003^989124+16471933Robert Price10/2020
3012^1567006+1888099471716Enzo Doria05/2017
3022^1563067+1889813470531Enzo Doria08/2017
3032^1549797+60197466536Enzo Doria02/2018
3042^1549030+1887619466305Enzo Doria05/2017
305416^177481-415^177481464840Jean-Louis Charton12/2016
306(78^245183-1)/77463908Paul Bourdelais02/2021
3072^1534770+20809462012Enzo Doria08/2023
30810^459480-11459480Mischa Rodermond04/2023
309(5^656657-2^656657)/3458984Jon Grantham08/2023
3102^1522569+71657458339Enzo Doria04/2018
3112^1518191+75353457022Ben Maloney / Five or Bust01/2009
3126^584279-5454658Paul Bourdelais02/2021
3132^1509037-13454266Stefano Morozzi12/2022
314(52^264697-1)/51454220Paul Bourdelais10/2021
3152^1506029+1890167453360Enzo Doria02/2018
316(34^294277+1)/35450678Paul Bourdelais06/2018
3172^1495434+1890439450171Enzo Doria12/2017
3182^1494634+7449930Stefano Morozzi10/2022
3192^1493170+784129449489Enzo Doria08/2017
3202^1489873+1888277448497Enzo Doria06/2017
3212^1485203+71663447091Enzo Doria09/2023
3222^1484671+1888463446931Enzo Doria06/2017
3232^1482867+1886783446388Enzo Doria04/2017
3242^1482148+284011446172Enzo Doria04/2017
3252^1479356+1888291445331Enzo Doria06/2017
3262^1473184+212671443473Enzo Doria09/2023
3272^1466432+20371441441Enzo Doria08/2023
32814^384558+3440753Paul Bourdelais01/2021
3292^1461244+784531439879Enzo Doria10/2017
3303^919094+5*2^919094438520Jon Grantham08/2023
331(67^239053+1)/68436527Paul Bourdelais09/2021
3322^1448122+74209435929Enzo Doria08/2023
3332^1446263+74333435369Enzo Doria08/2023
334(80^228419+1)/81434701Paul Bourdelais02/2021
3352^1443089+60227434414Enzo Doria10/2017
336(21^328129-1)/20433858Paul Bourdelais06/2014
337(35^280979+1)/36433850Paul Bourdelais09/2021
3382^1434400+3431798Paul Bourdelais06/2019
3392^1432308+1888801431168Enzo Doria10/2017
340(2^1430131+1)/(3*356468732537*36519993971459)430487Gord Palameta12/2018
341(7^508867-2^508867)/5430042Jon Grantham08/2023
3422^1425483+1886813429114Enzo Doria04/2017
343(63^238481+1)/64429107Paul Bourdelais12/2020
344(17^348259+1)/18428514Paul Bourdelais05/2014
345(10^427912+89)/9427912Serge Batalov12/2014
3462^1421089+1890167427791Enzo Doria09/2017
34720^326600+3424917Paul Bourdelais01/2021
348(10^424861-7)/3424861Leonid Durman01/2012
34910^424821-11424821Mischa Rodermond04/2023
350(2^1411200+13)/7424813Stefano Morozzi09/2022
3511+3^605376+5^605376423140Jon Grantham08/2023
3522^1404213+184217422711Enzo Doria09/2017
3532^1401872+1884385422006Enzo Doria04/2017
3542^1401257+6077421821Enzo Doria09/2017
355138^196873-137^196873421285Jean-Louis Charton12/2009
3562^1398726+7421059Stefano Morozzi10/2022
3572^1398269+131595420921Makoto Morimoto10/2013
3582^1397071+684443420561Enzo Doria07/2017
359953^141023-952^141023420121Jean-Louis Charton10/2016
3602^1393111+1867211419369Enzo Doria09/2023
361(3^877843-1)/2418838Paul Bourdelais07/2010
3622^1386321+60299417325Enzo Doria02/2018
3632^1386320+184531417324Enzo Doria09/2017
3642^1382074+1883587416046Enzo Doria01/2017
3652^1379907+1885223415394Enzo Doria03/2017
3662^1375574+1886719414090Enzo Doria04/2017
3672^1373111+1884833413348Enzo Doria02/2017
3682^1372996+15413313Stefano Morozzi10/2022
3692^1368632+1889731412000Enzo Doria10/2017
370(89*10^411590+1)/9411591Serge Batalov09/2014
371F(1968721)411439Henri Lifchitz11/2009
3722^1366066+683749411227Enzo Doria02/2017
3732^1355826+15408145Stefano Morozzi10/2022
3742^1355790+1888939408134Enzo Doria07/2017
3752^1355635+1884203408087Enzo Doria01/2017
376(88^208739+1)/89405888Paul Bourdelais12/2020
377(2^1347781-2^673891+1)/5405722Borys Jaworski10/2008
3782^1347744-3405712Paul Bourdelais07/2019
3799*10^404644-11404645Mischa Rodermond04/2023
3801215^131072+242^131072404302Kellen Shenton08/2022
3811196^131072+595^131072403405Kellen Shenton08/2022
38210^400000+1415223400001Patrick De Geest10/2020
38310^400000-339233400000Patrick De Geest10/2020
384Tau(863^24630)397727Nik Lygeros / Olivier Rozier01/2016
3852^1320057+211517397377Enzo Doria08/2023
3862^1319770+1884949397291Enzo Doria06/2017
3872^1313062+1888849395272Enzo Doria08/2017
388(1073516^81920+1)/(1073516^16384+1)395236Serge Batalov01/2017
389(1059995^81920+1)/(1059995^16384+1)394875Serge Batalov01/2017
3902^1311618+783529394837Enzo Doria01/2017
3912^1308000+1883521393748Enzo Doria02/2017
392(1009565^81920+1)/(1009565^16384+1)393487Serge Batalov01/2017
393(995042^81920+1)/(995042^16384+1)393075Serge Batalov01/2017
394(988945^81920+1)/(988945^16384+1)392900Serge Batalov01/2017
395(988823^81920+1)/(988823^16384+1)392897Serge Batalov01/2017
396(2^1304983-1)/52199321392832Tony Prest / Never Odd Or Even03/2014
397(978970^81920+1)/(978970^16384+1)392612Serge Batalov01/2017
3982^1303102+1866409392273Enzo Doria09/2017
3992^1302818+283429392188Enzo Doria01/2017
400(934422^81920+1)/(934422^16384+1)391286Serge Batalov01/2017
4012^1299181+1886867391093Enzo Doria04/2017
402(37^249341-1)/36391016Paul Bourdelais08/2020
4032^1298304+1882891390829Enzo Doria01/2017
40495196^12497+12497^95196390000Hans Havermann12/2021
40586206^33381+33381^86206389953Hans Havermann05/2023
406(874207^81920+1)/(874207^16384+1)389390Serge Batalov01/2017
407(7^457871-5^457871)/2386946Jon Grantham08/2023
40879455^73828+73828^79455386805Hans Havermann03/2023
40981650^54369+54369^81650386642Yusuf AttarBashi06/2021
41080565^62824+62824^80565386561Hans Havermann08/2021
41183747^41272+41272^83747386548Hans Havermann08/2021
41215^328574+328574^15386434Serge Batalov05/2014
4132^1280078+1885099385342Enzo Doria08/2017
4142^1279921+17385295Stefano Morozzi10/2022
4152^1276977+71657384409Enzo Doria08/2023
4162^1274941+1880717383796Enzo Doria10/2016
4172^1272632+383431383101Enzo Doria01/2017
4182^1271346+1889839382714Enzo Doria08/2017
4195*3^798534-2^798534380999Jon Grantham08/2023
420(10^380976-7)/3380976Leonid Durman01/2012
421(4*10^380056+11)/3380057Tyler Busby03/2023
4222^1257787+1447761378632Makoto Morimoto10/2013
423(2^1257787+32270)/(2*233*281*2207*3011)378620Makoto Morimoto12/2016
4242^1257728+20851378614Enzo Doria08/2023
425(77^200657-1)/76378536Paul Bourdelais08/2020
426(98^189619+1)/99377573Paul Bourdelais02/2021
427F(1803059)376817Henri Lifchitz06/2009
428(10^376417-3^376417)/7376417Jon Grantham08/2023
4292^1245230+19374852Stefano Morozzi10/2022
4307^442674+4374103Paul Bourdelais02/2021
431(97^187393-1)/96372306Paul Bourdelais09/2020
43210^371696+7371697Alfred Reich05/2021
4332^1234709+883127371685Enzo Doria12/2016
4342^1234119+21803371507Enzo Doria09/2023
435(67^203431+1)/68371479Paul Bourdelais09/2021
4362^1231466+283819370709Enzo Doria07/2017
43773^197880+197880368715Kellen Shenton06/2023
4385*3^771723-2^771723368207Jon Grantham08/2023
439(2^1222097+19)/3367888Stefano Morozzi09/2022
4402^1220335+1881263367358Enzo Doria11/2016
4412^1216694+1884769366262Enzo Doria02/2017
4422^1215889-3366020Paul Bourdelais06/2019
4432^1215296+1885441365841Enzo Doria03/2017
444(80^192133+1)/81365645Paul Bourdelais01/2021
4452^1214307+1888115365543Enzo Doria05/2017
4462^1213815+3365395Paul Bourdelais06/2019
447(80^191953+1)/81365302Paul Bourdelais01/2021
4482^1208276+22201363728Enzo Doria09/2023
4492^1207345+1882577363448Enzo Doria12/2016
4502^1207073+883727363366Enzo Doria03/2017
4513^761457-2363308Ryan Propper07/2015
452(10^363030+7)/337/443363025Alfred Reich12/2021
4532^1200972+141811361529Stefano Morozzi10/2022
454(2^1200924+324730)/2361514Stefano Morozzi06/2021
455(2^1200912+274110)/2361511Stefano Morozzi01/2021
4562^1200906+165249361509Stefano Morozzi07/2022
4572^1200890+166339361504Stefano Morozzi01/2023
458(2^1200887+344126)/2361503Stefano Morozzi10/2020
4592^1200877+186755361500Stefano Morozzi09/2022
4602^1200861+198521361495Stefano Morozzi11/2021
461(2^1200856+305790)/2361494Stefano Morozzi10/2020
462(2^1200853+372822)/2361493Stefano Morozzi06/2021
4632^1200812+324178)/2361481Stefano Morozzi06/2021
464(2^1200768+380458)/2361467Stefano Morozzi01/2021
4652^1200756+140917361464Stefano Morozzi05/2022
4662^1200741+184781361460Stefano Morozzi09/2022
467(2^1200741+293402)/2361459Stefano Morozzi07/2021
4682^1200734+142653361457Stefano Morozzi02/2023
4702^1200672+1880881361439Enzo Doria10/2016
4692^1200672+141535361439Stefano Morozzi09/2022
4712^1200669+178805361438Stefano Morozzi11/2022
4722^1200660+198555361435Stefano Morozzi12/2021
4732^1200657+164837361434Stefano Morozzi05/2022
4742^1200631+166431361426Stefano Morozzi02/2023
4752^1200627+150669361425Stefano Morozzi02/2023
476(2^1200603+356030)/2361418Stefano Morozzi10/2020
477(2^1200590+275854)/2361414Stefano Morozzi03/2021
4782^1200550+139297361402Stefano Morozzi10/2021
4792^1200486+172855361383Stefano Morozzi01/2023
480(2^1200456+320526)/2361373Stefano Morozzi10/2020
4812^1200443+142121361370Stefano Morozzi01/2023
4822^1200416+164065361362Stefano Morozzi01/2022
4832^1200331+155429361336Stefano Morozzi10/2021
485(2^1200289+348366)/2361323Stefano Morozzi10/2020
4842^1200289+141885361323Stefano Morozzi11/2022
486(2^1200284+273162)/2361322Stefano Morozzi10/2020
4872^1200252+194535361312Stefano Morozzi11/2021
488(2^1200250+364230)/2361311Stefano Morozzi10/2020
4892^1200227+156881361305Stefano Morozzi05/2022
490(2^1200209+305990)/2361299Stefano Morozzi10/2020
491(2^1200210+376278)/2361299Stefano Morozzi10/2020
492(2^1200182+274462)/2361291Stefano Morozzi01/2021
4932^1200178+149193361290Stefano Morozzi07/2022
4942^1200168+140403361287Stefano Morozzi03/2022
495(2^1200162+275910)/2361285Stefano Morozzi03/2021
4962^1200157+168927361284Stefano Morozzi02/2023
4972^1200134+141385361277Stefano Morozzi08/2022
498(2^1200131+360150)/2361276Stefano Morozzi10/2020
499(2^1200118+290718)/2361272Stefano Morozzi01/2021
5002^1200022+192777361243Stefano Morozzi09/2022


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: September, 29 2023 15:19 (Time in France)

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