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	2^454199-113697	136728	Enzo Doria	09/2014
5252	30785^27622+27622^30785	136725	Hans Havermann	05/2021
5253	32973^14014+14014^32973	136725	Hans Havermann	05/2021
5255	7*10^136716+69	136717	Robert Price	07/2019
5254	36002^6273+6273^36002	136717	Hans Havermann	05/2021
5256	6*10^136692+53	136693	Robert Price	05/2020
5257	Phi(568997,2)	136692	Henri Lifchitz	02/2026
5258	(13*10^136687+47)/3	136688	Robert Price	10/2018
5259	F(2*453976)%(2^453976)	136661	Henri Lifchitz	06/2025
5260	2^453935-2791357	136649	Enzo Doria	01/2016
5261	2^453906-69131	136640	Enzo Doria	11/2015
5262	33232^12915+12915^33232	136620	Hans Havermann	05/2021
5263	2^453791+1873913	136605	Enzo Doria	06/2016
5264	34166^9951+9951^34166	136592	Hans Havermann	05/2021
5265	(21*2^453740-1)/2735	136588	Lelio R Paula	07/2015
5266	31102^24635+24635^31102	136587	Hans Havermann	05/2021
5267	580^49413+49413^580	136550	Norbert Schneider	02/2019
5268	2^453503-2788297	136519	Enzo Doria	11/2015
5269	34989^7958+7958^34989	136486	Hans Havermann	12/2020
5270	(2*10^136484+187)/9	136484	Robert Price	06/2022
5271	(5^653025)%L(653025)	136475	Henri Lifchitz	06/2025
5272	31007^25158+25158^31007	136452	Hans Havermann	11/2020
5273	2^453267-113827	136447	Enzo Doria	09/2014
5274	32234^17085+17085^32234	136435	Hans Havermann	12/2020
5275	2^453102+1877629	136398	Enzo Doria	08/2016
5276	31016^24981+24981^31016	136397	Hans Havermann	12/2020
5277	(62*10^136384-791)/9	136385	Robert Price	06/2019
5278	34171^9798+9798^34171	136382	Hans Havermann	12/2020
5279	(17*10^136354-113)/3	136355	Robert Price	06/2021
5280	32756^14541+14541^32756	136350	Hans Havermann	11/2020
5281	32205^17086+17086^32205	136313	Hans Havermann	12/2020
5282	(25*10^136303+161)/3	136304	Robert Price	09/2019
5283	35337^7196+7196^35337	136299	Hans Havermann	12/2020
5284	(182*10^136291+1)/3	136293	Robert Price	02/2020
5285	(88*10^136234+83)/9	136235	Robert Price	03/2022
5286	23*10^136225-7	136227	Robert Price	02/2020
5287	L(651821)	136223	Henri Lifchitz	09/2008
5288	25519^30908-30908^25519	136208	Frank Doornink	02/2024
5289	2^452460+77701	136205	Enzo Doria	05/2016
5290	2^452440-114755	136199	Enzo Doria	04/2015
5291	28625^30558-30558^28625	136190	Frank Doornink	05/2024
5292	32286^16489+16489^32286	136157	Hans Havermann	11/2020
5293	(47*10^136141+493)/9	136142	Robert Price	03/2019
5294	27140^30699-30699^27140	136108	Frank Doornink	01/2024
5295	Phi(199391,-5)	136098	Henri Lifchitz	12/2025
5296	40392^2339+2339^40392	136082	Hans Havermann	12/2020
5297	2*10^136057-43	136058	Robert Price	04/2018
5298	2^451971+21563	136057	Enzo Doria	08/2023
5299	(2^451956-5)/181	136051	Lelio R Paula	07/2015
5300	2^451947-22165	136050	Enzo Doria	07/2013
5301	(3^451810)%(2^451810)	136008	Henri Lifchitz	06/2025
5302	2^451787-21805	136002	Enzo Doria	07/2013
5303	2^451734-112817	135986	Enzo Doria	06/2014
5304	(11*2^451714+1)/75	135979	Lelio R Paula	07/2015
5305	2^451705-21879	135977	Enzo Doria	07/2013
5306	(4666^37249-1)/(4666^193-1)	135957	Ryan Propper	11/2023
5307	2^451560-112349	135934	Enzo Doria	06/2014
5308	2^451530+45	135925	Lelio R Paula	08/2017
5309	26594^30719-30719^26594	135925	Frank Doornink	03/2024
5310	31622^19875+19875^31622	135922	Hans Havermann	11/2020
5311	(25*10^135906-73)/3	135907	Robert Price	09/2019
5312	2^451450-21743	135900	Enzo Doria	07/2013
5313	(7*10^135879+11)/9	135879	Tyler Busby	01/2023
5314	35218^7199+7199^35218	135846	Hans Havermann	11/2020
5315	35661^6446+6446^35661	135844	Hans Havermann	11/2020
5316	(7*33^89453-4743239)/32	135835	Eric Chen	12/2023
5317	31869^18248+18248^31869	135801	Hans Havermann	12/2020
5318	(77*10^135789+157)/9	135790	Robert Price	05/2022
5319	Phi(286219,-3)	135763	Henri Lifchitz	12/2025
5320	2^450958+60529	135752	Enzo Doria	08/2023
5321	2^450805+65	135706	Lelio R Paula	08/2017
5322	10^135669+21	135670	Boyan Hu	12/2024
5323	30761^25728+25728^30761	135669	Hans Havermann	12/2020
5324	2*10^135663+69	135664	Robert Price	06/2020
5325	33962^9867+9867^33962	135651	Hans Havermann	11/2020
5326	34474^8605+8605^34474	135647	Hans Havermann	11/2020
5327	34501^8508+8508^34501	135583	Hans Havermann	12/2020
5328	35487^6614+6614^35487	135577	Hans Havermann	12/2020
5329	(13725^32768+1)/131074	135573	Lelio R Paula	03/2012
5330	(313007#+121876)/(230469424867)	135559	Makoto Morimoto	08/2020
5332	(5^193939+1)/6	135557	Paul Bourdelais	12/2008
5331	Phi(193939,-5)	135557	Henri Lifchitz	12/2025
5333	(76*10^135553-49)/9	135554	Robert Price	07/2022
5334	5*3^284077+2^284077	135540	Jon Grantham	08/2023
5335	(844*10^135527-7)/9	135529	Robert Price	05/2021
5336	27191^30560-30560^27191	135517	Frank Doornink	01/2024
5337	40387^2260+2260^40387	135463	Hans Havermann	12/2020
5338	2^449944-113247	135447	Enzo Doria	07/2014
5339	Phi(70509,-1105)	135418	Henri Lifchitz	12/2025
5340	2^449770-113247	135395	Enzo Doria	07/2014
5341	2^449637-21471	135355	Enzo Doria	07/2013
5342	26061^30650-30650^26061	135351	Frank Doornink	03/2024
5343	2^449571-75	135335	Lelio R Paula	08/2017
5344	(14*10^135301-53)/3	135302	Robert Price	12/2018
5345	(3*2^449494+1)/61340334013	135301	Lelio R Paula	07/2015
5346	(13*10^135279+437)/9	135280	Robert Price	04/2018
5347	2^449330-35	135262	Lelio R Paula	08/2017
5348	(19*2^449325+1)/9	135261	Lelio R Paula	07/2015
5349	(2709^39601+1)/(2709^199+1)	135260	Martin Hopf	12/2023
5350	(13*10^135184-43)/3	135185	Robert Price	11/2018
5351	2^449049-115309	135178	Enzo Doria	07/2015
5352	(10^135174+191)/3	135174	Robert Price	02/2018
5353	2^449030-15	135172	Lelio R Paula	08/2017
5354	(157*10^135151-1)/3	135153	Robert Price	01/2022
5355	(2^448966+100280245065)	135153	Paul Bourdelais	05/2022
5356	(27*2^448936-1)/11	135144	Lelio R Paula	07/2015
5357	(37*10^135099+251)/9	135100	Robert Price	09/2021
5358	32221^15586+15586^32221	135095	Hans Havermann	12/2020
5359	2^448762-351401	135091	Enzo Doria	07/2015
5360	2*10^135083-43	135084	Robert Price	04/2018
5361	31357^20278+20278^31357	135056	Hans Havermann	12/2020
5362	32242^15445+15445^32242	135055	Hans Havermann	12/2020
5363	k(198476)	135054	Robert Price	07/2020
5364	32461^14470+14470^32461	135053	Hans Havermann	12/2020
5365	31353^20288+20288^31353	135045	Hans Havermann	12/2020
5366	5*10^135019+77	135020	Robert Price	12/2018
5367	(10^135011+719)/9	135011	Serge Batalov	12/2014
5368	(197*10^134978+7)/3	134980	Robert Price	12/2020
5369	2^448386-2786261	134978	Enzo Doria	03/2016
5370	26480^30517-30517^26480	134975	Frank Doornink	03/2024
5371	(73*10^134939+143)/9	134940	Robert Price	07/2019
5372	33957^9392+9392^33957	134903	Hans Havermann	12/2020
5373	2^448122+20809	134899	Enzo Doria	08/2023
5374	2^448113-113949	134896	Enzo Doria	11/2014
5375	30958^22755+22755^30958	134887	Hans Havermann	12/2020
5376	2^447888-2786639	134828	Enzo Doria	03/2016
5377	2^447870-396765	134823	Enzo Doria	07/2013
5378	10^(2*67404+1)-10^67404-1	134809	Robert Price	07/2023
5379	2^447766-21791	134791	Enzo Doria	07/2013
5380	(19*10^134786-49)/3	134787	Robert Price	05/2019
5381	Phi(202173,10)/10064306514895399941409	134758	Makoto Kamada	05/2019
5382	(23*2^447647+1)/155	134755	Lelio R Paula	07/2015
5383	2^447552-1019	134727	Yves Minet	02/2014
5384	(2*10^134720-41)/3	134720	Robert Price	02/2018
5385	(25*10^134695-97)/9	134696	Robert Price	01/2022
5386	2^447437-113569	134692	Enzo Doria	08/2014
5387	2^447426-65	134689	Lelio R Paula	08/2017
5388	2^447357-2797573	134668	Enzo Doria	04/2016
5389	2^447278+93	134645	Lelio R Paula	08/2017
5390	33193^11370+11370^33193	134623	Hans Havermann	12/2020
5391	30736^23979+23979^30736	134619	Hans Havermann	11/2020
5392	2^447094-113193	134589	Enzo Doria	07/2014
5393	3^282041-9934	134568	Enzo Doria	05/2014
5394	2^447019-109039	134567	Enzo Doria	04/2014
5395	31376^19437+19437^31376	134561	Hans Havermann	12/2020
5396	2^446990-22041	134558	Enzo Doria	07/2013
5397	123^64370+122	134528	Karsten Bonath	04/2018
5398	30100^29461+29461^30100	134525	Hans Havermann	11/2020
5399	31251^20158+20158^31251	134519	Hans Havermann	11/2020
5400	2^446782-39701	134495	Enzo Doria	09/2015
5401	31817^16858+16858^31817	134485	Hans Havermann	12/2020
5402	32448^13937+13937^32448	134471	Hans Havermann	12/2020
5403	5^192321+3^192321-1	134427	Jon Grantham	08/2023
5404	2^446494-16485	134409	Enzo Doria	04/2013
5405	30042^29785+29785^30042	134408	Hans Havermann	12/2020
5406	29504^30069-30069^29504	134405	Norbert Schneider	12/2014
5407	2^446441+65	134393	Lelio R Paula	08/2017
5408	(10^134385+719)/9	134385	Serge Batalov	12/2014
5409	30043^29688+29688^30043	134370	Hans Havermann	12/2020
5410	(2*10^134364+529)/9	134364	Robert Price	01/2018
5411	34657^7512+7512^34657	134323	Hans Havermann	11/2020
5412	(13*2^446187-1)/661	134314	Lelio R Paula	07/2015
5413	5^192103+3^192103+2^192103+1	134275	Matthias Baur	12/2019
5414	42035^1564+1564^42035	134270	Hans Havermann	12/2020
5416	(2^446022-7)/339	134264	Lelio R Paula	07/2015
5415	30621^24248+24248^30621	134264	Hans Havermann	12/2020
5417	30341^26562+26562^30341	134237	Hans Havermann	11/2020
5418	(189^58967-1)/188	134234	Anonymous	06/2024
5419	10^134209+99867	134210	Patrick De Geest	05/2021
5420	10^134209-80000001	134209	Robert Price	04/2021
5421	10^134209-323283	134209	Patrick De Geest	05/2021
5422	29976^29953+29953^29976	134186	Hans Havermann	12/2020
5423	35038^6755+6755^35038	134183	Hans Havermann	12/2020
5424	63^74568+2	134174	Lelio R Paula	06/2017
5425	2^445671-22071	134161	Enzo Doria	07/2013
5426	532^49205+49205^532	134129	Norbert Schneider	02/2019
5427	36453^4780+4780^36453	134127	Hans Havermann	04/2021
5428	(28*10^134122-1)/9	134123	Serge Batalov	10/2014
5429	2^445515-113859	134114	Enzo Doria	10/2014
5431	(22*10^134111-37)/3	134112	Robert Price	04/2019
5430	31083^20636+20636^31083	134112	Hans Havermann	04/2021
5432	3*2^445478+5	134103	Jon Grantham	07/2023
5433	31622^17379+17379^31622	134079	Hans Havermann	04/2021
5434	5*2^445380-3	134074	Jon Grantham	07/2023
5435	(6*32^89076+4241)/31	134073	Eric Chen	11/2023
5436	(277*10^134059-7)/9	134061	Robert Price	02/2022
5437	2^445328-216917	134058	Enzo Doria	05/2014
5438	2^445202+1874899	134020	Enzo Doria	06/2016
5439	5^191739-3^191739-1	134020	Jon Grantham	08/2023
5440	(35*10^134003-89)/9	134004	Robert Price	02/2022
5441	(13*2^445102+1)/17	133989	Lelio R Paula	07/2015
5442	(35*10^133979-593)/9	133980	Robert Price	07/2018
5443	2*10^133955+51	133956	Robert Price	05/2018
5444	(49*10^133952+437)/9	133953	Robert Price	09/2021
5445	2^444964-113639	133948	Enzo Doria	08/2014
5446	31811^16240+16240^31811	133943	Hans Havermann	04/2021
5447	10^133902+167841	133903	Patrick De Geest	05/2021
5449	28118^30097-30097^28118	133902	Norbert Schneider	01/2015
5448	10^133902-100001	133902	Robert Price	07/2020
5450	2^444784-113859	133894	Enzo Doria	10/2014
5451	(132^63127-1)/131	133864	Anonymous	06/2024
5452	32303^13914+13914^32303	133846	Hans Havermann	04/2021
5453	(29^91493-3^91493)/26	133798	Robert Price	06/2025
5454	(2276213*2^444444+1)/3	133797	Alex_soldier	11/2022
5455	(1403559*2^444444+1)/5	133797	Alex_soldier	11/2022
5456	(1209887*2^444444+1)/9	133797	Alex_soldier	11/2022
5457	(608239*2^444444+1)/25	133796	Alex_soldier	11/2022
5458	(1824587*2^444444+1)/27	133796	Alex_soldier	11/2022
5459	(40795*2^444444+1)/7	133795	Alex_soldier	11/2022
5460	30739^22458+22458^30739	133757	Hans Havermann	04/2021
5461	34942^6721+6721^34942	133739	Hans Havermann	04/2021
5462	(3^280229-1)/1120918	133698	Aurel Gibier	03/2025
5463	(2^444046+100280245065)	133672	Paul Bourdelais	05/2022
5464	34792^6935+6935^34792	133638	Hans Havermann	04/2021
5465	(266*10^133603+1)/3	133605	Robert Price	04/2020
5466	32261^13842+13842^32261	133600	Hans Havermann	04/2021
5467	(89*10^133580+1)/9	133581	Serge Batalov	05/2010
5468	(134*10^133573-11)/3	133575	Robert Price	01/2022
5469	26726^30173-30173^26726	133574	Frank Doornink	03/2024
5470	2^443721+39527	133574	Enzo Doria	11/2024
5471	62^74521-61^74521	133571	Robert Price	05/2013
5472	(182*10^133543+1)/3	133545	Robert Price	02/2020
5473	(103*10^133535+11)/3	133537	Robert Price	01/2021
5474	32589^12520+12520^32589	133537	Hans Havermann	03/2021
5475	L(638839)/274700771	133502	Serge Batalov	07/2024
5476	34516^7373+7373^34516	133496	Hans Havermann	04/2021
5477	8*10^133487-37	133488	Robert Price	03/2022
5478	30135^26882+26882^30135	133482	Hans Havermann	04/2021
5479	2^443198-1867301	133416	Enzo Doria	03/2016
5480	27^93192+26	133392	Anonymous	09/2024
5481	(19*10^133390+101)/3	133391	Robert Price	09/2019
5482	(71^72043-1)/70	133369	Paul Bourdelais	09/2017
5483	(17508!^2+1)/(1453817*25094393)	133366	Michael Porter	09/2025
5484	36117^4910+4910^36117	133311	Hans Havermann	04/2021
5485	2^442799+1874633	133296	Enzo Doria	06/2016
5486	L(637751)	133283	Henri Lifchitz	09/2008
5487	109^65410-2	133269	Lelio R Paula	10/2017
5488	2^442688-113489	133263	Enzo Doria	08/2014
5489	(7*2^442640-1)/783	133246	Lelio R Paula	07/2015
5490	(9*2^442463+1)/17441	133192	Lelio R Paula	07/2015
5491	2^442437-1849993	133187	Enzo Doria	08/2015
5492	2^442430-2791721	133185	Enzo Doria	03/2016
5493	(13*2^442428-1)/309	133183	Lelio R Paula	07/2015
5494	29959^27870+27870^29959	133172	Hans Havermann	03/2021
5495	(25*2^442379-1)/71	133169	Lelio R Paula	07/2015
5496	2^442368+213691	133167	Enzo Doria	09/2023
5497	34240^7737+7737^34240	133145	Hans Havermann	03/2021
5498	452^50145+50145^452	133142	Norbert Schneider	09/2020
5499	(355^52201-1)/354	133122	Tom Wu	08/2024
5500	(3^278981-1)/14507014	133101	Paul Vanderveen	05/2025

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Probable Primes Top 10000

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