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 ?
6251	25080^11711+11711^25080	102041	Hans Havermann	02/2019
6252	2^338968+53461	102040	Stefano Morozzi	01/2022
6253	2^338969+160175	102040	Stefano Morozzi	03/2022
6254	2^338967+13409	102040	Stefano Morozzi	04/2022
6255	2^338969+67635	102040	Stefano Morozzi	09/2022
6256	2^338969-15913	102040	Stefano Morozzi	01/2023
6257	2^338963-127455	102039	Stefano Morozzi	12/2021
6258	2^338963+132195	102039	Stefano Morozzi	02/2022
6259	2^338966+137919	102039	Stefano Morozzi	04/2022
6260	2^338963-87529	102039	Stefano Morozzi	12/2022
6267	(2^338982-7)/1754517	102038	Lelio R Paula	12/2013
6261	2^338960+53935	102038	Stefano Morozzi	01/2022
6262	2^338962+83157	102038	Stefano Morozzi	02/2022
6263	2^338961+12341	102038	Stefano Morozzi	04/2022
6264	2^338960+63933	102038	Stefano Morozzi	05/2022
6265	2^338960+170791	102038	Stefano Morozzi	11/2022
6266	2^338962+21679	102038	Stefano Morozzi	11/2022
6268	2^338959-30919	102037	Stefano Morozzi	02/2022
6269	2^338959+164769	102037	Stefano Morozzi	05/2022
6270	2^338954-177003	102036	Stefano Morozzi	12/2021
6271	2^338954+154207	102036	Stefano Morozzi	01/2022
6272	2^338956+182493	102036	Stefano Morozzi	02/2022
6273	2^338954+162715	102036	Stefano Morozzi	04/2022
6274	2^338955-158241	102036	Stefano Morozzi	04/2022
6275	2^338956-33395	102036	Stefano Morozzi	04/2022
6276	2^338954+190915	102036	Stefano Morozzi	06/2022
6277	2^338955+41643	102036	Stefano Morozzi	09/2022
6278	2^338954+194427	102036	Stefano Morozzi	09/2022
6279	2^338956+117967	102036	Stefano Morozzi	09/2022
6280	2^338956+195495	102036	Stefano Morozzi	11/2022
6281	2^338954-186371	102036	Stefano Morozzi	12/2022
6282	2^338950+175077	102035	Stefano Morozzi	12/2021
6283	2^338951-51687	102035	Stefano Morozzi	12/2021
6284	2^338951+66123	102035	Stefano Morozzi	06/2022
6285	2^338950+19317	102035	Stefano Morozzi	09/2022
6286	2^338951-161479	102035	Stefano Morozzi	12/2022
6287	2^338950-66335	102035	Stefano Morozzi	01/2023
6288	2^338949+85449	102034	Stefano Morozzi	03/2022
6289	2^338949-184585	102034	Stefano Morozzi	04/2022
6290	2^338949-88555	102034	Stefano Morozzi	12/2022
6291	2^338943+127103	102033	Stefano Morozzi	12/2021
6292	2^338944-84003	102033	Stefano Morozzi	04/2022
6293	2^338945+138605	102033	Stefano Morozzi	05/2022
6294	2^338943+95133	102033	Stefano Morozzi	11/2022
6295	2^338943+147435	102033	Stefano Morozzi	11/2022
6296	2^338943-116067	102033	Stefano Morozzi	01/2023
6297	2^338940+78607	102032	Stefano Morozzi	01/2022
6298	2^338942-86687	102032	Stefano Morozzi	12/2022
6299	2^338939+151569	102031	Stefano Morozzi	12/2021
6300	2^338938+183975	102031	Stefano Morozzi	03/2022
6301	2^338937-33429	102031	Stefano Morozzi	04/2022
6302	2^338939-183259	102031	Stefano Morozzi	04/2022
6303	2^338937-139951	102031	Stefano Morozzi	01/2023
6304	2^338938-40151	102031	Stefano Morozzi	01/2023
6305	2^338935+179999	102030	Stefano Morozzi	01/2022
6306	2^338936+84147	102030	Stefano Morozzi	03/2022
6307	2^338935+171261	102030	Stefano Morozzi	11/2022
6308	2^338936-41355	102030	Stefano Morozzi	01/2023
6309	2^338931+2349	102029	Stefano Morozzi	12/2021
6310	2^338933+79935	102029	Stefano Morozzi	01/2022
6311	2^338930+33819	102029	Stefano Morozzi	03/2022
6312	2^338931-31555	102029	Stefano Morozzi	03/2022
6313	2^338933+64169	102029	Stefano Morozzi	05/2022
6314	2^338932-184965	102029	Stefano Morozzi	06/2022
6315	2^338932+66943	102029	Stefano Morozzi	09/2022
6316	2^338932+92995	102029	Stefano Morozzi	09/2022
6317	2^338931+97001	102029	Stefano Morozzi	11/2022
6318	2^338932-165453	102029	Stefano Morozzi	01/2023
6319	2^338933-40899	102029	Stefano Morozzi	01/2023
6320	2^338928+2367	102028	Stefano Morozzi	12/2021
6321	2^338927+52779	102028	Stefano Morozzi	01/2022
6322	2^338927-79539	102028	Stefano Morozzi	02/2022
6323	2^338929+60819	102028	Stefano Morozzi	03/2022
6324	2^338928-156959	102028	Stefano Morozzi	03/2022
6325	2^338927-63919	102028	Stefano Morozzi	12/2022
6326	2^338925+106631	102027	Stefano Morozzi	01/2022
6327	2^338926+80235	102027	Stefano Morozzi	01/2022
6328	2^338926+41607	102027	Stefano Morozzi	09/2022
6329	2^338925+195435	102027	Stefano Morozzi	11/2022
6330	2^338922-27291	102026	Stefano Morozzi	12/2021
6331	2^338919-103849	102025	Stefano Morozzi	01/2022
6332	2^338919+130221	102025	Stefano Morozzi	01/2022
6333	2^338914-79121	102024	Stefano Morozzi	02/2022
6334	2^338916+134047	102024	Stefano Morozzi	03/2022
6335	2^338914-11315	102024	Stefano Morozzi	12/2022
6336	2^338910+81027	102023	Stefano Morozzi	01/2022
6337	2^338912+179821	102023	Stefano Morozzi	01/2022
6338	2^338909+100769	102022	Stefano Morozzi	11/2021
6339	2^338908-100839	102022	Stefano Morozzi	12/2021
6340	2^338909-25951	102022	Stefano Morozzi	12/2021
6341	2^338909+66845	102022	Stefano Morozzi	09/2022
6342	2^338907+73509	102022	Stefano Morozzi	11/2022
6343	2^338906-25823	102021	Stefano Morozzi	12/2021
6344	2^338904+75951	102021	Stefano Morozzi	12/2021
6345	2^338906+6685	102021	Stefano Morozzi	01/2022
6346	2^338905+160365	102021	Stefano Morozzi	03/2022
6347	2^338906+92617	102021	Stefano Morozzi	09/2022
6348	2^338904+47065	102021	Stefano Morozzi	11/2022
6349	2^338905+70427	102021	Stefano Morozzi	11/2022
6350	2^338905-163975	102021	Stefano Morozzi	12/2022
6351	2^338903+4155	102020	Stefano Morozzi	01/2022
6352	2^338901+55571	102020	Stefano Morozzi	01/2022
6353	2^338901-55479	102020	Stefano Morozzi	02/2022
6354	2^338903+33555	102020	Stefano Morozzi	03/2022
6355	2^338901+39777	102020	Stefano Morozzi	05/2022
6356	2^338903+165981	102020	Stefano Morozzi	06/2022
6357	2^338901-34863	102020	Stefano Morozzi	06/2022
6358	2^338899-150051	102019	Stefano Morozzi	12/2021
6359	2^338899+125951	102019	Stefano Morozzi	12/2021
6360	2^338898+179623	102019	Stefano Morozzi	01/2022
6361	2^338899-154467	102019	Stefano Morozzi	02/2022
6362	2^338898-60753	102019	Stefano Morozzi	06/2022
6363	2^338898+68635	102019	Stefano Morozzi	09/2022
6364	2^338897-85963	102019	Stefano Morozzi	12/2022
6365	2^338894-133295	102018	Stefano Morozzi	04/2022
6366	2^338894+165573	102018	Stefano Morozzi	06/2022
6367	2^338894-60957	102018	Stefano Morozzi	06/2022
6368	2^338894-89463	102018	Stefano Morozzi	01/2023
6378	2^338891-18885	102017	Enzo Doria	05/2013
6369	2^338891+26499	102017	Stefano Morozzi	12/2021
6370	2^338891-2625	102017	Stefano Morozzi	12/2021
6371	2^338893+128727	102017	Stefano Morozzi	01/2022
6372	2^338890-52965	102017	Stefano Morozzi	01/2022
6373	2^338892-55467	102017	Stefano Morozzi	02/2022
6374	2^338892-83393	102017	Stefano Morozzi	04/2022
6375	2^338893+13649	102017	Stefano Morozzi	05/2022
6376	2^338892+117957	102017	Stefano Morozzi	09/2022
6377	2^338892-14643	102017	Stefano Morozzi	01/2023
6379	2^338887+154029	102016	Stefano Morozzi	01/2022
6380	2^338889-104293	102016	Stefano Morozzi	02/2022
6381	2^338887+147741	102016	Stefano Morozzi	11/2022
6382	2^338889+195975	102016	Stefano Morozzi	11/2022
6383	2^338886+177159	102015	Stefano Morozzi	12/2021
6384	2^338885+40425	102015	Stefano Morozzi	06/2022
6385	2^338884-13053	102015	Stefano Morozzi	12/2022
6386	2^338885-112569	102015	Stefano Morozzi	12/2022
6387	2^338880+11341	102014	Stefano Morozzi	03/2022
6388	2^338880-160383	102014	Stefano Morozzi	06/2022
6389	2^338880-161627	102014	Stefano Morozzi	12/2022
6390	2^338879-1059	102013	Stefano Morozzi	12/2021
6391	2^338879-54525	102013	Stefano Morozzi	02/2022
6392	2^338877-82813	102013	Stefano Morozzi	03/2022
6393	2^338878-185883	102013	Stefano Morozzi	06/2022
6394	2^338879-60355	102013	Stefano Morozzi	06/2022
6395	2^338878+43719	102013	Stefano Morozzi	09/2022
6396	2^338879+122049	102013	Stefano Morozzi	11/2022
6397	2^338874-15063	102012	Stefano Morozzi	01/2023
6398	2^338871+7679	102011	Stefano Morozzi	02/2022
6399	2^338872+61141	102011	Stefano Morozzi	03/2022
6400	2^338872-183923	102011	Stefano Morozzi	04/2022
6401	2^338873+19527	102011	Stefano Morozzi	09/2022
6402	2^338870+70719	102011	Stefano Morozzi	11/2022
6403	(19*10^102011+287)/9/3	102011	Alfred Reich	11/2022
6404	2^338870-37571	102011	Stefano Morozzi	12/2022
6405	2^338872-138573	102011	Stefano Morozzi	12/2022
6406	2^338873-63843	102011	Stefano Morozzi	12/2022
6407	2^338868-5985	102010	Stefano Morozzi	02/2022
6408	2^338867+38079	102010	Stefano Morozzi	05/2022
6409	2^338868+140437	102010	Stefano Morozzi	06/2022
6410	2^338868-110175	102010	Stefano Morozzi	06/2022
6411	2^338868+123337	102010	Stefano Morozzi	11/2022
6412	2^338867-13327	102010	Stefano Morozzi	12/2022
6413	2^338868-11279	102010	Stefano Morozzi	12/2022
6414	2^338868-115685	102010	Stefano Morozzi	01/2023
6415	2^338864+158191	102009	Stefano Morozzi	02/2022
6416	2^338865-39699	102009	Stefano Morozzi	01/2023
6417	2^338865-40789	102009	Stefano Morozzi	01/2023
6418	2^338862+60433	102008	Stefano Morozzi	03/2022
6419	2^338861-9453	102008	Stefano Morozzi	04/2022
6420	2^338861+98067	102008	Stefano Morozzi	11/2022
6421	2^338862+146545	102008	Stefano Morozzi	11/2022
6422	2^338863-186207	102008	Stefano Morozzi	12/2022
6423	2^338860-41429	102008	Stefano Morozzi	01/2023
6424	2^338862-115833	102008	Stefano Morozzi	01/2023
6425	2^338858-190185	102007	Stefano Morozzi	01/2023
6426	2^338855+102141	102006	Stefano Morozzi	12/2021
6427	2^338856-27173	102006	Stefano Morozzi	12/2021
6428	2^338856-102839	102006	Stefano Morozzi	01/2022
6429	2^338855+79629	102006	Stefano Morozzi	01/2022
6430	2^338856+47755	102006	Stefano Morozzi	11/2022
6431	2^338850+27987	102005	Stefano Morozzi	01/2022
6432	2^338853+111791	102005	Stefano Morozzi	04/2022
6433	2^338852+145797	102005	Stefano Morozzi	11/2022
6434	2^338852-88497	102005	Stefano Morozzi	12/2022
6435	2^338847+176013	102004	Stefano Morozzi	12/2021
6436	2^338847-2365	102004	Stefano Morozzi	12/2021
6437	2^338848+158941	102004	Stefano Morozzi	03/2022
6438	2^338848+16671	102004	Stefano Morozzi	06/2022
6439	2^338847-35061	102004	Stefano Morozzi	06/2022
6440	2^338848+145063	102004	Stefano Morozzi	11/2022
6441	2^338847-61885	102004	Stefano Morozzi	12/2022
6442	2^338845+135831	102003	Stefano Morozzi	03/2022
6443	2^338846+85695	102003	Stefano Morozzi	03/2022
6444	2^338845+186525	102003	Stefano Morozzi	04/2022
6445	2^338846-163473	102003	Stefano Morozzi	12/2022
6446	2^338844-16077	102003	Stefano Morozzi	01/2023
6447	2^338844-165143	102003	Stefano Morozzi	01/2023
6448	2^338843-127261	102002	Stefano Morozzi	12/2021
6449	2^338843+107205	102002	Stefano Morozzi	02/2022
6450	2^338842-33185	102002	Stefano Morozzi	04/2022
6451	2^338842+14227	102002	Stefano Morozzi	05/2022
6452	2^338842+147973	102002	Stefano Morozzi	11/2022
6460	8*10^102000+51	102001	Robert Price	08/2019
6453	2^338838+150837	102001	Stefano Morozzi	11/2021
6454	2^338838+141397	102001	Stefano Morozzi	06/2022
6455	2^338839+194363	102001	Stefano Morozzi	09/2022
6456	2^338838+95637	102001	Stefano Morozzi	11/2022
6457	2^338839+171545	102001	Stefano Morozzi	11/2022
6458	2^338837-40071	102001	Stefano Morozzi	01/2023
6459	2^338838-90251	102001	Stefano Morozzi	01/2023
6461	2^338835-150625	102000	Stefano Morozzi	12/2021
6462	2^338834-32877	102000	Stefano Morozzi	04/2022
6466	(2^338832+642)/2	101999	Stefano Morozzi	09/2020
6463	2^338833-100905	101999	Stefano Morozzi	12/2021
6464	2^338831+54419	101999	Stefano Morozzi	01/2022
6465	2^338831-63687	101999	Stefano Morozzi	12/2022
6473	2^338829-113239	101998	Enzo Doria	07/2014
6474	2^338828-113297	101998	Enzo Doria	07/2014
6467	2^338830+25017	101998	Stefano Morozzi	11/2021
6468	2^338831+321	101998	Stefano Morozzi	11/2021
6469	2^338827-26197	101998	Stefano Morozzi	12/2021
6470	2^338829+52727	101998	Stefano Morozzi	01/2022
6471	2^338827-55461	101998	Stefano Morozzi	02/2022
6472	2^338828-65859	101998	Stefano Morozzi	01/2023
6475	2^338825-27453	101997	Stefano Morozzi	12/2021
6476	2^338824+89355	101997	Stefano Morozzi	05/2022
6477	2^338825-10995	101997	Stefano Morozzi	06/2022
6478	2^338822+111175	101996	Stefano Morozzi	03/2022
6479	2^338822+187819	101996	Stefano Morozzi	04/2022
6480	2^338823+139545	101996	Stefano Morozzi	05/2022
6481	2^338823-184905	101996	Stefano Morozzi	06/2022
6482	2^338821-38919	101996	Stefano Morozzi	12/2022
6483	2^338820+41317	101995	Stefano Morozzi	06/2022
6484	2^338817+46019	101995	Stefano Morozzi	11/2022
6485	2^338820+148083	101995	Stefano Morozzi	11/2022
6486	2^338817-163251	101995	Stefano Morozzi	12/2022
6487	2^338819-63705	101995	Stefano Morozzi	12/2022
6488	2^338815+151175	101994	Stefano Morozzi	12/2021
6489	2^338814-30011	101994	Stefano Morozzi	02/2022
6490	2^338814+12309	101994	Stefano Morozzi	04/2022
6491	2^338816-60647	101994	Stefano Morozzi	06/2022
6492	2^338816+171043	101994	Stefano Morozzi	11/2022
6493	2^338814-11513	101994	Stefano Morozzi	12/2022
6494	2^338811-126999	101993	Stefano Morozzi	12/2021
6495	2^338811+131621	101993	Stefano Morozzi	02/2022
6496	2^338812-107637	101993	Stefano Morozzi	03/2022
6497	2^338813+192725	101993	Stefano Morozzi	09/2022
6498	2^338812+94731	101993	Stefano Morozzi	11/2022
6499	2^338809-152755	101992	Stefano Morozzi	01/2022
6500	2^338808+156531	101992	Stefano Morozzi	01/2022

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PRP Records

Probable Primes Top 10000

(291910 PRPs in the top)