Henri & Renaud Lifchitz's PRP Top records

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 ?
5251	(5^193939+1)/6	135557	Paul Bourdelais	12/2008
5252	(76*10^135553-49)/9	135554	Robert Price	07/2022
5253	5*3^284077+2^284077	135540	Jon Grantham	08/2023
5254	(844*10^135527-7)/9	135529	Robert Price	05/2021
5255	27191^30560-30560^27191	135517	Frank Doornink	01/2024
5256	40387^2260+2260^40387	135463	Hans Havermann	12/2020
5257	2^449944-113247	135447	Enzo Doria	07/2014
5258	Phi(70509,-1105)	135418	Henri Lifchitz	12/2025
5259	2^449770-113247	135395	Enzo Doria	07/2014
5260	2^449637-21471	135355	Enzo Doria	07/2013
5261	26061^30650-30650^26061	135351	Frank Doornink	03/2024
5262	2^449571-75	135335	Lelio R Paula	08/2017
5263	(14*10^135301-53)/3	135302	Robert Price	12/2018
5264	(3*2^449494+1)/61340334013	135301	Lelio R Paula	07/2015
5265	(13*10^135279+437)/9	135280	Robert Price	04/2018
5266	2^449330-35	135262	Lelio R Paula	08/2017
5267	(19*2^449325+1)/9	135261	Lelio R Paula	07/2015
5268	(2709^39601+1)/(2709^199+1)	135260	Martin Hopf	12/2023
5269	(13*10^135184-43)/3	135185	Robert Price	11/2018
5270	2^449049-115309	135178	Enzo Doria	07/2015
5271	(10^135174+191)/3	135174	Robert Price	02/2018
5272	2^449030-15	135172	Lelio R Paula	08/2017
5273	(157*10^135151-1)/3	135153	Robert Price	01/2022
5274	(2^448966+100280245065)	135153	Paul Bourdelais	05/2022
5275	(27*2^448936-1)/11	135144	Lelio R Paula	07/2015
5276	(37*10^135099+251)/9	135100	Robert Price	09/2021
5277	32221^15586+15586^32221	135095	Hans Havermann	12/2020
5278	2^448762-351401	135091	Enzo Doria	07/2015
5279	2*10^135083-43	135084	Robert Price	04/2018
5280	31357^20278+20278^31357	135056	Hans Havermann	12/2020
5281	32242^15445+15445^32242	135055	Hans Havermann	12/2020
5282	k(198476)	135054	Robert Price	07/2020
5283	32461^14470+14470^32461	135053	Hans Havermann	12/2020
5284	31353^20288+20288^31353	135045	Hans Havermann	12/2020
5285	5*10^135019+77	135020	Robert Price	12/2018
5286	(10^135011+719)/9	135011	Serge Batalov	12/2014
5287	(197*10^134978+7)/3	134980	Robert Price	12/2020
5288	2^448386-2786261	134978	Enzo Doria	03/2016
5289	26480^30517-30517^26480	134975	Frank Doornink	03/2024
5290	(73*10^134939+143)/9	134940	Robert Price	07/2019
5291	33957^9392+9392^33957	134903	Hans Havermann	12/2020
5292	2^448122+20809	134899	Enzo Doria	08/2023
5293	2^448113-113949	134896	Enzo Doria	11/2014
5294	30958^22755+22755^30958	134887	Hans Havermann	12/2020
5295	2^447888-2786639	134828	Enzo Doria	03/2016
5296	2^447870-396765	134823	Enzo Doria	07/2013
5297	10^(2*67404+1)-10^67404-1	134809	Robert Price	07/2023
5298	2^447766-21791	134791	Enzo Doria	07/2013
5299	(19*10^134786-49)/3	134787	Robert Price	05/2019
5300	Phi(202173,10)/10064306514895399941409	134758	Makoto Kamada	05/2019
5301	(23*2^447647+1)/155	134755	Lelio R Paula	07/2015
5302	2^447552-1019	134727	Yves Minet	02/2014
5303	(2*10^134720-41)/3	134720	Robert Price	02/2018
5304	(25*10^134695-97)/9	134696	Robert Price	01/2022
5305	2^447437-113569	134692	Enzo Doria	08/2014
5306	2^447426-65	134689	Lelio R Paula	08/2017
5307	2^447357-2797573	134668	Enzo Doria	04/2016
5308	2^447278+93	134645	Lelio R Paula	08/2017
5309	33193^11370+11370^33193	134623	Hans Havermann	12/2020
5310	30736^23979+23979^30736	134619	Hans Havermann	11/2020
5311	2^447094-113193	134589	Enzo Doria	07/2014
5312	3^282041-9934	134568	Enzo Doria	05/2014
5313	2^447019-109039	134567	Enzo Doria	04/2014
5314	31376^19437+19437^31376	134561	Hans Havermann	12/2020
5315	2^446990-22041	134558	Enzo Doria	07/2013
5316	123^64370+122	134528	Karsten Bonath	04/2018
5317	30100^29461+29461^30100	134525	Hans Havermann	11/2020
5318	31251^20158+20158^31251	134519	Hans Havermann	11/2020
5319	2^446782-39701	134495	Enzo Doria	09/2015
5320	31817^16858+16858^31817	134485	Hans Havermann	12/2020
5321	32448^13937+13937^32448	134471	Hans Havermann	12/2020
5322	5^192321+3^192321-1	134427	Jon Grantham	08/2023
5323	2^446494-16485	134409	Enzo Doria	04/2013
5324	30042^29785+29785^30042	134408	Hans Havermann	12/2020
5325	29504^30069-30069^29504	134405	Norbert Schneider	12/2014
5326	2^446441+65	134393	Lelio R Paula	08/2017
5327	(10^134385+719)/9	134385	Serge Batalov	12/2014
5328	30043^29688+29688^30043	134370	Hans Havermann	12/2020
5329	(2*10^134364+529)/9	134364	Robert Price	01/2018
5330	34657^7512+7512^34657	134323	Hans Havermann	11/2020
5331	(13*2^446187-1)/661	134314	Lelio R Paula	07/2015
5332	5^192103+3^192103+2^192103+1	134275	Matthias Baur	12/2019
5333	42035^1564+1564^42035	134270	Hans Havermann	12/2020
5335	(2^446022-7)/339	134264	Lelio R Paula	07/2015
5334	30621^24248+24248^30621	134264	Hans Havermann	12/2020
5336	30341^26562+26562^30341	134237	Hans Havermann	11/2020
5337	(189^58967-1)/188	134234	Anonymous	06/2024
5338	10^134209+99867	134210	Patrick De Geest	05/2021
5339	10^134209-80000001	134209	Robert Price	04/2021
5340	10^134209-323283	134209	Patrick De Geest	05/2021
5341	29976^29953+29953^29976	134186	Hans Havermann	12/2020
5342	35038^6755+6755^35038	134183	Hans Havermann	12/2020
5343	63^74568+2	134174	Lelio R Paula	06/2017
5344	2^445671-22071	134161	Enzo Doria	07/2013
5345	532^49205+49205^532	134129	Norbert Schneider	02/2019
5346	36453^4780+4780^36453	134127	Hans Havermann	04/2021
5347	(28*10^134122-1)/9	134123	Serge Batalov	10/2014
5348	2^445515-113859	134114	Enzo Doria	10/2014
5350	(22*10^134111-37)/3	134112	Robert Price	04/2019
5349	31083^20636+20636^31083	134112	Hans Havermann	04/2021
5351	3*2^445478+5	134103	Jon Grantham	07/2023
5352	31622^17379+17379^31622	134079	Hans Havermann	04/2021
5353	5*2^445380-3	134074	Jon Grantham	07/2023
5354	(6*32^89076+4241)/31	134073	Eric Chen	11/2023
5355	(277*10^134059-7)/9	134061	Robert Price	02/2022
5356	2^445328-216917	134058	Enzo Doria	05/2014
5357	2^445202+1874899	134020	Enzo Doria	06/2016
5358	5^191739-3^191739-1	134020	Jon Grantham	08/2023
5359	(35*10^134003-89)/9	134004	Robert Price	02/2022
5360	(13*2^445102+1)/17	133989	Lelio R Paula	07/2015
5361	(35*10^133979-593)/9	133980	Robert Price	07/2018
5362	2*10^133955+51	133956	Robert Price	05/2018
5363	(49*10^133952+437)/9	133953	Robert Price	09/2021
5364	2^444964-113639	133948	Enzo Doria	08/2014
5365	31811^16240+16240^31811	133943	Hans Havermann	04/2021
5366	10^133902+167841	133903	Patrick De Geest	05/2021
5368	28118^30097-30097^28118	133902	Norbert Schneider	01/2015
5367	10^133902-100001	133902	Robert Price	07/2020
5369	2^444784-113859	133894	Enzo Doria	10/2014
5370	(132^63127-1)/131	133864	Anonymous	06/2024
5371	32303^13914+13914^32303	133846	Hans Havermann	04/2021
5372	(29^91493-3^91493)/26	133798	Robert Price	06/2025
5373	(2276213*2^444444+1)/3	133797	Alex_soldier	11/2022
5374	(1403559*2^444444+1)/5	133797	Alex_soldier	11/2022
5375	(1209887*2^444444+1)/9	133797	Alex_soldier	11/2022
5376	(608239*2^444444+1)/25	133796	Alex_soldier	11/2022
5377	(1824587*2^444444+1)/27	133796	Alex_soldier	11/2022
5378	(40795*2^444444+1)/7	133795	Alex_soldier	11/2022
5379	30739^22458+22458^30739	133757	Hans Havermann	04/2021
5380	34942^6721+6721^34942	133739	Hans Havermann	04/2021
5381	(3^280229-1)/1120918	133698	Aurel Gibier	03/2025
5382	(2^444046+100280245065)	133672	Paul Bourdelais	05/2022
5383	34792^6935+6935^34792	133638	Hans Havermann	04/2021
5384	(266*10^133603+1)/3	133605	Robert Price	04/2020
5385	32261^13842+13842^32261	133600	Hans Havermann	04/2021
5386	(89*10^133580+1)/9	133581	Serge Batalov	05/2010
5387	(134*10^133573-11)/3	133575	Robert Price	01/2022
5388	26726^30173-30173^26726	133574	Frank Doornink	03/2024
5389	2^443721+39527	133574	Enzo Doria	11/2024
5390	62^74521-61^74521	133571	Robert Price	05/2013
5391	(182*10^133543+1)/3	133545	Robert Price	02/2020
5392	(103*10^133535+11)/3	133537	Robert Price	01/2021
5393	32589^12520+12520^32589	133537	Hans Havermann	03/2021
5394	L(638839)/274700771	133502	Serge Batalov	07/2024
5395	34516^7373+7373^34516	133496	Hans Havermann	04/2021
5396	8*10^133487-37	133488	Robert Price	03/2022
5397	30135^26882+26882^30135	133482	Hans Havermann	04/2021
5398	2^443198-1867301	133416	Enzo Doria	03/2016
5399	27^93192+26	133392	Anonymous	09/2024
5400	(19*10^133390+101)/3	133391	Robert Price	09/2019
5401	(71^72043-1)/70	133369	Paul Bourdelais	09/2017
5402	(17508!^2+1)/(1453817*25094393)	133366	Michael Porter	09/2025
5403	36117^4910+4910^36117	133311	Hans Havermann	04/2021
5404	2^442799+1874633	133296	Enzo Doria	06/2016
5405	L(637751)	133283	Henri Lifchitz	09/2008
5406	109^65410-2	133269	Lelio R Paula	10/2017
5407	2^442688-113489	133263	Enzo Doria	08/2014
5408	(7*2^442640-1)/783	133246	Lelio R Paula	07/2015
5409	(9*2^442463+1)/17441	133192	Lelio R Paula	07/2015
5410	2^442437-1849993	133187	Enzo Doria	08/2015
5411	2^442430-2791721	133185	Enzo Doria	03/2016
5412	(13*2^442428-1)/309	133183	Lelio R Paula	07/2015
5413	29959^27870+27870^29959	133172	Hans Havermann	03/2021
5414	(25*2^442379-1)/71	133169	Lelio R Paula	07/2015
5415	2^442368+213691	133167	Enzo Doria	09/2023
5416	34240^7737+7737^34240	133145	Hans Havermann	03/2021
5417	452^50145+50145^452	133142	Norbert Schneider	09/2020
5418	(355^52201-1)/354	133122	Tom Wu	08/2024
5419	(3^278981-1)/14507014	133101	Paul Vanderveen	05/2025
5420	30659^21796+21796^30659	133011	Hans Havermann	04/2021
5421	33276^9935+9935^33276	133010	Hans Havermann	04/2021
5422	30111^26122+26122^30111	133001	Hans Havermann	04/2021
5423	30790^20869+20869^30790	132998	Hans Havermann	04/2021
5425	(2^441799+78557)/5	132995	Lelio R Paula	07/2015
5424	8*10^132994-27	132995	Robert Price	10/2021
5426	(109*10^132992+11)/3	132994	Robert Price	06/2022
5427	2^441781-2787883	132990	Enzo Doria	03/2016
5428	fibonacci(636232)+4	132965	Jon Grantham	08/2023
5429	(3*2^441685+1)/749	132959	Lelio R Paula	07/2015
5430	2^441618+37	132941	Lelio R Paula	08/2017
5431	34857^6514+6514^34857	132940	Hans Havermann	04/2021
5432	34065^7988+7988^34065	132937	Hans Havermann	04/2021
5433	35571^5452+5452^35571	132914	Hans Havermann	04/2021
5434	2^441521-113575	132912	Enzo Doria	08/2014
5435	7*10^132884-99	132885	Robert Price	06/2019
5436	26987^29988-29988^26987	132882	Frank Doornink	03/2024
5437	(103*10^132879+17)/3	132881	Robert Price	08/2020
5438	2^441396-65	132874	Lelio R Paula	08/2017
5439	33350^9633+9633^33350	132859	Hans Havermann	04/2021
5440	2^441330+1871959	132854	Enzo Doria	05/2016
5441	25772^30111-30111^25772	132825	Frank Doornink	02/2024
5442	2^441063+383	132774	Lelio R Paula	06/2012
5443	(10^132753+7)/17/19	132751	Alfred Reich	06/2021
5444	(22*10^132746+53)/3	132747	Robert Price	07/2019
5445	(77*10^132744-149)/9	132745	Robert Price	03/2022
5446	(22*10^132732+119)/3	132733	Robert Price	04/2021
5447	2^440846+1870909	132708	Enzo Doria	05/2016
5448	(948^44579-1)/947	132701	Jinyuan Wang	04/2023
5449	2^440656-113489	132651	Enzo Doria	08/2014
5450	numbpart(14180123587)	132646	Serge Batalov	04/2017
5451	32950^10591+10591^32950	132622	Hans Havermann	04/2021
5452	33302^9597+9597^33302	132614	Hans Havermann	04/2021
5453	(19*10^132550+191)/3	132551	Robert Price	05/2019
5454	(2^440399-1)/(1621082028116197820931518475633880799)	132538	Dario Alpern	01/2015
5455	(38^83891+1)/39	132529	Robert Price	09/2013
5456	2*10^132493-43	132494	Robert Price	04/2018
5457	31352^16809+16809^31352	132480	Hans Havermann	04/2021
5458	(418*10^132441+23)/9	132443	Robert Price	02/2020
5459	2^439931-21	132433	Lelio R Paula	08/2017
5460	47^79201-46^79201	132432	Robert Price	10/2012
5461	2^439897-113653	132423	Enzo Doria	08/2014
5462	35505^5362+5362^35505	132410	Hans Havermann	03/2021
5463	30079^25222+25222^30079	132402	Hans Havermann	04/2021
5464	(5*2^439822+1)/9	132400	Lelio R Paula	06/2015
5465	(695*10^132356+7)/9	132358	Robert Price	12/2021
5466	(112*10^132337-1)/3	132339	Serge Batalov	12/2014
5467	2^439576-113247	132326	Enzo Doria	07/2014
5468	(7^156589-1)/65346468774	132323	Paul Vanderveen	05/2025
5469	30059^25230+25230^30059	132318	Hans Havermann	04/2021
5470	2^439497-29143	132302	Enzo Doria	07/2015
5471	2^439409-114193	132276	Enzo Doria	12/2014
5472	(39^83137+2^83137)/41	132275	Robert Price	12/2024
5473	(44*10^132233-233)/9	132234	Robert Price	01/2019
5474	25507^30000-30000^25507	132200	Frank Doornink	02/2024
5475	9*10^132148-7	132149	Robert Price	09/2015
5476	V(790390)	132144	Serge Batalov	07/2024
5477	(47*10^132125-119)/9	132126	Robert Price	05/2019
5478	2^438900+214051	132123	Enzo Doria	10/2023
5479	2^438845+1870217	132106	Enzo Doria	05/2016
5480	Phi(293229,-5)	132106	Henri Lifchitz	02/2026
5481	2^438789+87855	132089	Lelio R Paula	01/2016
5482	2^438774-2786411	132085	Enzo Doria	03/2016
5483	2^438755-1848205	132079	Enzo Doria	07/2015
5484	30502^21381+21381^30502	132075	Hans Havermann	04/2021
5485	2^438739-112087	132074	Enzo Doria	06/2014
5486	(588859*29^90289-19)/28	132043	Eric Chen	06/2025
5487	(2^438438+100280245065)	131983	Paul Bourdelais	05/2022
5488	35872^4777+4777^35872	131979	Hans Havermann	04/2021
5489	31198^16945+16945^31198	131938	Hans Havermann	03/2021
5490	13907#+(318259#)/(13907#)	131923	Makoto Morimoto	10/2017
5491	L(631181)	131910	Henri Lifchitz	09/2008
5492	(47*10^131886-119)/9	131887	Robert Price	05/2019
5493	5*2^438096-3	131881	Jon Grantham	07/2023
5494	(3*2^438121+1)/4308193883	131879	Lelio R Paula	06/2015
5495	2^438079-1863877	131875	Enzo Doria	03/2016
5496	(16*10^131872-37)/3	131873	Robert Price	05/2021
5497	(2^438067+5)/329	131869	Lelio R Paula	06/2015
5498	2^437908-113855	131824	Enzo Doria	09/2014
5499	2^437884-286349	131817	Enzo Doria	07/2015
5500	15^112072+14	131807	Alfred Reich	10/2023

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Probable Primes Top 10000

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