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 ?
6001	2^340000-19877	102351	Enzo Doria	06/2013
6002	2^339990-114845	102348	Enzo Doria	05/2015
6003	(3^214516-2)/51383	102346	Lelio R Paula	12/2013
6004	20^78661-99	102341	Lelio R Paula	09/2016
6006	2^339951-19585	102336	Enzo Doria	05/2013
6005	(17*10^102335-167)/3	102336	Robert Price	05/2022
6007	(13*2^339943+1)/45	102333	Lelio R Paula	12/2013
6008	(236282#+121441)/(121441*25499429)	102332	Makoto Morimoto	08/2020
6009	5*10^102323-91	102324	Robert Price	03/2021
6011	2^339889+29327	102317	Yves Minet	06/2010
6010	(167*10^102315-17)/3	102317	Robert Price	03/2020
6012	26348^7641+7641^26348	102314	Hans Havermann	03/2019
6013	Phi(239414,10)/6333218543	102303	Makoto Kamada	08/2019
6014	2^339834-109493	102301	Enzo Doria	04/2014
6015	(16*10^102299-19)/3	102300	Robert Price	02/2019
6016	(11^98221-5^98221)/6	102286	Robert Price	01/2013
6017	3^214365+1820	102279	Lelio R Paula	10/2016
6018	31978^1579+1579^31978	102278	Hans Havermann	03/2019
6019	(89*10^102262-467)/9	102263	Robert Price	04/2022
6020	(11*2^339705-1)/183	102261	Lelio R Paula	03/2014
6021	2^339694-16995	102259	Lelio R Paula	09/2016
6022	(56*10^102255+691)/9	102256	Robert Price	05/2019
6023	122^49008+121	102249	Norbert Schneider	10/2018
6024	(2^339652+3178)/2	102246	Stefano Morozzi	09/2020
6025	7^120985-38	102245	Lelio R Paula	10/2016
6026	10^102244+122961	102245	Patrick De Geest	12/2016
6027	10^102244-27	102244	Lelio R Paula	09/2016
6028	7^120982-62	102242	Lelio R Paula	10/2016
6029	(2^339640+2670)/2	102242	Stefano Morozzi	09/2020
6030	4*6^131382-5	102236	Lelio R Paula	11/2014
6031	(2^339607+3290)/2	102232	Stefano Morozzi	02/2021
6032	2^339586-1091	102226	Yves Minet	11/2012
6033	11^98161-3072000	102225	Enzo Doria	12/2012
6034	9*7^120961-4	102225	Lelio R Paula	11/2014
6035	5*3^214250+2	102224	Serge Batalov	10/2010
6036	12^94713-59	102213	Lelio R Paula	10/2016
6037	12^94705+89	102204	Lelio R Paula	10/2016
6038	2^339407-177	102172	Lelio R Paula	08/2011
6039	4*10^102163-57	102164	Robert Price	10/2018
6040	2^339355+65	102157	Lelio R Paula	07/2011
6041	(28*10^102142-31)/3	102143	Robert Price	12/2019
6042	(2^339323+47)/880715	102141	Lelio R Paula	12/2013
6043	(2^339268+1758)/2	102130	Stefano Morozzi	09/2020
6044	s(178551)	102122	Robert Price	05/2020
6045	(797*10^102112-23)/9	102114	Robert Price	01/2022
6046	(2^339175+2790)/2	102102	Stefano Morozzi	02/2021
6048	2^339168+21	102100	Lelio R Paula	07/2011
6049	2^339167-108807	102100	Enzo Doria	03/2014
6047	(2^339169+42)/2	102100	Stefano Morozzi	09/2020
6050	2^339156+163	102097	Lelio R Paula	08/2011
6051	(2^339149+746)/2	102094	Stefano Morozzi	09/2020
6052	(25*10^102076-67)/3	102077	Robert Price	06/2019
6053	2^339081-4543	102074	Yves Minet	03/2019
6054	(3435^28867-1)/3434	102069	Serge Batalov	06/2022
6055	2*10^102062+77	102063	Robert Price	08/2020
6057	24327^15668+15668^24327	102053	Hans Havermann	02/2019
6056	10^102052+66793	102053	Patrick De Geest	09/2022
6059	10^102052-7000001	102052	Robert Price	06/2021
6058	10^102052-618623	102052	Patrick De Geest	09/2022
6060	2^339000-175635	102050	Stefano Morozzi	12/2021
6061	2^339000-151667	102050	Stefano Morozzi	12/2021
6062	2^338999+79289	102049	Stefano Morozzi	01/2022
6063	2^338994+188757	102048	Stefano Morozzi	05/2022
6064	2^338992+181591	102047	Stefano Morozzi	01/2022
6065	2^338992+136171	102047	Stefano Morozzi	03/2022
6066	2^338991-109435	102047	Stefano Morozzi	04/2022
6067	2^338991+193611	102047	Stefano Morozzi	09/2022
6068	2^338988-134619	102046	Stefano Morozzi	04/2022
6069	2^338986-60141	102045	Stefano Morozzi	06/2022
6070	2^338981+106391	102044	Stefano Morozzi	01/2022
6071	2^338982+34069	102044	Stefano Morozzi	03/2022
6072	2^338982-58781	102044	Stefano Morozzi	04/2022
6073	2^338977+83007	102043	Stefano Morozzi	02/2022
6074	2^338979-83601	102043	Stefano Morozzi	04/2022
6075	2^338975+28355	102042	Stefano Morozzi	01/2022
6076	2^338973+134619	102042	Stefano Morozzi	03/2022
6077	2^338974+183777	102042	Stefano Morozzi	03/2022
6078	2^338975+69293	102042	Stefano Morozzi	09/2022
6083	25080^11711+11711^25080	102041	Hans Havermann	02/2019
6079	2^338972+152343	102041	Stefano Morozzi	12/2021
6080	2^338972-180623	102041	Stefano Morozzi	02/2022
6081	2^338972+84441	102041	Stefano Morozzi	03/2022
6082	2^338971+64875	102041	Stefano Morozzi	05/2022
6084	2^338968+53461	102040	Stefano Morozzi	01/2022
6085	2^338969+160175	102040	Stefano Morozzi	03/2022
6086	2^338967+13409	102040	Stefano Morozzi	04/2022
6087	2^338969+67635	102040	Stefano Morozzi	09/2022
6088	2^338963-127455	102039	Stefano Morozzi	12/2021
6089	2^338963+132195	102039	Stefano Morozzi	02/2022
6090	2^338966+137919	102039	Stefano Morozzi	04/2022
6095	(2^338982-7)/1754517	102038	Lelio R Paula	12/2013
6091	2^338960+53935	102038	Stefano Morozzi	01/2022
6092	2^338962+83157	102038	Stefano Morozzi	02/2022
6093	2^338961+12341	102038	Stefano Morozzi	04/2022
6094	2^338960+63933	102038	Stefano Morozzi	05/2022
6096	2^338959-30919	102037	Stefano Morozzi	02/2022
6097	2^338959+164769	102037	Stefano Morozzi	05/2022
6098	2^338954-177003	102036	Stefano Morozzi	12/2021
6099	2^338954+154207	102036	Stefano Morozzi	01/2022
6100	2^338956+182493	102036	Stefano Morozzi	02/2022
6101	2^338954+162715	102036	Stefano Morozzi	04/2022
6102	2^338955-158241	102036	Stefano Morozzi	04/2022
6103	2^338956-33395	102036	Stefano Morozzi	04/2022
6104	2^338954+190915	102036	Stefano Morozzi	06/2022
6105	2^338955+41643	102036	Stefano Morozzi	09/2022
6106	2^338954+194427	102036	Stefano Morozzi	09/2022
6107	2^338956+117967	102036	Stefano Morozzi	09/2022
6108	2^338950+175077	102035	Stefano Morozzi	12/2021
6109	2^338951-51687	102035	Stefano Morozzi	12/2021
6110	2^338951+66123	102035	Stefano Morozzi	06/2022
6111	2^338950+19317	102035	Stefano Morozzi	09/2022
6112	2^338949+85449	102034	Stefano Morozzi	03/2022
6113	2^338949-184585	102034	Stefano Morozzi	04/2022
6114	2^338943+127103	102033	Stefano Morozzi	12/2021
6115	2^338944-84003	102033	Stefano Morozzi	04/2022
6116	2^338945+138605	102033	Stefano Morozzi	05/2022
6117	2^338940+78607	102032	Stefano Morozzi	01/2022
6118	2^338939+151569	102031	Stefano Morozzi	12/2021
6119	2^338938+183975	102031	Stefano Morozzi	03/2022
6120	2^338937-33429	102031	Stefano Morozzi	04/2022
6121	2^338939-183259	102031	Stefano Morozzi	04/2022
6122	2^338935+179999	102030	Stefano Morozzi	01/2022
6123	2^338936+84147	102030	Stefano Morozzi	03/2022
6124	2^338931+2349	102029	Stefano Morozzi	12/2021
6125	2^338933+79935	102029	Stefano Morozzi	01/2022
6126	2^338930+33819	102029	Stefano Morozzi	03/2022
6127	2^338931-31555	102029	Stefano Morozzi	03/2022
6128	2^338933+64169	102029	Stefano Morozzi	05/2022
6129	2^338932-184965	102029	Stefano Morozzi	06/2022
6130	2^338932+66943	102029	Stefano Morozzi	09/2022
6131	2^338932+92995	102029	Stefano Morozzi	09/2022
6132	2^338928+2367	102028	Stefano Morozzi	12/2021
6133	2^338927+52779	102028	Stefano Morozzi	01/2022
6134	2^338927-79539	102028	Stefano Morozzi	02/2022
6135	2^338929+60819	102028	Stefano Morozzi	03/2022
6136	2^338928-156959	102028	Stefano Morozzi	03/2022
6137	2^338925+106631	102027	Stefano Morozzi	01/2022
6138	2^338926+80235	102027	Stefano Morozzi	01/2022
6139	2^338926+41607	102027	Stefano Morozzi	09/2022
6140	2^338922-27291	102026	Stefano Morozzi	12/2021
6141	2^338919-103849	102025	Stefano Morozzi	01/2022
6142	2^338919+130221	102025	Stefano Morozzi	01/2022
6143	2^338914-79121	102024	Stefano Morozzi	02/2022
6144	2^338916+134047	102024	Stefano Morozzi	03/2022
6145	2^338910+81027	102023	Stefano Morozzi	01/2022
6146	2^338912+179821	102023	Stefano Morozzi	01/2022
6147	2^338909+100769	102022	Stefano Morozzi	11/2021
6148	2^338908-100839	102022	Stefano Morozzi	12/2021
6149	2^338909-25951	102022	Stefano Morozzi	12/2021
6150	2^338909+66845	102022	Stefano Morozzi	09/2022
6151	2^338906-25823	102021	Stefano Morozzi	12/2021
6152	2^338904+75951	102021	Stefano Morozzi	12/2021
6153	2^338906+6685	102021	Stefano Morozzi	01/2022
6154	2^338905+160365	102021	Stefano Morozzi	03/2022
6155	2^338906+92617	102021	Stefano Morozzi	09/2022
6156	2^338903+4155	102020	Stefano Morozzi	01/2022
6157	2^338901+55571	102020	Stefano Morozzi	01/2022
6158	2^338901-55479	102020	Stefano Morozzi	02/2022
6159	2^338903+33555	102020	Stefano Morozzi	03/2022
6160	2^338901+39777	102020	Stefano Morozzi	05/2022
6161	2^338903+165981	102020	Stefano Morozzi	06/2022
6162	2^338901-34863	102020	Stefano Morozzi	06/2022
6163	2^338899-150051	102019	Stefano Morozzi	12/2021
6164	2^338899+125951	102019	Stefano Morozzi	12/2021
6165	2^338898+179623	102019	Stefano Morozzi	01/2022
6166	2^338899-154467	102019	Stefano Morozzi	02/2022
6167	2^338898-60753	102019	Stefano Morozzi	06/2022
6168	2^338898+68635	102019	Stefano Morozzi	09/2022
6169	2^338894-133295	102018	Stefano Morozzi	04/2022
6170	2^338894+165573	102018	Stefano Morozzi	06/2022
6171	2^338894-60957	102018	Stefano Morozzi	06/2022
6180	2^338891-18885	102017	Enzo Doria	05/2013
6172	2^338891+26499	102017	Stefano Morozzi	12/2021
6173	2^338891-2625	102017	Stefano Morozzi	12/2021
6174	2^338893+128727	102017	Stefano Morozzi	01/2022
6175	2^338890-52965	102017	Stefano Morozzi	01/2022
6176	2^338892-55467	102017	Stefano Morozzi	02/2022
6177	2^338892-83393	102017	Stefano Morozzi	04/2022
6178	2^338893+13649	102017	Stefano Morozzi	05/2022
6179	2^338892+117957	102017	Stefano Morozzi	09/2022
6181	2^338887+154029	102016	Stefano Morozzi	01/2022
6182	2^338889-104293	102016	Stefano Morozzi	02/2022
6183	2^338886+177159	102015	Stefano Morozzi	12/2021
6184	2^338885+40425	102015	Stefano Morozzi	06/2022
6185	2^338880+11341	102014	Stefano Morozzi	03/2022
6186	2^338880-160383	102014	Stefano Morozzi	06/2022
6187	2^338879-1059	102013	Stefano Morozzi	12/2021
6188	2^338879-54525	102013	Stefano Morozzi	02/2022
6189	2^338877-82813	102013	Stefano Morozzi	03/2022
6190	2^338878-185883	102013	Stefano Morozzi	06/2022
6191	2^338879-60355	102013	Stefano Morozzi	06/2022
6192	2^338878+43719	102013	Stefano Morozzi	09/2022
6193	2^338871+7679	102011	Stefano Morozzi	02/2022
6194	2^338872+61141	102011	Stefano Morozzi	03/2022
6195	2^338872-183923	102011	Stefano Morozzi	04/2022
6196	2^338873+19527	102011	Stefano Morozzi	09/2022
6197	2^338868-5985	102010	Stefano Morozzi	02/2022
6198	2^338867+38079	102010	Stefano Morozzi	05/2022
6199	2^338868+140437	102010	Stefano Morozzi	06/2022
6200	2^338868-110175	102010	Stefano Morozzi	06/2022
6201	2^338864+158191	102009	Stefano Morozzi	02/2022
6202	2^338862+60433	102008	Stefano Morozzi	03/2022
6203	2^338861-9453	102008	Stefano Morozzi	04/2022
6204	2^338855+102141	102006	Stefano Morozzi	12/2021
6205	2^338856-27173	102006	Stefano Morozzi	12/2021
6206	2^338856-102839	102006	Stefano Morozzi	01/2022
6207	2^338855+79629	102006	Stefano Morozzi	01/2022
6208	2^338850+27987	102005	Stefano Morozzi	01/2022
6209	2^338853+111791	102005	Stefano Morozzi	04/2022
6210	2^338847+176013	102004	Stefano Morozzi	12/2021
6211	2^338847-2365	102004	Stefano Morozzi	12/2021
6212	2^338848+158941	102004	Stefano Morozzi	03/2022
6213	2^338848+16671	102004	Stefano Morozzi	06/2022
6214	2^338847-35061	102004	Stefano Morozzi	06/2022
6215	2^338845+135831	102003	Stefano Morozzi	03/2022
6216	2^338846+85695	102003	Stefano Morozzi	03/2022
6217	2^338845+186525	102003	Stefano Morozzi	04/2022
6218	2^338843-127261	102002	Stefano Morozzi	12/2021
6219	2^338843+107205	102002	Stefano Morozzi	02/2022
6220	2^338842-33185	102002	Stefano Morozzi	04/2022
6221	2^338842+14227	102002	Stefano Morozzi	05/2022
6225	8*10^102000+51	102001	Robert Price	08/2019
6222	2^338838+150837	102001	Stefano Morozzi	11/2021
6223	2^338838+141397	102001	Stefano Morozzi	06/2022
6224	2^338839+194363	102001	Stefano Morozzi	09/2022
6226	2^338835-150625	102000	Stefano Morozzi	12/2021
6227	2^338834-32877	102000	Stefano Morozzi	04/2022
6230	(2^338832+642)/2	101999	Stefano Morozzi	09/2020
6228	2^338833-100905	101999	Stefano Morozzi	12/2021
6229	2^338831+54419	101999	Stefano Morozzi	01/2022
6236	2^338829-113239	101998	Enzo Doria	07/2014
6237	2^338828-113297	101998	Enzo Doria	07/2014
6231	2^338830+25017	101998	Stefano Morozzi	11/2021
6232	2^338831+321	101998	Stefano Morozzi	11/2021
6233	2^338827-26197	101998	Stefano Morozzi	12/2021
6234	2^338829+52727	101998	Stefano Morozzi	01/2022
6235	2^338827-55461	101998	Stefano Morozzi	02/2022
6238	2^338825-27453	101997	Stefano Morozzi	12/2021
6239	2^338824+89355	101997	Stefano Morozzi	05/2022
6240	2^338825-10995	101997	Stefano Morozzi	06/2022
6241	2^338822+111175	101996	Stefano Morozzi	03/2022
6242	2^338822+187819	101996	Stefano Morozzi	04/2022
6243	2^338823+139545	101996	Stefano Morozzi	05/2022
6244	2^338823-184905	101996	Stefano Morozzi	06/2022
6245	2^338820+41317	101995	Stefano Morozzi	06/2022
6246	2^338815+151175	101994	Stefano Morozzi	12/2021
6247	2^338814-30011	101994	Stefano Morozzi	02/2022
6248	2^338814+12309	101994	Stefano Morozzi	04/2022
6249	2^338816-60647	101994	Stefano Morozzi	06/2022
6250	2^338811-126999	101993	Stefano Morozzi	12/2021

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PRP Records

Probable Primes Top 10000

(291192 PRPs in the top)