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	34166^9951+9951^34166	136592	Hans Havermann	05/2021
5252	(21*2^453740-1)/2735	136588	Lelio R Paula	07/2015
5253	31102^24635+24635^31102	136587	Hans Havermann	05/2021
5254	580^49413+49413^580	136550	Norbert Schneider	02/2019
5255	2^453503-2788297	136519	Enzo Doria	11/2015
5256	34989^7958+7958^34989	136486	Hans Havermann	12/2020
5257	(2*10^136484+187)/9	136484	Robert Price	06/2022
5258	(5^653025)%L(653025)	136475	Henri Lifchitz	06/2025
5259	31007^25158+25158^31007	136452	Hans Havermann	11/2020
5260	2^453267-113827	136447	Enzo Doria	09/2014
5261	32234^17085+17085^32234	136435	Hans Havermann	12/2020
5262	2^453102+1877629	136398	Enzo Doria	08/2016
5263	31016^24981+24981^31016	136397	Hans Havermann	12/2020
5264	(62*10^136384-791)/9	136385	Robert Price	06/2019
5265	34171^9798+9798^34171	136382	Hans Havermann	12/2020
5266	(17*10^136354-113)/3	136355	Robert Price	06/2021
5267	32756^14541+14541^32756	136350	Hans Havermann	11/2020
5268	32205^17086+17086^32205	136313	Hans Havermann	12/2020
5269	(25*10^136303+161)/3	136304	Robert Price	09/2019
5270	35337^7196+7196^35337	136299	Hans Havermann	12/2020
5271	(182*10^136291+1)/3	136293	Robert Price	02/2020
5272	(88*10^136234+83)/9	136235	Robert Price	03/2022
5273	23*10^136225-7	136227	Robert Price	02/2020
5274	L(651821)	136223	Henri Lifchitz	09/2008
5275	25519^30908-30908^25519	136208	Frank Doornink	02/2024
5276	2^452460+77701	136205	Enzo Doria	05/2016
5277	2^452440-114755	136199	Enzo Doria	04/2015
5278	28625^30558-30558^28625	136190	Frank Doornink	05/2024
5279	32286^16489+16489^32286	136157	Hans Havermann	11/2020
5280	(47*10^136141+493)/9	136142	Robert Price	03/2019
5281	27140^30699-30699^27140	136108	Frank Doornink	01/2024
5282	Phi(199391,-5)	136098	Henri Lifchitz	12/2025
5283	40392^2339+2339^40392	136082	Hans Havermann	12/2020
5284	2*10^136057-43	136058	Robert Price	04/2018
5285	2^451971+21563	136057	Enzo Doria	08/2023
5286	(2^451956-5)/181	136051	Lelio R Paula	07/2015
5287	2^451947-22165	136050	Enzo Doria	07/2013
5288	(3^451810)%(2^451810)	136008	Henri Lifchitz	06/2025
5289	2^451787-21805	136002	Enzo Doria	07/2013
5290	2^451734-112817	135986	Enzo Doria	06/2014
5291	(11*2^451714+1)/75	135979	Lelio R Paula	07/2015
5292	2^451705-21879	135977	Enzo Doria	07/2013
5293	(4666^37249-1)/(4666^193-1)	135957	Ryan Propper	11/2023
5294	2^451560-112349	135934	Enzo Doria	06/2014
5295	2^451530+45	135925	Lelio R Paula	08/2017
5296	26594^30719-30719^26594	135925	Frank Doornink	03/2024
5297	31622^19875+19875^31622	135922	Hans Havermann	11/2020
5298	(25*10^135906-73)/3	135907	Robert Price	09/2019
5299	2^451450-21743	135900	Enzo Doria	07/2013
5300	(7*10^135879+11)/9	135879	Tyler Busby	01/2023
5301	35218^7199+7199^35218	135846	Hans Havermann	11/2020
5302	35661^6446+6446^35661	135844	Hans Havermann	11/2020
5303	(7*33^89453-4743239)/32	135835	Eric Chen	12/2023
5304	31869^18248+18248^31869	135801	Hans Havermann	12/2020
5305	(77*10^135789+157)/9	135790	Robert Price	05/2022
5306	Phi(286219,-3)	135763	Henri Lifchitz	12/2025
5307	2^450958+60529	135752	Enzo Doria	08/2023
5308	2^450805+65	135706	Lelio R Paula	08/2017
5309	10^135669+21	135670	Boyan Hu	12/2024
5310	30761^25728+25728^30761	135669	Hans Havermann	12/2020
5311	2*10^135663+69	135664	Robert Price	06/2020
5312	33962^9867+9867^33962	135651	Hans Havermann	11/2020
5313	34474^8605+8605^34474	135647	Hans Havermann	11/2020
5314	34501^8508+8508^34501	135583	Hans Havermann	12/2020
5315	35487^6614+6614^35487	135577	Hans Havermann	12/2020
5316	(13725^32768+1)/131074	135573	Lelio R Paula	03/2012
5317	(313007#+121876)/(230469424867)	135559	Makoto Morimoto	08/2020
5319	(5^193939+1)/6	135557	Paul Bourdelais	12/2008
5318	Phi(193939,-5)	135557	Henri Lifchitz	12/2025
5320	(76*10^135553-49)/9	135554	Robert Price	07/2022
5321	5*3^284077+2^284077	135540	Jon Grantham	08/2023
5322	(844*10^135527-7)/9	135529	Robert Price	05/2021
5323	27191^30560-30560^27191	135517	Frank Doornink	01/2024
5324	40387^2260+2260^40387	135463	Hans Havermann	12/2020
5325	2^449944-113247	135447	Enzo Doria	07/2014
5326	Phi(70509,-1105)	135418	Henri Lifchitz	12/2025
5327	2^449770-113247	135395	Enzo Doria	07/2014
5328	2^449637-21471	135355	Enzo Doria	07/2013
5329	26061^30650-30650^26061	135351	Frank Doornink	03/2024
5330	2^449571-75	135335	Lelio R Paula	08/2017
5331	(14*10^135301-53)/3	135302	Robert Price	12/2018
5332	(3*2^449494+1)/61340334013	135301	Lelio R Paula	07/2015
5333	(13*10^135279+437)/9	135280	Robert Price	04/2018
5334	2^449330-35	135262	Lelio R Paula	08/2017
5335	(19*2^449325+1)/9	135261	Lelio R Paula	07/2015
5336	(2709^39601+1)/(2709^199+1)	135260	Martin Hopf	12/2023
5337	(13*10^135184-43)/3	135185	Robert Price	11/2018
5338	2^449049-115309	135178	Enzo Doria	07/2015
5339	(10^135174+191)/3	135174	Robert Price	02/2018
5340	2^449030-15	135172	Lelio R Paula	08/2017
5341	(157*10^135151-1)/3	135153	Robert Price	01/2022
5342	(2^448966+100280245065)	135153	Paul Bourdelais	05/2022
5343	(27*2^448936-1)/11	135144	Lelio R Paula	07/2015
5344	(37*10^135099+251)/9	135100	Robert Price	09/2021
5345	32221^15586+15586^32221	135095	Hans Havermann	12/2020
5346	2^448762-351401	135091	Enzo Doria	07/2015
5347	2*10^135083-43	135084	Robert Price	04/2018
5348	31357^20278+20278^31357	135056	Hans Havermann	12/2020
5349	32242^15445+15445^32242	135055	Hans Havermann	12/2020
5350	k(198476)	135054	Robert Price	07/2020
5351	32461^14470+14470^32461	135053	Hans Havermann	12/2020
5352	31353^20288+20288^31353	135045	Hans Havermann	12/2020
5353	5*10^135019+77	135020	Robert Price	12/2018
5354	(10^135011+719)/9	135011	Serge Batalov	12/2014
5355	(197*10^134978+7)/3	134980	Robert Price	12/2020
5356	2^448386-2786261	134978	Enzo Doria	03/2016
5357	26480^30517-30517^26480	134975	Frank Doornink	03/2024
5358	(73*10^134939+143)/9	134940	Robert Price	07/2019
5359	33957^9392+9392^33957	134903	Hans Havermann	12/2020
5360	2^448122+20809	134899	Enzo Doria	08/2023
5361	2^448113-113949	134896	Enzo Doria	11/2014
5362	30958^22755+22755^30958	134887	Hans Havermann	12/2020
5363	2^447888-2786639	134828	Enzo Doria	03/2016
5364	2^447870-396765	134823	Enzo Doria	07/2013
5365	10^(2*67404+1)-10^67404-1	134809	Robert Price	07/2023
5366	2^447766-21791	134791	Enzo Doria	07/2013
5367	(19*10^134786-49)/3	134787	Robert Price	05/2019
5368	Phi(202173,10)/10064306514895399941409	134758	Makoto Kamada	05/2019
5369	(23*2^447647+1)/155	134755	Lelio R Paula	07/2015
5370	2^447552-1019	134727	Yves Minet	02/2014
5371	(2*10^134720-41)/3	134720	Robert Price	02/2018
5372	(25*10^134695-97)/9	134696	Robert Price	01/2022
5373	2^447437-113569	134692	Enzo Doria	08/2014
5374	2^447426-65	134689	Lelio R Paula	08/2017
5375	2^447357-2797573	134668	Enzo Doria	04/2016
5376	2^447278+93	134645	Lelio R Paula	08/2017
5377	33193^11370+11370^33193	134623	Hans Havermann	12/2020
5378	30736^23979+23979^30736	134619	Hans Havermann	11/2020
5379	2^447094-113193	134589	Enzo Doria	07/2014
5380	3^282041-9934	134568	Enzo Doria	05/2014
5381	2^447019-109039	134567	Enzo Doria	04/2014
5382	31376^19437+19437^31376	134561	Hans Havermann	12/2020
5383	2^446990-22041	134558	Enzo Doria	07/2013
5384	123^64370+122	134528	Karsten Bonath	04/2018
5385	30100^29461+29461^30100	134525	Hans Havermann	11/2020
5386	31251^20158+20158^31251	134519	Hans Havermann	11/2020
5387	2^446782-39701	134495	Enzo Doria	09/2015
5388	31817^16858+16858^31817	134485	Hans Havermann	12/2020
5389	32448^13937+13937^32448	134471	Hans Havermann	12/2020
5390	5^192321+3^192321-1	134427	Jon Grantham	08/2023
5391	2^446494-16485	134409	Enzo Doria	04/2013
5392	30042^29785+29785^30042	134408	Hans Havermann	12/2020
5393	29504^30069-30069^29504	134405	Norbert Schneider	12/2014
5394	2^446441+65	134393	Lelio R Paula	08/2017
5395	(10^134385+719)/9	134385	Serge Batalov	12/2014
5396	30043^29688+29688^30043	134370	Hans Havermann	12/2020
5397	(2*10^134364+529)/9	134364	Robert Price	01/2018
5398	34657^7512+7512^34657	134323	Hans Havermann	11/2020
5399	(13*2^446187-1)/661	134314	Lelio R Paula	07/2015
5400	5^192103+3^192103+2^192103+1	134275	Matthias Baur	12/2019
5401	42035^1564+1564^42035	134270	Hans Havermann	12/2020
5403	(2^446022-7)/339	134264	Lelio R Paula	07/2015
5402	30621^24248+24248^30621	134264	Hans Havermann	12/2020
5404	30341^26562+26562^30341	134237	Hans Havermann	11/2020
5405	(189^58967-1)/188	134234	Anonymous	06/2024
5406	10^134209+99867	134210	Patrick De Geest	05/2021
5407	10^134209-80000001	134209	Robert Price	04/2021
5408	10^134209-323283	134209	Patrick De Geest	05/2021
5409	29976^29953+29953^29976	134186	Hans Havermann	12/2020
5410	35038^6755+6755^35038	134183	Hans Havermann	12/2020
5411	63^74568+2	134174	Lelio R Paula	06/2017
5412	2^445671-22071	134161	Enzo Doria	07/2013
5413	532^49205+49205^532	134129	Norbert Schneider	02/2019
5414	36453^4780+4780^36453	134127	Hans Havermann	04/2021
5415	(28*10^134122-1)/9	134123	Serge Batalov	10/2014
5416	2^445515-113859	134114	Enzo Doria	10/2014
5418	(22*10^134111-37)/3	134112	Robert Price	04/2019
5417	31083^20636+20636^31083	134112	Hans Havermann	04/2021
5419	3*2^445478+5	134103	Jon Grantham	07/2023
5420	31622^17379+17379^31622	134079	Hans Havermann	04/2021
5421	5*2^445380-3	134074	Jon Grantham	07/2023
5422	(6*32^89076+4241)/31	134073	Eric Chen	11/2023
5423	(277*10^134059-7)/9	134061	Robert Price	02/2022
5424	2^445328-216917	134058	Enzo Doria	05/2014
5425	2^445202+1874899	134020	Enzo Doria	06/2016
5426	5^191739-3^191739-1	134020	Jon Grantham	08/2023
5427	(35*10^134003-89)/9	134004	Robert Price	02/2022
5428	(13*2^445102+1)/17	133989	Lelio R Paula	07/2015
5429	(35*10^133979-593)/9	133980	Robert Price	07/2018
5430	2*10^133955+51	133956	Robert Price	05/2018
5431	(49*10^133952+437)/9	133953	Robert Price	09/2021
5432	2^444964-113639	133948	Enzo Doria	08/2014
5433	31811^16240+16240^31811	133943	Hans Havermann	04/2021
5434	10^133902+167841	133903	Patrick De Geest	05/2021
5436	28118^30097-30097^28118	133902	Norbert Schneider	01/2015
5435	10^133902-100001	133902	Robert Price	07/2020
5437	2^444784-113859	133894	Enzo Doria	10/2014
5438	(132^63127-1)/131	133864	Anonymous	06/2024
5439	32303^13914+13914^32303	133846	Hans Havermann	04/2021
5440	(29^91493-3^91493)/26	133798	Robert Price	06/2025
5441	(2276213*2^444444+1)/3	133797	Alex_soldier	11/2022
5442	(1403559*2^444444+1)/5	133797	Alex_soldier	11/2022
5443	(1209887*2^444444+1)/9	133797	Alex_soldier	11/2022
5444	(608239*2^444444+1)/25	133796	Alex_soldier	11/2022
5445	(1824587*2^444444+1)/27	133796	Alex_soldier	11/2022
5446	(40795*2^444444+1)/7	133795	Alex_soldier	11/2022
5447	30739^22458+22458^30739	133757	Hans Havermann	04/2021
5448	34942^6721+6721^34942	133739	Hans Havermann	04/2021
5449	(3^280229-1)/1120918	133698	Aurel Gibier	03/2025
5450	(2^444046+100280245065)	133672	Paul Bourdelais	05/2022
5451	34792^6935+6935^34792	133638	Hans Havermann	04/2021
5452	(266*10^133603+1)/3	133605	Robert Price	04/2020
5453	32261^13842+13842^32261	133600	Hans Havermann	04/2021
5454	(89*10^133580+1)/9	133581	Serge Batalov	05/2010
5455	(134*10^133573-11)/3	133575	Robert Price	01/2022
5456	26726^30173-30173^26726	133574	Frank Doornink	03/2024
5457	2^443721+39527	133574	Enzo Doria	11/2024
5458	62^74521-61^74521	133571	Robert Price	05/2013
5459	(182*10^133543+1)/3	133545	Robert Price	02/2020
5460	(103*10^133535+11)/3	133537	Robert Price	01/2021
5461	32589^12520+12520^32589	133537	Hans Havermann	03/2021
5462	L(638839)/274700771	133502	Serge Batalov	07/2024
5463	34516^7373+7373^34516	133496	Hans Havermann	04/2021
5464	8*10^133487-37	133488	Robert Price	03/2022
5465	30135^26882+26882^30135	133482	Hans Havermann	04/2021
5466	2^443198-1867301	133416	Enzo Doria	03/2016
5467	27^93192+26	133392	Anonymous	09/2024
5468	(19*10^133390+101)/3	133391	Robert Price	09/2019
5469	(71^72043-1)/70	133369	Paul Bourdelais	09/2017
5470	(17508!^2+1)/(1453817*25094393)	133366	Michael Porter	09/2025
5471	36117^4910+4910^36117	133311	Hans Havermann	04/2021
5472	2^442799+1874633	133296	Enzo Doria	06/2016
5473	L(637751)	133283	Henri Lifchitz	09/2008
5474	109^65410-2	133269	Lelio R Paula	10/2017
5475	2^442688-113489	133263	Enzo Doria	08/2014
5476	(7*2^442640-1)/783	133246	Lelio R Paula	07/2015
5477	(9*2^442463+1)/17441	133192	Lelio R Paula	07/2015
5478	2^442437-1849993	133187	Enzo Doria	08/2015
5479	2^442430-2791721	133185	Enzo Doria	03/2016
5480	(13*2^442428-1)/309	133183	Lelio R Paula	07/2015
5481	29959^27870+27870^29959	133172	Hans Havermann	03/2021
5482	(25*2^442379-1)/71	133169	Lelio R Paula	07/2015
5483	2^442368+213691	133167	Enzo Doria	09/2023
5484	34240^7737+7737^34240	133145	Hans Havermann	03/2021
5485	452^50145+50145^452	133142	Norbert Schneider	09/2020
5486	(355^52201-1)/354	133122	Tom Wu	08/2024
5487	(3^278981-1)/14507014	133101	Paul Vanderveen	05/2025
5488	30659^21796+21796^30659	133011	Hans Havermann	04/2021
5489	33276^9935+9935^33276	133010	Hans Havermann	04/2021
5490	30111^26122+26122^30111	133001	Hans Havermann	04/2021
5491	30790^20869+20869^30790	132998	Hans Havermann	04/2021
5493	(2^441799+78557)/5	132995	Lelio R Paula	07/2015
5492	8*10^132994-27	132995	Robert Price	10/2021
5494	(109*10^132992+11)/3	132994	Robert Price	06/2022
5495	2^441781-2787883	132990	Enzo Doria	03/2016
5496	fibonacci(636232)+4	132965	Jon Grantham	08/2023
5497	(3*2^441685+1)/749	132959	Lelio R Paula	07/2015
5498	2^441618+37	132941	Lelio R Paula	08/2017
5499	34857^6514+6514^34857	132940	Hans Havermann	04/2021
5500	34065^7988+7988^34065	132937	Hans Havermann	04/2021

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Probable Primes Top 10000

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