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 ?
8502	(2^338982-7)/1754517	102038	Lelio R Paula	12/2013
8501	2^338962+21679	102038	Stefano Morozzi	11/2022
8503	2^338959-30919	102037	Stefano Morozzi	02/2022
8504	2^338959+164769	102037	Stefano Morozzi	05/2022
8505	2^338958-43161	102037	Stefano Morozzi	02/2023
8506	2^338954-177003	102036	Stefano Morozzi	12/2021
8507	2^338954+154207	102036	Stefano Morozzi	01/2022
8508	2^338956+182493	102036	Stefano Morozzi	02/2022
8509	2^338954+162715	102036	Stefano Morozzi	04/2022
8510	2^338955-158241	102036	Stefano Morozzi	04/2022
8511	2^338956-33395	102036	Stefano Morozzi	04/2022
8512	2^338954+190915	102036	Stefano Morozzi	06/2022
8513	2^338955+41643	102036	Stefano Morozzi	09/2022
8514	2^338954+194427	102036	Stefano Morozzi	09/2022
8515	2^338956+117967	102036	Stefano Morozzi	09/2022
8516	2^338956+195495	102036	Stefano Morozzi	11/2022
8517	2^338954-186371	102036	Stefano Morozzi	12/2022
8518	2^338950+175077	102035	Stefano Morozzi	12/2021
8519	2^338951-51687	102035	Stefano Morozzi	12/2021
8520	2^338951+66123	102035	Stefano Morozzi	06/2022
8521	2^338950+19317	102035	Stefano Morozzi	09/2022
8522	2^338951-161479	102035	Stefano Morozzi	12/2022
8523	2^338950-66335	102035	Stefano Morozzi	01/2023
8524	2^338951-41611	102035	Stefano Morozzi	02/2023
8525	2^338952-142887	102035	Stefano Morozzi	02/2023
8526	2^338949+85449	102034	Stefano Morozzi	03/2022
8527	2^338949-184585	102034	Stefano Morozzi	04/2022
8528	2^338949-88555	102034	Stefano Morozzi	12/2022
8529	2^338948+49393	102034	Stefano Morozzi	02/2023
8530	2^338949-17601	102034	Stefano Morozzi	02/2023
8531	2^338943+127103	102033	Stefano Morozzi	12/2021
8532	2^338944-84003	102033	Stefano Morozzi	04/2022
8533	2^338945+138605	102033	Stefano Morozzi	05/2022
8534	2^338943+95133	102033	Stefano Morozzi	11/2022
8535	2^338943+147435	102033	Stefano Morozzi	11/2022
8536	2^338943-116067	102033	Stefano Morozzi	01/2023
8537	2^338940+78607	102032	Stefano Morozzi	01/2022
8538	2^338942-86687	102032	Stefano Morozzi	12/2022
8539	2^338939+151569	102031	Stefano Morozzi	12/2021
8540	2^338938+183975	102031	Stefano Morozzi	03/2022
8541	2^338937-33429	102031	Stefano Morozzi	04/2022
8542	2^338939-183259	102031	Stefano Morozzi	04/2022
8543	2^338937-139951	102031	Stefano Morozzi	01/2023
8544	2^338938-40151	102031	Stefano Morozzi	01/2023
8545	2^338938+74449	102031	Stefano Morozzi	02/2023
8546	2^338935+179999	102030	Stefano Morozzi	01/2022
8547	2^338936+84147	102030	Stefano Morozzi	03/2022
8548	2^338935+171261	102030	Stefano Morozzi	11/2022
8549	2^338936-41355	102030	Stefano Morozzi	01/2023
8550	2^338931+2349	102029	Stefano Morozzi	12/2021
8551	2^338933+79935	102029	Stefano Morozzi	01/2022
8552	2^338930+33819	102029	Stefano Morozzi	03/2022
8553	2^338931-31555	102029	Stefano Morozzi	03/2022
8554	2^338933+64169	102029	Stefano Morozzi	05/2022
8555	2^338932-184965	102029	Stefano Morozzi	06/2022
8556	2^338932+66943	102029	Stefano Morozzi	09/2022
8557	2^338932+92995	102029	Stefano Morozzi	09/2022
8558	2^338931+97001	102029	Stefano Morozzi	11/2022
8559	2^338932-165453	102029	Stefano Morozzi	01/2023
8560	2^338933-40899	102029	Stefano Morozzi	01/2023
8561	2^338928+2367	102028	Stefano Morozzi	12/2021
8562	2^338927+52779	102028	Stefano Morozzi	01/2022
8563	2^338927-79539	102028	Stefano Morozzi	02/2022
8564	2^338929+60819	102028	Stefano Morozzi	03/2022
8565	2^338928-156959	102028	Stefano Morozzi	03/2022
8566	2^338927-63919	102028	Stefano Morozzi	12/2022
8567	2^338925+106631	102027	Stefano Morozzi	01/2022
8568	2^338926+80235	102027	Stefano Morozzi	01/2022
8569	2^338926+41607	102027	Stefano Morozzi	09/2022
8570	2^338925+195435	102027	Stefano Morozzi	11/2022
8571	2^338924-92885	102027	Stefano Morozzi	02/2023
8572	2^338922-27291	102026	Stefano Morozzi	12/2021
8573	2^338919-103849	102025	Stefano Morozzi	01/2022
8574	2^338919+130221	102025	Stefano Morozzi	01/2022
8575	2^338918-91967	102025	Stefano Morozzi	02/2023
8576	2^338917+561057	102025	Boyan Hu	03/2024
8577	2^338914-79121	102024	Stefano Morozzi	02/2022
8578	2^338916+134047	102024	Stefano Morozzi	03/2022
8579	2^338914-11315	102024	Stefano Morozzi	12/2022
8580	2^338910+81027	102023	Stefano Morozzi	01/2022
8581	2^338912+179821	102023	Stefano Morozzi	01/2022
8582	2^338909+100769	102022	Stefano Morozzi	11/2021
8583	2^338908-100839	102022	Stefano Morozzi	12/2021
8584	2^338909-25951	102022	Stefano Morozzi	12/2021
8585	2^338909+66845	102022	Stefano Morozzi	09/2022
8586	2^338907+73509	102022	Stefano Morozzi	11/2022
8587	2^338906-25823	102021	Stefano Morozzi	12/2021
8588	2^338904+75951	102021	Stefano Morozzi	12/2021
8589	2^338906+6685	102021	Stefano Morozzi	01/2022
8590	2^338905+160365	102021	Stefano Morozzi	03/2022
8591	2^338906+92617	102021	Stefano Morozzi	09/2022
8592	2^338904+47065	102021	Stefano Morozzi	11/2022
8593	2^338905+70427	102021	Stefano Morozzi	11/2022
8594	2^338905-163975	102021	Stefano Morozzi	12/2022
8595	2^338903+4155	102020	Stefano Morozzi	01/2022
8596	2^338901+55571	102020	Stefano Morozzi	01/2022
8597	2^338901-55479	102020	Stefano Morozzi	02/2022
8598	2^338903+33555	102020	Stefano Morozzi	03/2022
8599	2^338901+39777	102020	Stefano Morozzi	05/2022
8600	2^338903+165981	102020	Stefano Morozzi	06/2022
8601	2^338901-34863	102020	Stefano Morozzi	06/2022
8602	2^338899-150051	102019	Stefano Morozzi	12/2021
8603	2^338899+125951	102019	Stefano Morozzi	12/2021
8604	2^338898+179623	102019	Stefano Morozzi	01/2022
8605	2^338899-154467	102019	Stefano Morozzi	02/2022
8606	2^338898-60753	102019	Stefano Morozzi	06/2022
8607	2^338898+68635	102019	Stefano Morozzi	09/2022
8608	2^338897-85963	102019	Stefano Morozzi	12/2022
8609	2^338898+174129	102019	Stefano Morozzi	02/2023
8610	2^338894-133295	102018	Stefano Morozzi	04/2022
8611	2^338894+165573	102018	Stefano Morozzi	06/2022
8612	2^338894-60957	102018	Stefano Morozzi	06/2022
8613	2^338894-89463	102018	Stefano Morozzi	01/2023
8623	2^338891-18885	102017	Enzo Doria	05/2013
8614	2^338891+26499	102017	Stefano Morozzi	12/2021
8615	2^338891-2625	102017	Stefano Morozzi	12/2021
8616	2^338893+128727	102017	Stefano Morozzi	01/2022
8617	2^338890-52965	102017	Stefano Morozzi	01/2022
8618	2^338892-55467	102017	Stefano Morozzi	02/2022
8619	2^338892-83393	102017	Stefano Morozzi	04/2022
8620	2^338893+13649	102017	Stefano Morozzi	05/2022
8621	2^338892+117957	102017	Stefano Morozzi	09/2022
8622	2^338892-14643	102017	Stefano Morozzi	01/2023
8624	2^338887+154029	102016	Stefano Morozzi	01/2022
8625	2^338889-104293	102016	Stefano Morozzi	02/2022
8626	2^338887+147741	102016	Stefano Morozzi	11/2022
8627	2^338889+195975	102016	Stefano Morozzi	11/2022
8628	2^338889-117873	102016	Stefano Morozzi	02/2023
8629	2^338886+177159	102015	Stefano Morozzi	12/2021
8630	2^338885+40425	102015	Stefano Morozzi	06/2022
8631	2^338884-13053	102015	Stefano Morozzi	12/2022
8632	2^338885-112569	102015	Stefano Morozzi	12/2022
8633	2^338880+11341	102014	Stefano Morozzi	03/2022
8634	2^338880-160383	102014	Stefano Morozzi	06/2022
8635	2^338880-161627	102014	Stefano Morozzi	12/2022
8636	2^338879-1059	102013	Stefano Morozzi	12/2021
8637	2^338879-54525	102013	Stefano Morozzi	02/2022
8638	2^338877-82813	102013	Stefano Morozzi	03/2022
8639	2^338878-185883	102013	Stefano Morozzi	06/2022
8640	2^338879-60355	102013	Stefano Morozzi	06/2022
8641	2^338878+43719	102013	Stefano Morozzi	09/2022
8642	2^338879+122049	102013	Stefano Morozzi	11/2022
8643	2^338874-15063	102012	Stefano Morozzi	01/2023
8644	2^338874+148993	102012	Stefano Morozzi	02/2023
8645	2^338871+7679	102011	Stefano Morozzi	02/2022
8646	2^338872+61141	102011	Stefano Morozzi	03/2022
8647	2^338872-183923	102011	Stefano Morozzi	04/2022
8648	2^338873+19527	102011	Stefano Morozzi	09/2022
8649	2^338870+70719	102011	Stefano Morozzi	11/2022
8650	(19*10^102011+287)/9/3	102011	Alfred Reich	11/2022
8651	2^338870-37571	102011	Stefano Morozzi	12/2022
8652	2^338872-138573	102011	Stefano Morozzi	12/2022
8653	2^338873-63843	102011	Stefano Morozzi	12/2022
8654	2^338868-5985	102010	Stefano Morozzi	02/2022
8655	2^338867+38079	102010	Stefano Morozzi	05/2022
8656	2^338868+140437	102010	Stefano Morozzi	06/2022
8657	2^338868-110175	102010	Stefano Morozzi	06/2022
8658	2^338868+123337	102010	Stefano Morozzi	11/2022
8659	2^338867-13327	102010	Stefano Morozzi	12/2022
8660	2^338868-11279	102010	Stefano Morozzi	12/2022
8661	2^338868-115685	102010	Stefano Morozzi	01/2023
8662	2^338864+158191	102009	Stefano Morozzi	02/2022
8663	2^338865-39699	102009	Stefano Morozzi	01/2023
8664	2^338865-40789	102009	Stefano Morozzi	01/2023
8665	2^338862+60433	102008	Stefano Morozzi	03/2022
8666	2^338861-9453	102008	Stefano Morozzi	04/2022
8667	2^338861+98067	102008	Stefano Morozzi	11/2022
8668	2^338862+146545	102008	Stefano Morozzi	11/2022
8669	2^338863-186207	102008	Stefano Morozzi	12/2022
8670	2^338860-41429	102008	Stefano Morozzi	01/2023
8671	2^338862-115833	102008	Stefano Morozzi	01/2023
8672	2^338863+74259	102008	Stefano Morozzi	02/2023
8673	2^338863-193017	102008	Stefano Morozzi	02/2023
8674	2^338858-190185	102007	Stefano Morozzi	01/2023
8675	2^338855+102141	102006	Stefano Morozzi	12/2021
8676	2^338856-27173	102006	Stefano Morozzi	12/2021
8677	2^338856-102839	102006	Stefano Morozzi	01/2022
8678	2^338855+79629	102006	Stefano Morozzi	01/2022
8679	2^338856+47755	102006	Stefano Morozzi	11/2022
8680	2^338850+27987	102005	Stefano Morozzi	01/2022
8681	2^338853+111791	102005	Stefano Morozzi	04/2022
8682	2^338852+145797	102005	Stefano Morozzi	11/2022
8683	2^338852-88497	102005	Stefano Morozzi	12/2022
8684	2^338850+124843	102005	Stefano Morozzi	02/2023
8685	2^338853-167695	102005	Stefano Morozzi	02/2023
8686	2^338847+176013	102004	Stefano Morozzi	12/2021
8687	2^338847-2365	102004	Stefano Morozzi	12/2021
8688	2^338848+158941	102004	Stefano Morozzi	03/2022
8689	2^338848+16671	102004	Stefano Morozzi	06/2022
8690	2^338847-35061	102004	Stefano Morozzi	06/2022
8691	2^338848+145063	102004	Stefano Morozzi	11/2022
8692	2^338847-61885	102004	Stefano Morozzi	12/2022
8693	2^338845+135831	102003	Stefano Morozzi	03/2022
8694	2^338846+85695	102003	Stefano Morozzi	03/2022
8695	2^338845+186525	102003	Stefano Morozzi	04/2022
8696	2^338846-163473	102003	Stefano Morozzi	12/2022
8697	2^338844-16077	102003	Stefano Morozzi	01/2023
8698	2^338844-165143	102003	Stefano Morozzi	01/2023
8699	2^338843-127261	102002	Stefano Morozzi	12/2021
8700	2^338843+107205	102002	Stefano Morozzi	02/2022
8701	2^338842-33185	102002	Stefano Morozzi	04/2022
8702	2^338842+14227	102002	Stefano Morozzi	05/2022
8703	2^338842+147973	102002	Stefano Morozzi	11/2022
8711	8*10^102000+51	102001	Robert Price	08/2019
8704	2^338838+150837	102001	Stefano Morozzi	11/2021
8705	2^338838+141397	102001	Stefano Morozzi	06/2022
8706	2^338839+194363	102001	Stefano Morozzi	09/2022
8707	2^338838+95637	102001	Stefano Morozzi	11/2022
8708	2^338839+171545	102001	Stefano Morozzi	11/2022
8709	2^338837-40071	102001	Stefano Morozzi	01/2023
8710	2^338838-90251	102001	Stefano Morozzi	01/2023
8712	2^338835-150625	102000	Stefano Morozzi	12/2021
8713	2^338834-32877	102000	Stefano Morozzi	04/2022
8717	(2^338832+642)/2	101999	Stefano Morozzi	09/2020
8714	2^338833-100905	101999	Stefano Morozzi	12/2021
8715	2^338831+54419	101999	Stefano Morozzi	01/2022
8716	2^338831-63687	101999	Stefano Morozzi	12/2022
8725	2^338829-113239	101998	Enzo Doria	07/2014
8726	2^338828-113297	101998	Enzo Doria	07/2014
8718	2^338830+25017	101998	Stefano Morozzi	11/2021
8719	2^338831+321	101998	Stefano Morozzi	11/2021
8720	2^338827-26197	101998	Stefano Morozzi	12/2021
8721	2^338829+52727	101998	Stefano Morozzi	01/2022
8722	2^338827-55461	101998	Stefano Morozzi	02/2022
8723	2^338828-65859	101998	Stefano Morozzi	01/2023
8724	2^338829+99365	101998	Stefano Morozzi	02/2023
8727	2^338825-27453	101997	Stefano Morozzi	12/2021
8728	2^338824+89355	101997	Stefano Morozzi	05/2022
8729	2^338825-10995	101997	Stefano Morozzi	06/2022
8730	2^338824+149865	101997	Stefano Morozzi	02/2023
8731	2^338822+111175	101996	Stefano Morozzi	03/2022
8732	2^338822+187819	101996	Stefano Morozzi	04/2022
8733	2^338823+139545	101996	Stefano Morozzi	05/2022
8734	2^338823-184905	101996	Stefano Morozzi	06/2022
8735	2^338821-38919	101996	Stefano Morozzi	12/2022
8736	2^338820+41317	101995	Stefano Morozzi	06/2022
8737	2^338817+46019	101995	Stefano Morozzi	11/2022
8738	2^338820+148083	101995	Stefano Morozzi	11/2022
8739	2^338817-163251	101995	Stefano Morozzi	12/2022
8740	2^338819-63705	101995	Stefano Morozzi	12/2022
8741	2^338817-92509	101995	Stefano Morozzi	02/2023
8742	2^338815+151175	101994	Stefano Morozzi	12/2021
8743	2^338814-30011	101994	Stefano Morozzi	02/2022
8744	2^338814+12309	101994	Stefano Morozzi	04/2022
8745	2^338816-60647	101994	Stefano Morozzi	06/2022
8746	2^338816+171043	101994	Stefano Morozzi	11/2022
8747	2^338814-11513	101994	Stefano Morozzi	12/2022
8748	2^338811-126999	101993	Stefano Morozzi	12/2021
8749	2^338811+131621	101993	Stefano Morozzi	02/2022
8750	2^338812-107637	101993	Stefano Morozzi	03/2022

Find by discoverer :

PRP Records

Probable Primes Top 10000

(300560 PRPs in the top)