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	7*10^136716+69	136717	Robert Price	07/2019
5252	6*10^136692+53	136693	Robert Price	05/2020
5253	Phi(568997,2)	136692	Henri Lifchitz	02/2026
5254	(13*10^136687+47)/3	136688	Robert Price	10/2018
5255	F(2*453976)%(2^453976)	136661	Henri Lifchitz	06/2025
5256	2^453935-2791357	136649	Enzo Doria	01/2016
5257	2^453906-69131	136640	Enzo Doria	11/2015
5258	33232^12915+12915^33232	136620	Hans Havermann	05/2021
5259	2^453791+1873913	136605	Enzo Doria	06/2016
5260	34166^9951+9951^34166	136592	Hans Havermann	05/2021
5261	(21*2^453740-1)/2735	136588	Lelio R Paula	07/2015
5262	31102^24635+24635^31102	136587	Hans Havermann	05/2021
5263	580^49413+49413^580	136550	Norbert Schneider	02/2019
5264	2^453503-2788297	136519	Enzo Doria	11/2015
5265	34989^7958+7958^34989	136486	Hans Havermann	12/2020
5266	(2*10^136484+187)/9	136484	Robert Price	06/2022
5267	(5^653025)%L(653025)	136475	Henri Lifchitz	06/2025
5268	31007^25158+25158^31007	136452	Hans Havermann	11/2020
5269	2^453267-113827	136447	Enzo Doria	09/2014
5270	32234^17085+17085^32234	136435	Hans Havermann	12/2020
5271	2^453102+1877629	136398	Enzo Doria	08/2016
5272	31016^24981+24981^31016	136397	Hans Havermann	12/2020
5273	(62*10^136384-791)/9	136385	Robert Price	06/2019
5274	34171^9798+9798^34171	136382	Hans Havermann	12/2020
5275	(17*10^136354-113)/3	136355	Robert Price	06/2021
5276	32756^14541+14541^32756	136350	Hans Havermann	11/2020
5277	32205^17086+17086^32205	136313	Hans Havermann	12/2020
5278	(25*10^136303+161)/3	136304	Robert Price	09/2019
5279	35337^7196+7196^35337	136299	Hans Havermann	12/2020
5280	(182*10^136291+1)/3	136293	Robert Price	02/2020
5281	(88*10^136234+83)/9	136235	Robert Price	03/2022
5282	23*10^136225-7	136227	Robert Price	02/2020
5283	L(651821)	136223	Henri Lifchitz	09/2008
5284	25519^30908-30908^25519	136208	Frank Doornink	02/2024
5285	2^452460+77701	136205	Enzo Doria	05/2016
5286	2^452440-114755	136199	Enzo Doria	04/2015
5287	28625^30558-30558^28625	136190	Frank Doornink	05/2024
5288	32286^16489+16489^32286	136157	Hans Havermann	11/2020
5289	(47*10^136141+493)/9	136142	Robert Price	03/2019
5290	27140^30699-30699^27140	136108	Frank Doornink	01/2024
5291	Phi(199391,-5)	136098	Henri Lifchitz	12/2025
5292	40392^2339+2339^40392	136082	Hans Havermann	12/2020
5293	2*10^136057-43	136058	Robert Price	04/2018
5294	2^451971+21563	136057	Enzo Doria	08/2023
5295	(2^451956-5)/181	136051	Lelio R Paula	07/2015
5296	2^451947-22165	136050	Enzo Doria	07/2013
5297	(3^451810)%(2^451810)	136008	Henri Lifchitz	06/2025
5298	2^451787-21805	136002	Enzo Doria	07/2013
5299	2^451734-112817	135986	Enzo Doria	06/2014
5300	(11*2^451714+1)/75	135979	Lelio R Paula	07/2015
5301	2^451705-21879	135977	Enzo Doria	07/2013
5302	(4666^37249-1)/(4666^193-1)	135957	Ryan Propper	11/2023
5303	2^451560-112349	135934	Enzo Doria	06/2014
5304	2^451530+45	135925	Lelio R Paula	08/2017
5305	26594^30719-30719^26594	135925	Frank Doornink	03/2024
5306	31622^19875+19875^31622	135922	Hans Havermann	11/2020
5307	(25*10^135906-73)/3	135907	Robert Price	09/2019
5308	2^451450-21743	135900	Enzo Doria	07/2013
5309	(7*10^135879+11)/9	135879	Tyler Busby	01/2023
5310	35218^7199+7199^35218	135846	Hans Havermann	11/2020
5311	35661^6446+6446^35661	135844	Hans Havermann	11/2020
5312	(7*33^89453-4743239)/32	135835	Eric Chen	12/2023
5313	31869^18248+18248^31869	135801	Hans Havermann	12/2020
5314	(77*10^135789+157)/9	135790	Robert Price	05/2022
5315	Phi(286219,-3)	135763	Henri Lifchitz	12/2025
5316	2^450958+60529	135752	Enzo Doria	08/2023
5317	2^450805+65	135706	Lelio R Paula	08/2017
5318	10^135669+21	135670	Boyan Hu	12/2024
5319	30761^25728+25728^30761	135669	Hans Havermann	12/2020
5320	2*10^135663+69	135664	Robert Price	06/2020
5321	33962^9867+9867^33962	135651	Hans Havermann	11/2020
5322	34474^8605+8605^34474	135647	Hans Havermann	11/2020
5323	34501^8508+8508^34501	135583	Hans Havermann	12/2020
5324	35487^6614+6614^35487	135577	Hans Havermann	12/2020
5325	(13725^32768+1)/131074	135573	Lelio R Paula	03/2012
5326	(313007#+121876)/(230469424867)	135559	Makoto Morimoto	08/2020
5328	(5^193939+1)/6	135557	Paul Bourdelais	12/2008
5327	Phi(193939,-5)	135557	Henri Lifchitz	12/2025
5329	(76*10^135553-49)/9	135554	Robert Price	07/2022
5330	5*3^284077+2^284077	135540	Jon Grantham	08/2023
5331	(844*10^135527-7)/9	135529	Robert Price	05/2021
5332	27191^30560-30560^27191	135517	Frank Doornink	01/2024
5333	40387^2260+2260^40387	135463	Hans Havermann	12/2020
5334	2^449944-113247	135447	Enzo Doria	07/2014
5335	Phi(70509,-1105)	135418	Henri Lifchitz	12/2025
5336	2^449770-113247	135395	Enzo Doria	07/2014
5337	2^449637-21471	135355	Enzo Doria	07/2013
5338	26061^30650-30650^26061	135351	Frank Doornink	03/2024
5339	2^449571-75	135335	Lelio R Paula	08/2017
5340	(14*10^135301-53)/3	135302	Robert Price	12/2018
5341	(3*2^449494+1)/61340334013	135301	Lelio R Paula	07/2015
5342	(13*10^135279+437)/9	135280	Robert Price	04/2018
5343	2^449330-35	135262	Lelio R Paula	08/2017
5344	(19*2^449325+1)/9	135261	Lelio R Paula	07/2015
5345	(2709^39601+1)/(2709^199+1)	135260	Martin Hopf	12/2023
5346	(13*10^135184-43)/3	135185	Robert Price	11/2018
5347	2^449049-115309	135178	Enzo Doria	07/2015
5348	(10^135174+191)/3	135174	Robert Price	02/2018
5349	2^449030-15	135172	Lelio R Paula	08/2017
5350	(157*10^135151-1)/3	135153	Robert Price	01/2022
5351	(2^448966+100280245065)	135153	Paul Bourdelais	05/2022
5352	(27*2^448936-1)/11	135144	Lelio R Paula	07/2015
5353	(37*10^135099+251)/9	135100	Robert Price	09/2021
5354	32221^15586+15586^32221	135095	Hans Havermann	12/2020
5355	2^448762-351401	135091	Enzo Doria	07/2015
5356	2*10^135083-43	135084	Robert Price	04/2018
5357	31357^20278+20278^31357	135056	Hans Havermann	12/2020
5358	32242^15445+15445^32242	135055	Hans Havermann	12/2020
5359	k(198476)	135054	Robert Price	07/2020
5360	32461^14470+14470^32461	135053	Hans Havermann	12/2020
5361	31353^20288+20288^31353	135045	Hans Havermann	12/2020
5362	5*10^135019+77	135020	Robert Price	12/2018
5363	(10^135011+719)/9	135011	Serge Batalov	12/2014
5364	(197*10^134978+7)/3	134980	Robert Price	12/2020
5365	2^448386-2786261	134978	Enzo Doria	03/2016
5366	26480^30517-30517^26480	134975	Frank Doornink	03/2024
5367	(73*10^134939+143)/9	134940	Robert Price	07/2019
5368	33957^9392+9392^33957	134903	Hans Havermann	12/2020
5369	2^448122+20809	134899	Enzo Doria	08/2023
5370	2^448113-113949	134896	Enzo Doria	11/2014
5371	30958^22755+22755^30958	134887	Hans Havermann	12/2020
5372	2^447888-2786639	134828	Enzo Doria	03/2016
5373	2^447870-396765	134823	Enzo Doria	07/2013
5374	10^(2*67404+1)-10^67404-1	134809	Robert Price	07/2023
5375	2^447766-21791	134791	Enzo Doria	07/2013
5376	(19*10^134786-49)/3	134787	Robert Price	05/2019
5377	Phi(202173,10)/10064306514895399941409	134758	Makoto Kamada	05/2019
5378	(23*2^447647+1)/155	134755	Lelio R Paula	07/2015
5379	2^447552-1019	134727	Yves Minet	02/2014
5380	(2*10^134720-41)/3	134720	Robert Price	02/2018
5381	(25*10^134695-97)/9	134696	Robert Price	01/2022
5382	2^447437-113569	134692	Enzo Doria	08/2014
5383	2^447426-65	134689	Lelio R Paula	08/2017
5384	2^447357-2797573	134668	Enzo Doria	04/2016
5385	2^447278+93	134645	Lelio R Paula	08/2017
5386	33193^11370+11370^33193	134623	Hans Havermann	12/2020
5387	30736^23979+23979^30736	134619	Hans Havermann	11/2020
5388	2^447094-113193	134589	Enzo Doria	07/2014
5389	3^282041-9934	134568	Enzo Doria	05/2014
5390	2^447019-109039	134567	Enzo Doria	04/2014
5391	31376^19437+19437^31376	134561	Hans Havermann	12/2020
5392	2^446990-22041	134558	Enzo Doria	07/2013
5393	123^64370+122	134528	Karsten Bonath	04/2018
5394	30100^29461+29461^30100	134525	Hans Havermann	11/2020
5395	31251^20158+20158^31251	134519	Hans Havermann	11/2020
5396	2^446782-39701	134495	Enzo Doria	09/2015
5397	31817^16858+16858^31817	134485	Hans Havermann	12/2020
5398	32448^13937+13937^32448	134471	Hans Havermann	12/2020
5399	5^192321+3^192321-1	134427	Jon Grantham	08/2023
5400	2^446494-16485	134409	Enzo Doria	04/2013
5401	30042^29785+29785^30042	134408	Hans Havermann	12/2020
5402	29504^30069-30069^29504	134405	Norbert Schneider	12/2014
5403	2^446441+65	134393	Lelio R Paula	08/2017
5404	(10^134385+719)/9	134385	Serge Batalov	12/2014
5405	30043^29688+29688^30043	134370	Hans Havermann	12/2020
5406	(2*10^134364+529)/9	134364	Robert Price	01/2018
5407	34657^7512+7512^34657	134323	Hans Havermann	11/2020
5408	(13*2^446187-1)/661	134314	Lelio R Paula	07/2015
5409	5^192103+3^192103+2^192103+1	134275	Matthias Baur	12/2019
5410	42035^1564+1564^42035	134270	Hans Havermann	12/2020
5412	(2^446022-7)/339	134264	Lelio R Paula	07/2015
5411	30621^24248+24248^30621	134264	Hans Havermann	12/2020
5413	30341^26562+26562^30341	134237	Hans Havermann	11/2020
5414	(189^58967-1)/188	134234	Anonymous	06/2024
5415	10^134209+99867	134210	Patrick De Geest	05/2021
5416	10^134209-80000001	134209	Robert Price	04/2021
5417	10^134209-323283	134209	Patrick De Geest	05/2021
5418	29976^29953+29953^29976	134186	Hans Havermann	12/2020
5419	35038^6755+6755^35038	134183	Hans Havermann	12/2020
5420	63^74568+2	134174	Lelio R Paula	06/2017
5421	2^445671-22071	134161	Enzo Doria	07/2013
5422	532^49205+49205^532	134129	Norbert Schneider	02/2019
5423	36453^4780+4780^36453	134127	Hans Havermann	04/2021
5424	(28*10^134122-1)/9	134123	Serge Batalov	10/2014
5425	2^445515-113859	134114	Enzo Doria	10/2014
5427	(22*10^134111-37)/3	134112	Robert Price	04/2019
5426	31083^20636+20636^31083	134112	Hans Havermann	04/2021
5428	3*2^445478+5	134103	Jon Grantham	07/2023
5429	31622^17379+17379^31622	134079	Hans Havermann	04/2021
5430	5*2^445380-3	134074	Jon Grantham	07/2023
5431	(6*32^89076+4241)/31	134073	Eric Chen	11/2023
5432	(277*10^134059-7)/9	134061	Robert Price	02/2022
5433	2^445328-216917	134058	Enzo Doria	05/2014
5434	2^445202+1874899	134020	Enzo Doria	06/2016
5435	5^191739-3^191739-1	134020	Jon Grantham	08/2023
5436	(35*10^134003-89)/9	134004	Robert Price	02/2022
5437	(13*2^445102+1)/17	133989	Lelio R Paula	07/2015
5438	(35*10^133979-593)/9	133980	Robert Price	07/2018
5439	2*10^133955+51	133956	Robert Price	05/2018
5440	(49*10^133952+437)/9	133953	Robert Price	09/2021
5441	2^444964-113639	133948	Enzo Doria	08/2014
5442	31811^16240+16240^31811	133943	Hans Havermann	04/2021
5443	10^133902+167841	133903	Patrick De Geest	05/2021
5445	28118^30097-30097^28118	133902	Norbert Schneider	01/2015
5444	10^133902-100001	133902	Robert Price	07/2020
5446	2^444784-113859	133894	Enzo Doria	10/2014
5447	(132^63127-1)/131	133864	Anonymous	06/2024
5448	32303^13914+13914^32303	133846	Hans Havermann	04/2021
5449	(29^91493-3^91493)/26	133798	Robert Price	06/2025
5450	(2276213*2^444444+1)/3	133797	Alex_soldier	11/2022
5451	(1403559*2^444444+1)/5	133797	Alex_soldier	11/2022
5452	(1209887*2^444444+1)/9	133797	Alex_soldier	11/2022
5453	(608239*2^444444+1)/25	133796	Alex_soldier	11/2022
5454	(1824587*2^444444+1)/27	133796	Alex_soldier	11/2022
5455	(40795*2^444444+1)/7	133795	Alex_soldier	11/2022
5456	30739^22458+22458^30739	133757	Hans Havermann	04/2021
5457	34942^6721+6721^34942	133739	Hans Havermann	04/2021
5458	(3^280229-1)/1120918	133698	Aurel Gibier	03/2025
5459	(2^444046+100280245065)	133672	Paul Bourdelais	05/2022
5460	34792^6935+6935^34792	133638	Hans Havermann	04/2021
5461	(266*10^133603+1)/3	133605	Robert Price	04/2020
5462	32261^13842+13842^32261	133600	Hans Havermann	04/2021
5463	(89*10^133580+1)/9	133581	Serge Batalov	05/2010
5464	(134*10^133573-11)/3	133575	Robert Price	01/2022
5465	26726^30173-30173^26726	133574	Frank Doornink	03/2024
5466	2^443721+39527	133574	Enzo Doria	11/2024
5467	62^74521-61^74521	133571	Robert Price	05/2013
5468	(182*10^133543+1)/3	133545	Robert Price	02/2020
5469	(103*10^133535+11)/3	133537	Robert Price	01/2021
5470	32589^12520+12520^32589	133537	Hans Havermann	03/2021
5471	L(638839)/274700771	133502	Serge Batalov	07/2024
5472	34516^7373+7373^34516	133496	Hans Havermann	04/2021
5473	8*10^133487-37	133488	Robert Price	03/2022
5474	30135^26882+26882^30135	133482	Hans Havermann	04/2021
5475	2^443198-1867301	133416	Enzo Doria	03/2016
5476	27^93192+26	133392	Anonymous	09/2024
5477	(19*10^133390+101)/3	133391	Robert Price	09/2019
5478	(71^72043-1)/70	133369	Paul Bourdelais	09/2017
5479	(17508!^2+1)/(1453817*25094393)	133366	Michael Porter	09/2025
5480	36117^4910+4910^36117	133311	Hans Havermann	04/2021
5481	2^442799+1874633	133296	Enzo Doria	06/2016
5482	L(637751)	133283	Henri Lifchitz	09/2008
5483	109^65410-2	133269	Lelio R Paula	10/2017
5484	2^442688-113489	133263	Enzo Doria	08/2014
5485	(7*2^442640-1)/783	133246	Lelio R Paula	07/2015
5486	(9*2^442463+1)/17441	133192	Lelio R Paula	07/2015
5487	2^442437-1849993	133187	Enzo Doria	08/2015
5488	2^442430-2791721	133185	Enzo Doria	03/2016
5489	(13*2^442428-1)/309	133183	Lelio R Paula	07/2015
5490	29959^27870+27870^29959	133172	Hans Havermann	03/2021
5491	(25*2^442379-1)/71	133169	Lelio R Paula	07/2015
5492	2^442368+213691	133167	Enzo Doria	09/2023
5493	34240^7737+7737^34240	133145	Hans Havermann	03/2021
5494	452^50145+50145^452	133142	Norbert Schneider	09/2020
5495	(355^52201-1)/354	133122	Tom Wu	08/2024
5496	(3^278981-1)/14507014	133101	Paul Vanderveen	05/2025
5497	30659^21796+21796^30659	133011	Hans Havermann	04/2021
5498	33276^9935+9935^33276	133010	Hans Havermann	04/2021
5499	30111^26122+26122^30111	133001	Hans Havermann	04/2021
5500	30790^20869+20869^30790	132998	Hans Havermann	04/2021

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Probable Primes Top 10000

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