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) !!!

Submit your PRPs

See the Top discoverers
See the Latest PRPs
Search by form


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 ?
9251	2^338991+193611	102047	Stefano Morozzi	09/2022
9252	2^338988-134619	102046	Stefano Morozzi	04/2022
9253	2^338987-62557	102046	Stefano Morozzi	12/2022
9254	2^338986-60141	102045	Stefano Morozzi	06/2022
9255	2^338986+98209	102045	Stefano Morozzi	11/2022
9256	2^338981+106391	102044	Stefano Morozzi	01/2022
9257	2^338982+34069	102044	Stefano Morozzi	03/2022
9258	2^338982-58781	102044	Stefano Morozzi	04/2022
9259	2^338980+70833	102044	Stefano Morozzi	11/2022
9260	2^338982-92111	102044	Stefano Morozzi	02/2023
9261	2^338977+83007	102043	Stefano Morozzi	02/2022
9262	2^338979-83601	102043	Stefano Morozzi	04/2022
9263	2^338975+28355	102042	Stefano Morozzi	01/2022
9264	2^338973+134619	102042	Stefano Morozzi	03/2022
9265	2^338974+183777	102042	Stefano Morozzi	03/2022
9266	2^338975+69293	102042	Stefano Morozzi	09/2022
9274	25080^11711+11711^25080	102041	Hans Havermann	02/2019
9267	2^338972+152343	102041	Stefano Morozzi	12/2021
9268	2^338972-180623	102041	Stefano Morozzi	02/2022
9269	2^338972+84441	102041	Stefano Morozzi	03/2022
9270	2^338971+64875	102041	Stefano Morozzi	05/2022
9271	2^338971+44985	102041	Stefano Morozzi	11/2022
9272	2^338971+145065	102041	Stefano Morozzi	11/2022
9273	2^338972-16635	102041	Stefano Morozzi	01/2023
9275	2^338968+53461	102040	Stefano Morozzi	01/2022
9276	2^338969+160175	102040	Stefano Morozzi	03/2022
9277	2^338967+13409	102040	Stefano Morozzi	04/2022
9278	2^338969+67635	102040	Stefano Morozzi	09/2022
9279	2^338969-15913	102040	Stefano Morozzi	01/2023
9280	2^338963-127455	102039	Stefano Morozzi	12/2021
9281	2^338963+132195	102039	Stefano Morozzi	02/2022
9282	2^338966+137919	102039	Stefano Morozzi	04/2022
9283	2^338963-87529	102039	Stefano Morozzi	12/2022
9284	2^338963-116859	102039	Stefano Morozzi	02/2023
9291	(2^338982-7)/1754517	102038	Lelio R Paula	12/2013
9285	2^338960+53935	102038	Stefano Morozzi	01/2022
9286	2^338962+83157	102038	Stefano Morozzi	02/2022
9287	2^338961+12341	102038	Stefano Morozzi	04/2022
9288	2^338960+63933	102038	Stefano Morozzi	05/2022
9289	2^338960+170791	102038	Stefano Morozzi	11/2022
9290	2^338962+21679	102038	Stefano Morozzi	11/2022
9292	2^338959-30919	102037	Stefano Morozzi	02/2022
9293	2^338959+164769	102037	Stefano Morozzi	05/2022
9294	2^338958-43161	102037	Stefano Morozzi	02/2023
9295	2^338954-177003	102036	Stefano Morozzi	12/2021
9296	2^338954+154207	102036	Stefano Morozzi	01/2022
9297	2^338956+182493	102036	Stefano Morozzi	02/2022
9298	2^338954+162715	102036	Stefano Morozzi	04/2022
9299	2^338955-158241	102036	Stefano Morozzi	04/2022
9300	2^338956-33395	102036	Stefano Morozzi	04/2022
9301	2^338954+190915	102036	Stefano Morozzi	06/2022
9302	2^338955+41643	102036	Stefano Morozzi	09/2022
9303	2^338954+194427	102036	Stefano Morozzi	09/2022
9304	2^338956+117967	102036	Stefano Morozzi	09/2022
9305	2^338956+195495	102036	Stefano Morozzi	11/2022
9306	2^338954-186371	102036	Stefano Morozzi	12/2022
9307	2^338950+175077	102035	Stefano Morozzi	12/2021
9308	2^338951-51687	102035	Stefano Morozzi	12/2021
9309	2^338951+66123	102035	Stefano Morozzi	06/2022
9310	2^338950+19317	102035	Stefano Morozzi	09/2022
9311	2^338951-161479	102035	Stefano Morozzi	12/2022
9312	2^338950-66335	102035	Stefano Morozzi	01/2023
9313	2^338951-41611	102035	Stefano Morozzi	02/2023
9314	2^338952-142887	102035	Stefano Morozzi	02/2023
9315	2^338949+85449	102034	Stefano Morozzi	03/2022
9316	2^338949-184585	102034	Stefano Morozzi	04/2022
9317	2^338949-88555	102034	Stefano Morozzi	12/2022
9318	2^338948+49393	102034	Stefano Morozzi	02/2023
9319	2^338949-17601	102034	Stefano Morozzi	02/2023
9320	2^338943+127103	102033	Stefano Morozzi	12/2021
9321	2^338944-84003	102033	Stefano Morozzi	04/2022
9322	2^338945+138605	102033	Stefano Morozzi	05/2022
9323	2^338943+95133	102033	Stefano Morozzi	11/2022
9324	2^338943+147435	102033	Stefano Morozzi	11/2022
9325	2^338943-116067	102033	Stefano Morozzi	01/2023
9326	2^338940+78607	102032	Stefano Morozzi	01/2022
9327	2^338942-86687	102032	Stefano Morozzi	12/2022
9328	2^338939+151569	102031	Stefano Morozzi	12/2021
9329	2^338938+183975	102031	Stefano Morozzi	03/2022
9330	2^338937-33429	102031	Stefano Morozzi	04/2022
9331	2^338939-183259	102031	Stefano Morozzi	04/2022
9332	2^338937-139951	102031	Stefano Morozzi	01/2023
9333	2^338938-40151	102031	Stefano Morozzi	01/2023
9334	2^338938+74449	102031	Stefano Morozzi	02/2023
9335	2^338935+179999	102030	Stefano Morozzi	01/2022
9336	2^338936+84147	102030	Stefano Morozzi	03/2022
9337	2^338935+171261	102030	Stefano Morozzi	11/2022
9338	2^338936-41355	102030	Stefano Morozzi	01/2023
9339	2^338931+2349	102029	Stefano Morozzi	12/2021
9340	2^338933+79935	102029	Stefano Morozzi	01/2022
9341	2^338930+33819	102029	Stefano Morozzi	03/2022
9342	2^338931-31555	102029	Stefano Morozzi	03/2022
9343	2^338933+64169	102029	Stefano Morozzi	05/2022
9344	2^338932-184965	102029	Stefano Morozzi	06/2022
9345	2^338932+66943	102029	Stefano Morozzi	09/2022
9346	2^338932+92995	102029	Stefano Morozzi	09/2022
9347	2^338931+97001	102029	Stefano Morozzi	11/2022
9348	2^338932-165453	102029	Stefano Morozzi	01/2023
9349	2^338933-40899	102029	Stefano Morozzi	01/2023
9350	2^338928+2367	102028	Stefano Morozzi	12/2021
9351	2^338927+52779	102028	Stefano Morozzi	01/2022
9352	2^338927-79539	102028	Stefano Morozzi	02/2022
9353	2^338929+60819	102028	Stefano Morozzi	03/2022
9354	2^338928-156959	102028	Stefano Morozzi	03/2022
9355	2^338927-63919	102028	Stefano Morozzi	12/2022
9356	2^338925+106631	102027	Stefano Morozzi	01/2022
9357	2^338926+80235	102027	Stefano Morozzi	01/2022
9358	2^338926+41607	102027	Stefano Morozzi	09/2022
9359	2^338925+195435	102027	Stefano Morozzi	11/2022
9360	2^338924-92885	102027	Stefano Morozzi	02/2023
9361	2^338922-27291	102026	Stefano Morozzi	12/2021
9362	2^338919-103849	102025	Stefano Morozzi	01/2022
9363	2^338919+130221	102025	Stefano Morozzi	01/2022
9364	2^338918-91967	102025	Stefano Morozzi	02/2023
9365	2^338917+561057	102025	Boyan Hu	03/2024
9366	2^338914-79121	102024	Stefano Morozzi	02/2022
9367	2^338916+134047	102024	Stefano Morozzi	03/2022
9368	2^338914-11315	102024	Stefano Morozzi	12/2022
9369	2^338910+81027	102023	Stefano Morozzi	01/2022
9370	2^338912+179821	102023	Stefano Morozzi	01/2022
9371	2^338909+100769	102022	Stefano Morozzi	11/2021
9372	2^338908-100839	102022	Stefano Morozzi	12/2021
9373	2^338909-25951	102022	Stefano Morozzi	12/2021
9374	2^338909+66845	102022	Stefano Morozzi	09/2022
9375	2^338907+73509	102022	Stefano Morozzi	11/2022
9376	2^338906-25823	102021	Stefano Morozzi	12/2021
9377	2^338904+75951	102021	Stefano Morozzi	12/2021
9378	2^338906+6685	102021	Stefano Morozzi	01/2022
9379	2^338905+160365	102021	Stefano Morozzi	03/2022
9380	2^338906+92617	102021	Stefano Morozzi	09/2022
9381	2^338904+47065	102021	Stefano Morozzi	11/2022
9382	2^338905+70427	102021	Stefano Morozzi	11/2022
9383	2^338905-163975	102021	Stefano Morozzi	12/2022
9384	2^338903+4155	102020	Stefano Morozzi	01/2022
9385	2^338901+55571	102020	Stefano Morozzi	01/2022
9386	2^338901-55479	102020	Stefano Morozzi	02/2022
9387	2^338903+33555	102020	Stefano Morozzi	03/2022
9388	2^338901+39777	102020	Stefano Morozzi	05/2022
9389	2^338903+165981	102020	Stefano Morozzi	06/2022
9390	2^338901-34863	102020	Stefano Morozzi	06/2022
9391	2^338899-150051	102019	Stefano Morozzi	12/2021
9392	2^338899+125951	102019	Stefano Morozzi	12/2021
9393	2^338898+179623	102019	Stefano Morozzi	01/2022
9394	2^338899-154467	102019	Stefano Morozzi	02/2022
9395	2^338898-60753	102019	Stefano Morozzi	06/2022
9396	2^338898+68635	102019	Stefano Morozzi	09/2022
9397	2^338897-85963	102019	Stefano Morozzi	12/2022
9398	2^338898+174129	102019	Stefano Morozzi	02/2023
9399	2^338894-133295	102018	Stefano Morozzi	04/2022
9400	2^338894+165573	102018	Stefano Morozzi	06/2022
9401	2^338894-60957	102018	Stefano Morozzi	06/2022
9402	2^338894-89463	102018	Stefano Morozzi	01/2023
9412	2^338891-18885	102017	Enzo Doria	05/2013
9403	2^338891+26499	102017	Stefano Morozzi	12/2021
9404	2^338891-2625	102017	Stefano Morozzi	12/2021
9405	2^338893+128727	102017	Stefano Morozzi	01/2022
9406	2^338890-52965	102017	Stefano Morozzi	01/2022
9407	2^338892-55467	102017	Stefano Morozzi	02/2022
9408	2^338892-83393	102017	Stefano Morozzi	04/2022
9409	2^338893+13649	102017	Stefano Morozzi	05/2022
9410	2^338892+117957	102017	Stefano Morozzi	09/2022
9411	2^338892-14643	102017	Stefano Morozzi	01/2023
9413	2^338887+154029	102016	Stefano Morozzi	01/2022
9414	2^338889-104293	102016	Stefano Morozzi	02/2022
9415	2^338887+147741	102016	Stefano Morozzi	11/2022
9416	2^338889+195975	102016	Stefano Morozzi	11/2022
9417	2^338889-117873	102016	Stefano Morozzi	02/2023
9418	2^338886+177159	102015	Stefano Morozzi	12/2021
9419	2^338885+40425	102015	Stefano Morozzi	06/2022
9420	2^338884-13053	102015	Stefano Morozzi	12/2022
9421	2^338885-112569	102015	Stefano Morozzi	12/2022
9422	2^338880+11341	102014	Stefano Morozzi	03/2022
9423	2^338880-160383	102014	Stefano Morozzi	06/2022
9424	2^338880-161627	102014	Stefano Morozzi	12/2022
9425	2^338879-1059	102013	Stefano Morozzi	12/2021
9426	2^338879-54525	102013	Stefano Morozzi	02/2022
9427	2^338877-82813	102013	Stefano Morozzi	03/2022
9428	2^338878-185883	102013	Stefano Morozzi	06/2022
9429	2^338879-60355	102013	Stefano Morozzi	06/2022
9430	2^338878+43719	102013	Stefano Morozzi	09/2022
9431	2^338879+122049	102013	Stefano Morozzi	11/2022
9432	2^338874-15063	102012	Stefano Morozzi	01/2023
9433	2^338874+148993	102012	Stefano Morozzi	02/2023
9434	2^338871+7679	102011	Stefano Morozzi	02/2022
9435	2^338872+61141	102011	Stefano Morozzi	03/2022
9436	2^338872-183923	102011	Stefano Morozzi	04/2022
9437	2^338873+19527	102011	Stefano Morozzi	09/2022
9438	2^338870+70719	102011	Stefano Morozzi	11/2022
9439	(19*10^102011+287)/9/3	102011	Alfred Reich	11/2022
9440	2^338870-37571	102011	Stefano Morozzi	12/2022
9441	2^338872-138573	102011	Stefano Morozzi	12/2022
9442	2^338873-63843	102011	Stefano Morozzi	12/2022
9443	2^338868-5985	102010	Stefano Morozzi	02/2022
9444	2^338867+38079	102010	Stefano Morozzi	05/2022
9445	2^338868+140437	102010	Stefano Morozzi	06/2022
9446	2^338868-110175	102010	Stefano Morozzi	06/2022
9447	2^338868+123337	102010	Stefano Morozzi	11/2022
9448	2^338867-13327	102010	Stefano Morozzi	12/2022
9449	2^338868-11279	102010	Stefano Morozzi	12/2022
9450	2^338868-115685	102010	Stefano Morozzi	01/2023
9451	2^338864+158191	102009	Stefano Morozzi	02/2022
9452	2^338865-39699	102009	Stefano Morozzi	01/2023
9453	2^338865-40789	102009	Stefano Morozzi	01/2023
9454	2^338862+60433	102008	Stefano Morozzi	03/2022
9455	2^338861-9453	102008	Stefano Morozzi	04/2022
9456	2^338861+98067	102008	Stefano Morozzi	11/2022
9457	2^338862+146545	102008	Stefano Morozzi	11/2022
9458	2^338863-186207	102008	Stefano Morozzi	12/2022
9459	2^338860-41429	102008	Stefano Morozzi	01/2023
9460	2^338862-115833	102008	Stefano Morozzi	01/2023
9461	2^338863+74259	102008	Stefano Morozzi	02/2023
9462	2^338863-193017	102008	Stefano Morozzi	02/2023
9463	2^338858-190185	102007	Stefano Morozzi	01/2023
9464	2^338855+102141	102006	Stefano Morozzi	12/2021
9465	2^338856-27173	102006	Stefano Morozzi	12/2021
9466	2^338856-102839	102006	Stefano Morozzi	01/2022
9467	2^338855+79629	102006	Stefano Morozzi	01/2022
9468	2^338856+47755	102006	Stefano Morozzi	11/2022
9469	2^338850+27987	102005	Stefano Morozzi	01/2022
9470	2^338853+111791	102005	Stefano Morozzi	04/2022
9471	2^338852+145797	102005	Stefano Morozzi	11/2022
9472	2^338852-88497	102005	Stefano Morozzi	12/2022
9473	2^338850+124843	102005	Stefano Morozzi	02/2023
9474	2^338853-167695	102005	Stefano Morozzi	02/2023
9475	2^338847+176013	102004	Stefano Morozzi	12/2021
9476	2^338847-2365	102004	Stefano Morozzi	12/2021
9477	2^338848+158941	102004	Stefano Morozzi	03/2022
9478	2^338848+16671	102004	Stefano Morozzi	06/2022
9479	2^338847-35061	102004	Stefano Morozzi	06/2022
9480	2^338848+145063	102004	Stefano Morozzi	11/2022
9481	2^338847-61885	102004	Stefano Morozzi	12/2022
9482	2^338845+135831	102003	Stefano Morozzi	03/2022
9483	2^338846+85695	102003	Stefano Morozzi	03/2022
9484	2^338845+186525	102003	Stefano Morozzi	04/2022
9485	2^338846-163473	102003	Stefano Morozzi	12/2022
9486	2^338844-16077	102003	Stefano Morozzi	01/2023
9487	2^338844-165143	102003	Stefano Morozzi	01/2023
9488	2^338843-127261	102002	Stefano Morozzi	12/2021
9489	2^338843+107205	102002	Stefano Morozzi	02/2022
9490	2^338842-33185	102002	Stefano Morozzi	04/2022
9491	2^338842+14227	102002	Stefano Morozzi	05/2022
9492	2^338842+147973	102002	Stefano Morozzi	11/2022
9500	8*10^102000+51	102001	Robert Price	08/2019
9493	2^338838+150837	102001	Stefano Morozzi	11/2021
9494	2^338838+141397	102001	Stefano Morozzi	06/2022
9495	2^338839+194363	102001	Stefano Morozzi	09/2022
9496	2^338838+95637	102001	Stefano Morozzi	11/2022
9497	2^338839+171545	102001	Stefano Morozzi	11/2022
9498	2^338837-40071	102001	Stefano Morozzi	01/2023
9499	2^338838-90251	102001	Stefano Morozzi	01/2023

Find by discoverer :

PRP Records

Probable Primes Top 10000

(301969 PRPs in the top)