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	28625^30558-30558^28625	136190	Frank Doornink	05/2024
5252	32286^16489+16489^32286	136157	Hans Havermann	11/2020
5253	(47*10^136141+493)/9	136142	Robert Price	03/2019
5254	27140^30699-30699^27140	136108	Frank Doornink	01/2024
5255	Phi(199391,-5)	136098	Henri Lifchitz	12/2025
5256	40392^2339+2339^40392	136082	Hans Havermann	12/2020
5257	2*10^136057-43	136058	Robert Price	04/2018
5258	2^451971+21563	136057	Enzo Doria	08/2023
5259	(2^451956-5)/181	136051	Lelio R Paula	07/2015
5260	2^451947-22165	136050	Enzo Doria	07/2013
5261	(3^451810)%(2^451810)	136008	Henri Lifchitz	06/2025
5262	2^451787-21805	136002	Enzo Doria	07/2013
5263	2^451734-112817	135986	Enzo Doria	06/2014
5264	(11*2^451714+1)/75	135979	Lelio R Paula	07/2015
5265	2^451705-21879	135977	Enzo Doria	07/2013
5266	(4666^37249-1)/(4666^193-1)	135957	Ryan Propper	11/2023
5267	2^451560-112349	135934	Enzo Doria	06/2014
5268	2^451530+45	135925	Lelio R Paula	08/2017
5269	26594^30719-30719^26594	135925	Frank Doornink	03/2024
5270	31622^19875+19875^31622	135922	Hans Havermann	11/2020
5271	(25*10^135906-73)/3	135907	Robert Price	09/2019
5272	2^451450-21743	135900	Enzo Doria	07/2013
5273	(7*10^135879+11)/9	135879	Tyler Busby	01/2023
5274	35218^7199+7199^35218	135846	Hans Havermann	11/2020
5275	35661^6446+6446^35661	135844	Hans Havermann	11/2020
5276	(7*33^89453-4743239)/32	135835	Eric Chen	12/2023
5277	31869^18248+18248^31869	135801	Hans Havermann	12/2020
5278	(77*10^135789+157)/9	135790	Robert Price	05/2022
5279	Phi(286219,-3)	135763	Henri Lifchitz	12/2025
5280	2^450958+60529	135752	Enzo Doria	08/2023
5281	2^450805+65	135706	Lelio R Paula	08/2017
5282	10^135669+21	135670	Boyan Hu	12/2024
5283	30761^25728+25728^30761	135669	Hans Havermann	12/2020
5284	2*10^135663+69	135664	Robert Price	06/2020
5285	33962^9867+9867^33962	135651	Hans Havermann	11/2020
5286	34474^8605+8605^34474	135647	Hans Havermann	11/2020
5287	34501^8508+8508^34501	135583	Hans Havermann	12/2020
5288	35487^6614+6614^35487	135577	Hans Havermann	12/2020
5289	(13725^32768+1)/131074	135573	Lelio R Paula	03/2012
5290	(313007#+121876)/(230469424867)	135559	Makoto Morimoto	08/2020
5292	(5^193939+1)/6	135557	Paul Bourdelais	12/2008
5291	Phi(193939,-5)	135557	Henri Lifchitz	12/2025
5293	(76*10^135553-49)/9	135554	Robert Price	07/2022
5294	5*3^284077+2^284077	135540	Jon Grantham	08/2023
5295	(844*10^135527-7)/9	135529	Robert Price	05/2021
5296	27191^30560-30560^27191	135517	Frank Doornink	01/2024
5297	40387^2260+2260^40387	135463	Hans Havermann	12/2020
5298	2^449944-113247	135447	Enzo Doria	07/2014
5299	Phi(70509,-1105)	135418	Henri Lifchitz	12/2025
5300	2^449770-113247	135395	Enzo Doria	07/2014
5301	2^449637-21471	135355	Enzo Doria	07/2013
5302	26061^30650-30650^26061	135351	Frank Doornink	03/2024
5303	2^449571-75	135335	Lelio R Paula	08/2017
5304	(14*10^135301-53)/3	135302	Robert Price	12/2018
5305	(3*2^449494+1)/61340334013	135301	Lelio R Paula	07/2015
5306	(13*10^135279+437)/9	135280	Robert Price	04/2018
5307	2^449330-35	135262	Lelio R Paula	08/2017
5308	(19*2^449325+1)/9	135261	Lelio R Paula	07/2015
5309	(2709^39601+1)/(2709^199+1)	135260	Martin Hopf	12/2023
5310	(13*10^135184-43)/3	135185	Robert Price	11/2018
5311	2^449049-115309	135178	Enzo Doria	07/2015
5312	(10^135174+191)/3	135174	Robert Price	02/2018
5313	2^449030-15	135172	Lelio R Paula	08/2017
5314	(157*10^135151-1)/3	135153	Robert Price	01/2022
5315	(2^448966+100280245065)	135153	Paul Bourdelais	05/2022
5316	(27*2^448936-1)/11	135144	Lelio R Paula	07/2015
5317	(37*10^135099+251)/9	135100	Robert Price	09/2021
5318	32221^15586+15586^32221	135095	Hans Havermann	12/2020
5319	2^448762-351401	135091	Enzo Doria	07/2015
5320	2*10^135083-43	135084	Robert Price	04/2018
5321	31357^20278+20278^31357	135056	Hans Havermann	12/2020
5322	32242^15445+15445^32242	135055	Hans Havermann	12/2020
5323	k(198476)	135054	Robert Price	07/2020
5324	32461^14470+14470^32461	135053	Hans Havermann	12/2020
5325	31353^20288+20288^31353	135045	Hans Havermann	12/2020
5326	5*10^135019+77	135020	Robert Price	12/2018
5327	(10^135011+719)/9	135011	Serge Batalov	12/2014
5328	(197*10^134978+7)/3	134980	Robert Price	12/2020
5329	2^448386-2786261	134978	Enzo Doria	03/2016
5330	26480^30517-30517^26480	134975	Frank Doornink	03/2024
5331	(73*10^134939+143)/9	134940	Robert Price	07/2019
5332	33957^9392+9392^33957	134903	Hans Havermann	12/2020
5333	2^448122+20809	134899	Enzo Doria	08/2023
5334	2^448113-113949	134896	Enzo Doria	11/2014
5335	30958^22755+22755^30958	134887	Hans Havermann	12/2020
5336	2^447888-2786639	134828	Enzo Doria	03/2016
5337	2^447870-396765	134823	Enzo Doria	07/2013
5338	10^(2*67404+1)-10^67404-1	134809	Robert Price	07/2023
5339	2^447766-21791	134791	Enzo Doria	07/2013
5340	(19*10^134786-49)/3	134787	Robert Price	05/2019
5341	Phi(202173,10)/10064306514895399941409	134758	Makoto Kamada	05/2019
5342	(23*2^447647+1)/155	134755	Lelio R Paula	07/2015
5343	2^447552-1019	134727	Yves Minet	02/2014
5344	(2*10^134720-41)/3	134720	Robert Price	02/2018
5345	(25*10^134695-97)/9	134696	Robert Price	01/2022
5346	2^447437-113569	134692	Enzo Doria	08/2014
5347	2^447426-65	134689	Lelio R Paula	08/2017
5348	2^447357-2797573	134668	Enzo Doria	04/2016
5349	2^447278+93	134645	Lelio R Paula	08/2017
5350	33193^11370+11370^33193	134623	Hans Havermann	12/2020
5351	30736^23979+23979^30736	134619	Hans Havermann	11/2020
5352	2^447094-113193	134589	Enzo Doria	07/2014
5353	3^282041-9934	134568	Enzo Doria	05/2014
5354	2^447019-109039	134567	Enzo Doria	04/2014
5355	31376^19437+19437^31376	134561	Hans Havermann	12/2020
5356	2^446990-22041	134558	Enzo Doria	07/2013
5357	123^64370+122	134528	Karsten Bonath	04/2018
5358	30100^29461+29461^30100	134525	Hans Havermann	11/2020
5359	31251^20158+20158^31251	134519	Hans Havermann	11/2020
5360	2^446782-39701	134495	Enzo Doria	09/2015
5361	31817^16858+16858^31817	134485	Hans Havermann	12/2020
5362	32448^13937+13937^32448	134471	Hans Havermann	12/2020
5363	5^192321+3^192321-1	134427	Jon Grantham	08/2023
5364	2^446494-16485	134409	Enzo Doria	04/2013
5365	30042^29785+29785^30042	134408	Hans Havermann	12/2020
5366	29504^30069-30069^29504	134405	Norbert Schneider	12/2014
5367	2^446441+65	134393	Lelio R Paula	08/2017
5368	(10^134385+719)/9	134385	Serge Batalov	12/2014
5369	30043^29688+29688^30043	134370	Hans Havermann	12/2020
5370	(2*10^134364+529)/9	134364	Robert Price	01/2018
5371	34657^7512+7512^34657	134323	Hans Havermann	11/2020
5372	(13*2^446187-1)/661	134314	Lelio R Paula	07/2015
5373	5^192103+3^192103+2^192103+1	134275	Matthias Baur	12/2019
5374	42035^1564+1564^42035	134270	Hans Havermann	12/2020
5376	(2^446022-7)/339	134264	Lelio R Paula	07/2015
5375	30621^24248+24248^30621	134264	Hans Havermann	12/2020
5377	30341^26562+26562^30341	134237	Hans Havermann	11/2020
5378	(189^58967-1)/188	134234	Anonymous	06/2024
5379	10^134209+99867	134210	Patrick De Geest	05/2021
5380	10^134209-80000001	134209	Robert Price	04/2021
5381	10^134209-323283	134209	Patrick De Geest	05/2021
5382	29976^29953+29953^29976	134186	Hans Havermann	12/2020
5383	35038^6755+6755^35038	134183	Hans Havermann	12/2020
5384	63^74568+2	134174	Lelio R Paula	06/2017
5385	2^445671-22071	134161	Enzo Doria	07/2013
5386	532^49205+49205^532	134129	Norbert Schneider	02/2019
5387	36453^4780+4780^36453	134127	Hans Havermann	04/2021
5388	(28*10^134122-1)/9	134123	Serge Batalov	10/2014
5389	2^445515-113859	134114	Enzo Doria	10/2014
5391	(22*10^134111-37)/3	134112	Robert Price	04/2019
5390	31083^20636+20636^31083	134112	Hans Havermann	04/2021
5392	3*2^445478+5	134103	Jon Grantham	07/2023
5393	31622^17379+17379^31622	134079	Hans Havermann	04/2021
5394	5*2^445380-3	134074	Jon Grantham	07/2023
5395	(6*32^89076+4241)/31	134073	Eric Chen	11/2023
5396	(277*10^134059-7)/9	134061	Robert Price	02/2022
5397	2^445328-216917	134058	Enzo Doria	05/2014
5398	2^445202+1874899	134020	Enzo Doria	06/2016
5399	5^191739-3^191739-1	134020	Jon Grantham	08/2023
5400	(35*10^134003-89)/9	134004	Robert Price	02/2022
5401	(13*2^445102+1)/17	133989	Lelio R Paula	07/2015
5402	(35*10^133979-593)/9	133980	Robert Price	07/2018
5403	2*10^133955+51	133956	Robert Price	05/2018
5404	(49*10^133952+437)/9	133953	Robert Price	09/2021
5405	2^444964-113639	133948	Enzo Doria	08/2014
5406	31811^16240+16240^31811	133943	Hans Havermann	04/2021
5407	10^133902+167841	133903	Patrick De Geest	05/2021
5409	28118^30097-30097^28118	133902	Norbert Schneider	01/2015
5408	10^133902-100001	133902	Robert Price	07/2020
5410	2^444784-113859	133894	Enzo Doria	10/2014
5411	(132^63127-1)/131	133864	Anonymous	06/2024
5412	32303^13914+13914^32303	133846	Hans Havermann	04/2021
5413	(29^91493-3^91493)/26	133798	Robert Price	06/2025
5414	(2276213*2^444444+1)/3	133797	Alex_soldier	11/2022
5415	(1403559*2^444444+1)/5	133797	Alex_soldier	11/2022
5416	(1209887*2^444444+1)/9	133797	Alex_soldier	11/2022
5417	(608239*2^444444+1)/25	133796	Alex_soldier	11/2022
5418	(1824587*2^444444+1)/27	133796	Alex_soldier	11/2022
5419	(40795*2^444444+1)/7	133795	Alex_soldier	11/2022
5420	30739^22458+22458^30739	133757	Hans Havermann	04/2021
5421	34942^6721+6721^34942	133739	Hans Havermann	04/2021
5422	(3^280229-1)/1120918	133698	Aurel Gibier	03/2025
5423	(2^444046+100280245065)	133672	Paul Bourdelais	05/2022
5424	34792^6935+6935^34792	133638	Hans Havermann	04/2021
5425	(266*10^133603+1)/3	133605	Robert Price	04/2020
5426	32261^13842+13842^32261	133600	Hans Havermann	04/2021
5427	(89*10^133580+1)/9	133581	Serge Batalov	05/2010
5428	(134*10^133573-11)/3	133575	Robert Price	01/2022
5429	26726^30173-30173^26726	133574	Frank Doornink	03/2024
5430	2^443721+39527	133574	Enzo Doria	11/2024
5431	62^74521-61^74521	133571	Robert Price	05/2013
5432	(182*10^133543+1)/3	133545	Robert Price	02/2020
5433	(103*10^133535+11)/3	133537	Robert Price	01/2021
5434	32589^12520+12520^32589	133537	Hans Havermann	03/2021
5435	L(638839)/274700771	133502	Serge Batalov	07/2024
5436	34516^7373+7373^34516	133496	Hans Havermann	04/2021
5437	8*10^133487-37	133488	Robert Price	03/2022
5438	30135^26882+26882^30135	133482	Hans Havermann	04/2021
5439	2^443198-1867301	133416	Enzo Doria	03/2016
5440	27^93192+26	133392	Anonymous	09/2024
5441	(19*10^133390+101)/3	133391	Robert Price	09/2019
5442	(71^72043-1)/70	133369	Paul Bourdelais	09/2017
5443	(17508!^2+1)/(1453817*25094393)	133366	Michael Porter	09/2025
5444	36117^4910+4910^36117	133311	Hans Havermann	04/2021
5445	2^442799+1874633	133296	Enzo Doria	06/2016
5446	L(637751)	133283	Henri Lifchitz	09/2008
5447	109^65410-2	133269	Lelio R Paula	10/2017
5448	2^442688-113489	133263	Enzo Doria	08/2014
5449	(7*2^442640-1)/783	133246	Lelio R Paula	07/2015
5450	(9*2^442463+1)/17441	133192	Lelio R Paula	07/2015
5451	2^442437-1849993	133187	Enzo Doria	08/2015
5452	2^442430-2791721	133185	Enzo Doria	03/2016
5453	(13*2^442428-1)/309	133183	Lelio R Paula	07/2015
5454	29959^27870+27870^29959	133172	Hans Havermann	03/2021
5455	(25*2^442379-1)/71	133169	Lelio R Paula	07/2015
5456	2^442368+213691	133167	Enzo Doria	09/2023
5457	34240^7737+7737^34240	133145	Hans Havermann	03/2021
5458	452^50145+50145^452	133142	Norbert Schneider	09/2020
5459	(355^52201-1)/354	133122	Tom Wu	08/2024
5460	(3^278981-1)/14507014	133101	Paul Vanderveen	05/2025
5461	30659^21796+21796^30659	133011	Hans Havermann	04/2021
5462	33276^9935+9935^33276	133010	Hans Havermann	04/2021
5463	30111^26122+26122^30111	133001	Hans Havermann	04/2021
5464	30790^20869+20869^30790	132998	Hans Havermann	04/2021
5466	(2^441799+78557)/5	132995	Lelio R Paula	07/2015
5465	8*10^132994-27	132995	Robert Price	10/2021
5467	(109*10^132992+11)/3	132994	Robert Price	06/2022
5468	2^441781-2787883	132990	Enzo Doria	03/2016
5469	fibonacci(636232)+4	132965	Jon Grantham	08/2023
5470	(3*2^441685+1)/749	132959	Lelio R Paula	07/2015
5471	2^441618+37	132941	Lelio R Paula	08/2017
5472	34857^6514+6514^34857	132940	Hans Havermann	04/2021
5473	34065^7988+7988^34065	132937	Hans Havermann	04/2021
5474	35571^5452+5452^35571	132914	Hans Havermann	04/2021
5475	2^441521-113575	132912	Enzo Doria	08/2014
5476	7*10^132884-99	132885	Robert Price	06/2019
5477	26987^29988-29988^26987	132882	Frank Doornink	03/2024
5478	(103*10^132879+17)/3	132881	Robert Price	08/2020
5479	2^441396-65	132874	Lelio R Paula	08/2017
5480	33350^9633+9633^33350	132859	Hans Havermann	04/2021
5481	2^441330+1871959	132854	Enzo Doria	05/2016
5482	25772^30111-30111^25772	132825	Frank Doornink	02/2024
5483	2^441063+383	132774	Lelio R Paula	06/2012
5484	(10^132753+7)/17/19	132751	Alfred Reich	06/2021
5485	(22*10^132746+53)/3	132747	Robert Price	07/2019
5486	(77*10^132744-149)/9	132745	Robert Price	03/2022
5487	(22*10^132732+119)/3	132733	Robert Price	04/2021
5488	2^440846+1870909	132708	Enzo Doria	05/2016
5489	(948^44579-1)/947	132701	Jinyuan Wang	04/2023
5490	2^440656-113489	132651	Enzo Doria	08/2014
5491	numbpart(14180123587)	132646	Serge Batalov	04/2017
5492	32950^10591+10591^32950	132622	Hans Havermann	04/2021
5493	33302^9597+9597^33302	132614	Hans Havermann	04/2021
5494	(19*10^132550+191)/3	132551	Robert Price	05/2019
5495	(2^440399-1)/(1621082028116197820931518475633880799)	132538	Dario Alpern	01/2015
5496	(38^83891+1)/39	132529	Robert Price	09/2013
5497	2*10^132493-43	132494	Robert Price	04/2018
5498	31352^16809+16809^31352	132480	Hans Havermann	04/2021
5499	(418*10^132441+23)/9	132443	Robert Price	02/2020
5500	2^439931-21	132433	Lelio R Paula	08/2017

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Probable Primes Top 10000

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