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 ?
7251	12^94705+89	102204	Lelio R Paula	10/2016
7252	2^339407-177	102172	Lelio R Paula	08/2011
7253	4*10^102163-57	102164	Robert Price	10/2018
7254	2^339355+65	102157	Lelio R Paula	07/2011
7255	(28*10^102142-31)/3	102143	Robert Price	12/2019
7256	(2^339323+47)/880715	102141	Lelio R Paula	12/2013
7257	(2^339268+1758)/2	102130	Stefano Morozzi	09/2020
7258	s(178551)	102122	Robert Price	05/2020
7259	(797*10^102112-23)/9	102114	Robert Price	01/2022
7260	(5*10^102107+7)/3	102108	Tyler Busby	02/2023
7261	(2^339175+2790)/2	102102	Stefano Morozzi	02/2021
7263	2^339168+21	102100	Lelio R Paula	07/2011
7264	2^339167-108807	102100	Enzo Doria	03/2014
7262	(2^339169+42)/2	102100	Stefano Morozzi	09/2020
7265	2^339156+163	102097	Lelio R Paula	08/2011
7266	(2^339149+746)/2	102094	Stefano Morozzi	09/2020
7267	(25*10^102076-67)/3	102077	Robert Price	06/2019
7268	2^339081-4543	102074	Yves Minet	03/2019
7269	(3435^28867-1)/3434	102069	Serge Batalov	06/2022
7270	2*10^102062+77	102063	Robert Price	08/2020
7272	24327^15668+15668^24327	102053	Hans Havermann	02/2019
7271	10^102052+66793	102053	Patrick De Geest	09/2022
7273	10^102052-7000001	102052	Robert Price	06/2021
7274	10^102052-618623	102052	Patrick De Geest	09/2022
7275	2^339000-175635	102050	Stefano Morozzi	12/2021
7276	2^339000-151667	102050	Stefano Morozzi	12/2021
7277	2^338999+79289	102049	Stefano Morozzi	01/2022
7278	2^338998-63897	102049	Stefano Morozzi	12/2022
7279	2^338997+99659	102049	Stefano Morozzi	02/2023
7280	2^338994+188757	102048	Stefano Morozzi	05/2022
7281	2^338995+70785	102048	Stefano Morozzi	11/2022
7282	2^338994-12183	102048	Stefano Morozzi	12/2022
7283	2^338992+181591	102047	Stefano Morozzi	01/2022
7284	2^338992+136171	102047	Stefano Morozzi	03/2022
7285	2^338991-109435	102047	Stefano Morozzi	04/2022
7286	2^338991+193611	102047	Stefano Morozzi	09/2022
7287	2^338988-134619	102046	Stefano Morozzi	04/2022
7288	2^338987-62557	102046	Stefano Morozzi	12/2022
7289	2^338986-60141	102045	Stefano Morozzi	06/2022
7290	2^338986+98209	102045	Stefano Morozzi	11/2022
7291	2^338981+106391	102044	Stefano Morozzi	01/2022
7292	2^338982+34069	102044	Stefano Morozzi	03/2022
7293	2^338982-58781	102044	Stefano Morozzi	04/2022
7294	2^338980+70833	102044	Stefano Morozzi	11/2022
7295	2^338982-92111	102044	Stefano Morozzi	02/2023
7296	2^338977+83007	102043	Stefano Morozzi	02/2022
7297	2^338979-83601	102043	Stefano Morozzi	04/2022
7298	2^338975+28355	102042	Stefano Morozzi	01/2022
7299	2^338973+134619	102042	Stefano Morozzi	03/2022
7300	2^338974+183777	102042	Stefano Morozzi	03/2022
7301	2^338975+69293	102042	Stefano Morozzi	09/2022
7309	25080^11711+11711^25080	102041	Hans Havermann	02/2019
7302	2^338972+152343	102041	Stefano Morozzi	12/2021
7303	2^338972-180623	102041	Stefano Morozzi	02/2022
7304	2^338972+84441	102041	Stefano Morozzi	03/2022
7305	2^338971+64875	102041	Stefano Morozzi	05/2022
7306	2^338971+44985	102041	Stefano Morozzi	11/2022
7307	2^338971+145065	102041	Stefano Morozzi	11/2022
7308	2^338972-16635	102041	Stefano Morozzi	01/2023
7310	2^338968+53461	102040	Stefano Morozzi	01/2022
7311	2^338969+160175	102040	Stefano Morozzi	03/2022
7312	2^338967+13409	102040	Stefano Morozzi	04/2022
7313	2^338969+67635	102040	Stefano Morozzi	09/2022
7314	2^338969-15913	102040	Stefano Morozzi	01/2023
7315	2^338963-127455	102039	Stefano Morozzi	12/2021
7316	2^338963+132195	102039	Stefano Morozzi	02/2022
7317	2^338966+137919	102039	Stefano Morozzi	04/2022
7318	2^338963-87529	102039	Stefano Morozzi	12/2022
7319	2^338963-116859	102039	Stefano Morozzi	02/2023
7326	(2^338982-7)/1754517	102038	Lelio R Paula	12/2013
7320	2^338960+53935	102038	Stefano Morozzi	01/2022
7321	2^338962+83157	102038	Stefano Morozzi	02/2022
7322	2^338961+12341	102038	Stefano Morozzi	04/2022
7323	2^338960+63933	102038	Stefano Morozzi	05/2022
7324	2^338960+170791	102038	Stefano Morozzi	11/2022
7325	2^338962+21679	102038	Stefano Morozzi	11/2022
7327	2^338959-30919	102037	Stefano Morozzi	02/2022
7328	2^338959+164769	102037	Stefano Morozzi	05/2022
7329	2^338958-43161	102037	Stefano Morozzi	02/2023
7330	2^338954-177003	102036	Stefano Morozzi	12/2021
7331	2^338954+154207	102036	Stefano Morozzi	01/2022
7332	2^338956+182493	102036	Stefano Morozzi	02/2022
7333	2^338954+162715	102036	Stefano Morozzi	04/2022
7334	2^338955-158241	102036	Stefano Morozzi	04/2022
7335	2^338956-33395	102036	Stefano Morozzi	04/2022
7336	2^338954+190915	102036	Stefano Morozzi	06/2022
7337	2^338955+41643	102036	Stefano Morozzi	09/2022
7338	2^338954+194427	102036	Stefano Morozzi	09/2022
7339	2^338956+117967	102036	Stefano Morozzi	09/2022
7340	2^338956+195495	102036	Stefano Morozzi	11/2022
7341	2^338954-186371	102036	Stefano Morozzi	12/2022
7342	2^338950+175077	102035	Stefano Morozzi	12/2021
7343	2^338951-51687	102035	Stefano Morozzi	12/2021
7344	2^338951+66123	102035	Stefano Morozzi	06/2022
7345	2^338950+19317	102035	Stefano Morozzi	09/2022
7346	2^338951-161479	102035	Stefano Morozzi	12/2022
7347	2^338950-66335	102035	Stefano Morozzi	01/2023
7348	2^338951-41611	102035	Stefano Morozzi	02/2023
7349	2^338952-142887	102035	Stefano Morozzi	02/2023
7350	2^338949+85449	102034	Stefano Morozzi	03/2022
7351	2^338949-184585	102034	Stefano Morozzi	04/2022
7352	2^338949-88555	102034	Stefano Morozzi	12/2022
7353	2^338948+49393	102034	Stefano Morozzi	02/2023
7354	2^338949-17601	102034	Stefano Morozzi	02/2023
7355	2^338943+127103	102033	Stefano Morozzi	12/2021
7356	2^338944-84003	102033	Stefano Morozzi	04/2022
7357	2^338945+138605	102033	Stefano Morozzi	05/2022
7358	2^338943+95133	102033	Stefano Morozzi	11/2022
7359	2^338943+147435	102033	Stefano Morozzi	11/2022
7360	2^338943-116067	102033	Stefano Morozzi	01/2023
7361	2^338940+78607	102032	Stefano Morozzi	01/2022
7362	2^338942-86687	102032	Stefano Morozzi	12/2022
7363	2^338939+151569	102031	Stefano Morozzi	12/2021
7364	2^338938+183975	102031	Stefano Morozzi	03/2022
7365	2^338937-33429	102031	Stefano Morozzi	04/2022
7366	2^338939-183259	102031	Stefano Morozzi	04/2022
7367	2^338937-139951	102031	Stefano Morozzi	01/2023
7368	2^338938-40151	102031	Stefano Morozzi	01/2023
7369	2^338938+74449	102031	Stefano Morozzi	02/2023
7370	2^338935+179999	102030	Stefano Morozzi	01/2022
7371	2^338936+84147	102030	Stefano Morozzi	03/2022
7372	2^338935+171261	102030	Stefano Morozzi	11/2022
7373	2^338936-41355	102030	Stefano Morozzi	01/2023
7374	2^338931+2349	102029	Stefano Morozzi	12/2021
7375	2^338933+79935	102029	Stefano Morozzi	01/2022
7376	2^338930+33819	102029	Stefano Morozzi	03/2022
7377	2^338931-31555	102029	Stefano Morozzi	03/2022
7378	2^338933+64169	102029	Stefano Morozzi	05/2022
7379	2^338932-184965	102029	Stefano Morozzi	06/2022
7380	2^338932+66943	102029	Stefano Morozzi	09/2022
7381	2^338932+92995	102029	Stefano Morozzi	09/2022
7382	2^338931+97001	102029	Stefano Morozzi	11/2022
7383	2^338932-165453	102029	Stefano Morozzi	01/2023
7384	2^338933-40899	102029	Stefano Morozzi	01/2023
7385	2^338928+2367	102028	Stefano Morozzi	12/2021
7386	2^338927+52779	102028	Stefano Morozzi	01/2022
7387	2^338927-79539	102028	Stefano Morozzi	02/2022
7388	2^338929+60819	102028	Stefano Morozzi	03/2022
7389	2^338928-156959	102028	Stefano Morozzi	03/2022
7390	2^338927-63919	102028	Stefano Morozzi	12/2022
7391	2^338925+106631	102027	Stefano Morozzi	01/2022
7392	2^338926+80235	102027	Stefano Morozzi	01/2022
7393	2^338926+41607	102027	Stefano Morozzi	09/2022
7394	2^338925+195435	102027	Stefano Morozzi	11/2022
7395	2^338924-92885	102027	Stefano Morozzi	02/2023
7396	2^338922-27291	102026	Stefano Morozzi	12/2021
7397	2^338919-103849	102025	Stefano Morozzi	01/2022
7398	2^338919+130221	102025	Stefano Morozzi	01/2022
7399	2^338918-91967	102025	Stefano Morozzi	02/2023
7400	2^338917+561057	102025	Boyan Hu	03/2024
7401	2^338914-79121	102024	Stefano Morozzi	02/2022
7402	2^338916+134047	102024	Stefano Morozzi	03/2022
7403	2^338914-11315	102024	Stefano Morozzi	12/2022
7404	2^338910+81027	102023	Stefano Morozzi	01/2022
7405	2^338912+179821	102023	Stefano Morozzi	01/2022
7406	2^338909+100769	102022	Stefano Morozzi	11/2021
7407	2^338908-100839	102022	Stefano Morozzi	12/2021
7408	2^338909-25951	102022	Stefano Morozzi	12/2021
7409	2^338909+66845	102022	Stefano Morozzi	09/2022
7410	2^338907+73509	102022	Stefano Morozzi	11/2022
7411	2^338906-25823	102021	Stefano Morozzi	12/2021
7412	2^338904+75951	102021	Stefano Morozzi	12/2021
7413	2^338906+6685	102021	Stefano Morozzi	01/2022
7414	2^338905+160365	102021	Stefano Morozzi	03/2022
7415	2^338906+92617	102021	Stefano Morozzi	09/2022
7416	2^338904+47065	102021	Stefano Morozzi	11/2022
7417	2^338905+70427	102021	Stefano Morozzi	11/2022
7418	2^338905-163975	102021	Stefano Morozzi	12/2022
7419	2^338903+4155	102020	Stefano Morozzi	01/2022
7420	2^338901+55571	102020	Stefano Morozzi	01/2022
7421	2^338901-55479	102020	Stefano Morozzi	02/2022
7422	2^338903+33555	102020	Stefano Morozzi	03/2022
7423	2^338901+39777	102020	Stefano Morozzi	05/2022
7424	2^338903+165981	102020	Stefano Morozzi	06/2022
7425	2^338901-34863	102020	Stefano Morozzi	06/2022
7426	2^338899-150051	102019	Stefano Morozzi	12/2021
7427	2^338899+125951	102019	Stefano Morozzi	12/2021
7428	2^338898+179623	102019	Stefano Morozzi	01/2022
7429	2^338899-154467	102019	Stefano Morozzi	02/2022
7430	2^338898-60753	102019	Stefano Morozzi	06/2022
7431	2^338898+68635	102019	Stefano Morozzi	09/2022
7432	2^338897-85963	102019	Stefano Morozzi	12/2022
7433	2^338898+174129	102019	Stefano Morozzi	02/2023
7434	2^338894-133295	102018	Stefano Morozzi	04/2022
7435	2^338894+165573	102018	Stefano Morozzi	06/2022
7436	2^338894-60957	102018	Stefano Morozzi	06/2022
7437	2^338894-89463	102018	Stefano Morozzi	01/2023
7447	2^338891-18885	102017	Enzo Doria	05/2013
7438	2^338891+26499	102017	Stefano Morozzi	12/2021
7439	2^338891-2625	102017	Stefano Morozzi	12/2021
7440	2^338893+128727	102017	Stefano Morozzi	01/2022
7441	2^338890-52965	102017	Stefano Morozzi	01/2022
7442	2^338892-55467	102017	Stefano Morozzi	02/2022
7443	2^338892-83393	102017	Stefano Morozzi	04/2022
7444	2^338893+13649	102017	Stefano Morozzi	05/2022
7445	2^338892+117957	102017	Stefano Morozzi	09/2022
7446	2^338892-14643	102017	Stefano Morozzi	01/2023
7448	2^338887+154029	102016	Stefano Morozzi	01/2022
7449	2^338889-104293	102016	Stefano Morozzi	02/2022
7450	2^338887+147741	102016	Stefano Morozzi	11/2022
7451	2^338889+195975	102016	Stefano Morozzi	11/2022
7452	2^338889-117873	102016	Stefano Morozzi	02/2023
7453	2^338886+177159	102015	Stefano Morozzi	12/2021
7454	2^338885+40425	102015	Stefano Morozzi	06/2022
7455	2^338884-13053	102015	Stefano Morozzi	12/2022
7456	2^338885-112569	102015	Stefano Morozzi	12/2022
7457	2^338880+11341	102014	Stefano Morozzi	03/2022
7458	2^338880-160383	102014	Stefano Morozzi	06/2022
7459	2^338880-161627	102014	Stefano Morozzi	12/2022
7460	2^338879-1059	102013	Stefano Morozzi	12/2021
7461	2^338879-54525	102013	Stefano Morozzi	02/2022
7462	2^338877-82813	102013	Stefano Morozzi	03/2022
7463	2^338878-185883	102013	Stefano Morozzi	06/2022
7464	2^338879-60355	102013	Stefano Morozzi	06/2022
7465	2^338878+43719	102013	Stefano Morozzi	09/2022
7466	2^338879+122049	102013	Stefano Morozzi	11/2022
7467	2^338874-15063	102012	Stefano Morozzi	01/2023
7468	2^338874+148993	102012	Stefano Morozzi	02/2023
7469	2^338871+7679	102011	Stefano Morozzi	02/2022
7470	2^338872+61141	102011	Stefano Morozzi	03/2022
7471	2^338872-183923	102011	Stefano Morozzi	04/2022
7472	2^338873+19527	102011	Stefano Morozzi	09/2022
7473	2^338870+70719	102011	Stefano Morozzi	11/2022
7474	(19*10^102011+287)/9/3	102011	Alfred Reich	11/2022
7475	2^338870-37571	102011	Stefano Morozzi	12/2022
7476	2^338872-138573	102011	Stefano Morozzi	12/2022
7477	2^338873-63843	102011	Stefano Morozzi	12/2022
7478	2^338868-5985	102010	Stefano Morozzi	02/2022
7479	2^338867+38079	102010	Stefano Morozzi	05/2022
7480	2^338868+140437	102010	Stefano Morozzi	06/2022
7481	2^338868-110175	102010	Stefano Morozzi	06/2022
7482	2^338868+123337	102010	Stefano Morozzi	11/2022
7483	2^338867-13327	102010	Stefano Morozzi	12/2022
7484	2^338868-11279	102010	Stefano Morozzi	12/2022
7485	2^338868-115685	102010	Stefano Morozzi	01/2023
7486	2^338864+158191	102009	Stefano Morozzi	02/2022
7487	2^338865-39699	102009	Stefano Morozzi	01/2023
7488	2^338865-40789	102009	Stefano Morozzi	01/2023
7489	2^338862+60433	102008	Stefano Morozzi	03/2022
7490	2^338861-9453	102008	Stefano Morozzi	04/2022
7491	2^338861+98067	102008	Stefano Morozzi	11/2022
7492	2^338862+146545	102008	Stefano Morozzi	11/2022
7493	2^338863-186207	102008	Stefano Morozzi	12/2022
7494	2^338860-41429	102008	Stefano Morozzi	01/2023
7495	2^338862-115833	102008	Stefano Morozzi	01/2023
7496	2^338863+74259	102008	Stefano Morozzi	02/2023
7497	2^338863-193017	102008	Stefano Morozzi	02/2023
7498	2^338858-190185	102007	Stefano Morozzi	01/2023
7499	2^338855+102141	102006	Stefano Morozzi	12/2021
7500	2^338856-27173	102006	Stefano Morozzi	12/2021

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