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	2^338381-35539	101863	Stefano Morozzi	06/2022
7252	2^338378-125841	101862	Stefano Morozzi	12/2021
7253	2^338375+27815	101862	Stefano Morozzi	01/2022
7254	2^338375-28509	101862	Stefano Morozzi	01/2022
7255	2^338375+29985	101862	Stefano Morozzi	01/2022
7256	2^338377+157881	101862	Stefano Morozzi	02/2022
7257	2^338375+59589	101862	Stefano Morozzi	03/2022
7258	2^338378+36399	101862	Stefano Morozzi	04/2022
7259	2^338378-159773	101862	Stefano Morozzi	04/2022
7260	2^338378+14883	101862	Stefano Morozzi	05/2022
7261	2^338376+140173	101862	Stefano Morozzi	06/2022
7262	2^338375+18761	101862	Stefano Morozzi	09/2022
7263	2^338373-75103	101861	Stefano Morozzi	12/2021
7264	2^338372+128877	101861	Stefano Morozzi	01/2022
7265	2^338374-28731	101861	Stefano Morozzi	01/2022
7266	2^338374-128427	101861	Stefano Morozzi	01/2022
7267	2^338372+37875	101861	Stefano Morozzi	04/2022
7268	2^338373+161541	101861	Stefano Morozzi	04/2022
7269	2^338374+37759	101861	Stefano Morozzi	04/2022
7270	2^338372+93235	101861	Stefano Morozzi	09/2022
7271	2^338373-63273	101861	Stefano Morozzi	12/2022
7272	2^338369+29427	101860	Stefano Morozzi	01/2022
7273	2^338370+179133	101860	Stefano Morozzi	01/2022
7274	2^338369+131501	101860	Stefano Morozzi	01/2022
7275	2^338369+181649	101860	Stefano Morozzi	02/2022
7276	2^338370-4787	101860	Stefano Morozzi	02/2022
7277	2^338371-133491	101860	Stefano Morozzi	04/2022
7278	2^338371+42023	101860	Stefano Morozzi	09/2022
7279	2^338371+145323	101860	Stefano Morozzi	11/2022
7280	2^338371-138145	101860	Stefano Morozzi	12/2022
7287	2^338368-20369	101859	Enzo Doria	06/2013
7288	2^338366+74179	101859	Enzo Doria	04/2016
7281	2^338366+53853	101859	Stefano Morozzi	01/2022
7282	2^338365-31665	101859	Stefano Morozzi	03/2022
7283	2^338368-156345	101859	Stefano Morozzi	03/2022
7284	2^338366-159867	101859	Stefano Morozzi	04/2022
7285	2^338368-63509	101859	Stefano Morozzi	12/2022
7286	2^338365-190975	101859	Stefano Morozzi	01/2023
7289	2^338362-180845	101858	Stefano Morozzi	02/2022
7290	2^338364-155769	101858	Stefano Morozzi	02/2022
7291	2^338362+142843	101858	Stefano Morozzi	09/2022
7292	2^338362+170019	101858	Stefano Morozzi	11/2022
7293	2^338361-100875	101857	Stefano Morozzi	12/2021
7294	2^338361+154169	101857	Stefano Morozzi	01/2022
7295	2^338359-189645	101857	Stefano Morozzi	01/2023
7296	2^338356+101271	101856	Stefano Morozzi	12/2021
7297	2^338356+53383	101856	Stefano Morozzi	01/2022
7298	2^338355+59393	101856	Stefano Morozzi	03/2022
7299	2^338356+60775	101856	Stefano Morozzi	03/2022
7300	2^338356-106257	101856	Stefano Morozzi	03/2022
7301	2^338357-58921	101856	Stefano Morozzi	04/2022
7302	2^338356+94605	101856	Stefano Morozzi	09/2022
7303	2^338356+117813	101856	Stefano Morozzi	09/2022
7304	2^338358-38475	101856	Stefano Morozzi	12/2022
7305	2^338353-190291	101855	Stefano Morozzi	01/2023
7306	2^338350-152933	101854	Stefano Morozzi	01/2022
7307	2^338350+6337	101854	Stefano Morozzi	01/2022
7308	2^338350+168759	101854	Stefano Morozzi	09/2022
7311	27088^5755+5755^27088	101853	Hans Havermann	01/2019
7309	2^338347+125901	101853	Stefano Morozzi	11/2021
7310	2^338346-10643	101853	Stefano Morozzi	06/2022
7312	2^338343+152271	101852	Stefano Morozzi	12/2021
7313	2^338345+154107	101852	Stefano Morozzi	01/2022
7314	2^338342+155397	101852	Stefano Morozzi	01/2022
7315	2^338342-130767	101852	Stefano Morozzi	02/2022
7316	2^338345-30123	101852	Stefano Morozzi	02/2022
7317	2^338345+35747	101852	Stefano Morozzi	03/2022
7318	2^338345-133131	101852	Stefano Morozzi	04/2022
7319	2^338345-134559	101852	Stefano Morozzi	04/2022
7320	2^338342+170073	101852	Stefano Morozzi	11/2022
7321	2^338344+46567	101852	Stefano Morozzi	11/2022
7322	2^338344+97141	101852	Stefano Morozzi	11/2022
7323	2^338342-162213	101852	Stefano Morozzi	12/2022
7324	2^338339+2753	101851	Stefano Morozzi	12/2021
7325	2^338341+128415	101851	Stefano Morozzi	01/2022
7326	2^338338+2677	101850	Stefano Morozzi	12/2021
7327	2^338336+54607	101850	Stefano Morozzi	01/2022
7328	2^338338+109999	101850	Stefano Morozzi	03/2022
7329	2^338336+161575	101850	Stefano Morozzi	04/2022
7330	2^338335+51975	101849	Stefano Morozzi	12/2021
7331	2^338335-152607	101849	Stefano Morozzi	01/2022
7332	2^338334+55273	101849	Stefano Morozzi	01/2022
7333	2^338332+34315	101849	Stefano Morozzi	03/2022
7334	2^338335+158759	101849	Stefano Morozzi	03/2022
7335	2^338332+67621	101849	Stefano Morozzi	09/2022
7336	2^338332-66099	101849	Stefano Morozzi	01/2023
7337	2^338334-191043	101849	Stefano Morozzi	01/2023
7338	2^338331+83403	101848	Stefano Morozzi	02/2022
7339	2^338330-110865	101848	Stefano Morozzi	06/2022
7340	2^338330+71047	101848	Stefano Morozzi	11/2022
7341	2^338328-5295	101847	Stefano Morozzi	02/2022
7342	2^338327+143585	101847	Stefano Morozzi	09/2022
7343	2^338324-179667	101846	Stefano Morozzi	02/2022
7344	2^338322+21903	101846	Stefano Morozzi	11/2022
7345	2^338324+98047	101846	Stefano Morozzi	11/2022
7346	2^338323-87729	101846	Stefano Morozzi	12/2022
7347	2^338322-16667	101846	Stefano Morozzi	01/2023
7348	2^338325-142159	101846	Stefano Morozzi	02/2023
7349	2^338316-175857	101844	Stefano Morozzi	12/2021
7350	2^338318+54405	101844	Stefano Morozzi	01/2022
7351	2^338316+32961	101844	Stefano Morozzi	02/2022
7352	2^338317+68175	101844	Stefano Morozzi	09/2022
7353	2^338318-86171	101844	Stefano Morozzi	12/2022
7354	2^338315-178635	101843	Stefano Morozzi	01/2022
7355	2^338315+34899	101843	Stefano Morozzi	03/2022
7356	2^338314-106973	101843	Stefano Morozzi	03/2022
7357	2^338313+170411	101843	Stefano Morozzi	11/2022
7358	2^338315-88807	101843	Stefano Morozzi	12/2022
7359	2^338311-51799	101842	Stefano Morozzi	12/2021
7360	2^338309+157259	101842	Stefano Morozzi	02/2022
7361	2^338310+40903	101842	Stefano Morozzi	06/2022
7362	2^338309-168051	101842	Stefano Morozzi	02/2023
7363	2^338308-55853	101841	Stefano Morozzi	02/2022
7364	2^338307+134871	101841	Stefano Morozzi	03/2022
7365	2^338307+19689	101841	Stefano Morozzi	09/2022
7366	2^338308+66873	101841	Stefano Morozzi	09/2022
7367	2^338306+124399	101841	Stefano Morozzi	02/2023
7368	2^338306-91913	101841	Stefano Morozzi	02/2023
7369	2^338304+78757	101840	Stefano Morozzi	01/2022
7370	2^338304-5807	101840	Stefano Morozzi	02/2022
7371	2^338305+110879	101840	Stefano Morozzi	03/2022
7372	2^338304+91147	101840	Stefano Morozzi	06/2022
7373	2^338304-64475	101840	Stefano Morozzi	01/2023
7374	2^338299+85611	101839	Stefano Morozzi	03/2022
7375	2^338299-189985	101839	Stefano Morozzi	01/2023
7376	2^338298-25571	101838	Stefano Morozzi	12/2021
7377	2^338297+35547	101838	Stefano Morozzi	03/2022
7378	2^338298+111199	101838	Stefano Morozzi	03/2022
7379	2^338297+145455	101838	Stefano Morozzi	11/2022
7380	2^338297-166285	101838	Stefano Morozzi	01/2023
7381	2^338294-150711	101837	Stefano Morozzi	12/2021
7382	2^338294+177597	101837	Stefano Morozzi	12/2021
7383	2^338294-177807	101837	Stefano Morozzi	01/2022
7384	2^338295-52929	101837	Stefano Morozzi	01/2022
7385	2^338293+37407	101837	Stefano Morozzi	04/2022
7386	2^338292+40573	101837	Stefano Morozzi	06/2022
7387	2^338294+172425	101837	Stefano Morozzi	11/2022
7388	2^338293-191799	101837	Stefano Morozzi	02/2023
7389	2^338289+30957	101836	Stefano Morozzi	01/2022
7390	2^338291+131825	101836	Stefano Morozzi	02/2022
7391	2^338291+110111	101836	Stefano Morozzi	03/2022
7392	2^338290-156423	101836	Stefano Morozzi	03/2022
7393	2^338291-157845	101836	Stefano Morozzi	03/2022
7394	2^338290+69243	101836	Stefano Morozzi	09/2022
7395	2^338291-189327	101836	Stefano Morozzi	01/2023
7396	2^338291+74079	101836	Stefano Morozzi	02/2023
7397	2^338288+26623	101835	Stefano Morozzi	12/2021
7398	2^338286+33325	101835	Stefano Morozzi	02/2022
7399	2^338287+132633	101835	Stefano Morozzi	02/2022
7400	2^338287+157149	101835	Stefano Morozzi	02/2022
7401	2^338288-107193	101835	Stefano Morozzi	03/2022
7402	2^338286-83333	101835	Stefano Morozzi	04/2022
7403	2^338287+114425	101835	Stefano Morozzi	05/2022
7404	2^338288+194403	101835	Stefano Morozzi	09/2022
7405	2^338288-113177	101835	Stefano Morozzi	12/2022
7406	2^338288-65747	101835	Stefano Morozzi	01/2023
7407	2^338285+82131	101834	Stefano Morozzi	02/2022
7408	2^338284-104217	101834	Stefano Morozzi	02/2022
7409	2^338282-84533	101834	Stefano Morozzi	04/2022
7410	2^338283+67545	101834	Stefano Morozzi	09/2022
7411	2^338283-65439	101834	Stefano Morozzi	01/2023
7420	2^338280-19745	101833	Enzo Doria	06/2013
7412	2^338279-125947	101833	Stefano Morozzi	12/2021
7413	2^338280-50343	101833	Stefano Morozzi	12/2021
7414	2^338279+133331	101833	Stefano Morozzi	02/2022
7415	2^338281-54561	101833	Stefano Morozzi	02/2022
7416	2^338280+192063	101833	Stefano Morozzi	09/2022
7417	2^338281+18971	101833	Stefano Morozzi	09/2022
7418	2^338281-186711	101833	Stefano Morozzi	12/2022
7419	2^338281-91273	101833	Stefano Morozzi	01/2023
7421	2^338278+188215	101832	Stefano Morozzi	05/2022
7422	2^338273+181101	101831	Stefano Morozzi	01/2022
7423	2^338275+32909	101831	Stefano Morozzi	02/2022
7424	2^338272+166431	101831	Stefano Morozzi	06/2022
7425	2^338272+22011	101831	Stefano Morozzi	11/2022
7426	2^338275+148271	101831	Stefano Morozzi	11/2022
7427	2^338270-135725	101830	Stefano Morozzi	06/2022
7428	2^338269-136951	101830	Stefano Morozzi	12/2022
7429	2^338270-192701	101830	Stefano Morozzi	02/2023
7430	2^338271-42831	101830	Stefano Morozzi	02/2023
7431	2^338266+110665	101829	Stefano Morozzi	03/2022
7432	2^338267+110481	101829	Stefano Morozzi	03/2022
7433	2^338267-166035	101829	Stefano Morozzi	01/2023
7434	2^338265-154893	101828	Stefano Morozzi	02/2022
7435	2^338264+163611	101828	Stefano Morozzi	05/2022
7436	2^338263-62767	101828	Stefano Morozzi	12/2022
7437	2^338261-188119	101827	Stefano Morozzi	12/2022
7438	2^338259-40327	101827	Stefano Morozzi	01/2023
7439	2^338256+5223	101826	Stefano Morozzi	01/2022
7440	2^338257+178425	101826	Stefano Morozzi	01/2022
7441	2^338256-180569	101826	Stefano Morozzi	02/2022
7442	2^338257-5965	101826	Stefano Morozzi	02/2022
7443	2^338258-9225	101826	Stefano Morozzi	04/2022
7444	2^338255-127021	101825	Stefano Morozzi	12/2021
7445	2^338253+159005	101825	Stefano Morozzi	03/2022
7446	2^338253+64817	101825	Stefano Morozzi	05/2022
7447	2^338254-85403	101825	Stefano Morozzi	06/2022
7448	2^338254+142947	101825	Stefano Morozzi	09/2022
7449	2^338253+121095	101825	Stefano Morozzi	11/2022
7450	2^338254+196725	101825	Stefano Morozzi	11/2022
7451	2^338254-91007	101825	Stefano Morozzi	01/2023
7452	2^338251+78975	101824	Stefano Morozzi	01/2022
7453	2^338252-178709	101824	Stefano Morozzi	01/2022
7454	2^338252+129703	101824	Stefano Morozzi	01/2022
7455	2^338252+132285	101824	Stefano Morozzi	02/2022
7456	2^338251-33381	101824	Stefano Morozzi	04/2022
7457	2^338252-13805	101824	Stefano Morozzi	12/2022
7458	2^338245-134755	101822	Stefano Morozzi	04/2022
7459	2^338244-59219	101822	Stefano Morozzi	04/2022
7460	2^338244-64703	101822	Stefano Morozzi	01/2023
7468	(2^338242+2782)/2	101821	Stefano Morozzi	02/2021
7461	2^338241+1391	101821	Stefano Morozzi	12/2021
7462	2^338242+151195	101821	Stefano Morozzi	12/2021
7463	2^338240-152495	101821	Stefano Morozzi	12/2021
7464	2^338240+81745	101821	Stefano Morozzi	02/2022
7465	2^338241-155551	101821	Stefano Morozzi	02/2022
7466	2^338242-108237	101821	Stefano Morozzi	04/2022
7467	2^338242+43045	101821	Stefano Morozzi	09/2022
7469	2^338238-126735	101820	Stefano Morozzi	12/2021
7470	2^338238+183855	101820	Stefano Morozzi	03/2022
7471	2^338238+141013	101820	Stefano Morozzi	06/2022
7472	2^338237+97227	101820	Stefano Morozzi	11/2022
7473	2^338238+48429	101820	Stefano Morozzi	11/2022
7474	2^338234-80925	101819	Stefano Morozzi	02/2022
7475	2^338234-154593	101819	Stefano Morozzi	02/2022
7476	2^338235-131787	101819	Stefano Morozzi	03/2022
7477	2^338233+89781	101819	Stefano Morozzi	05/2022
7478	2^338235+169971	101819	Stefano Morozzi	11/2022
7479	2^338233-113875	101819	Stefano Morozzi	12/2022
7486	(3*2^338236-1)/347	101818	Lelio R Paula	03/2014
7480	2^338232-175539	101818	Stefano Morozzi	12/2021
7481	2^338231+57345	101818	Stefano Morozzi	02/2022
7482	2^338232+36097	101818	Stefano Morozzi	03/2022
7483	2^338230+137403	101818	Stefano Morozzi	04/2022
7484	2^338231-59569	101818	Stefano Morozzi	04/2022
7485	2^338230-86633	101818	Stefano Morozzi	12/2022
7487	2^338228+159247	101817	Stefano Morozzi	03/2022
7488	2^338227-12631	101817	Stefano Morozzi	12/2022
7489	(34*10^101815+191)/9	101816	Robert Price	08/2021
7490	2^338224+185461	101816	Stefano Morozzi	03/2022
7491	2^338224+62295	101816	Stefano Morozzi	04/2022
7492	2^338225+162645	101816	Stefano Morozzi	04/2022
7493	2^338223+144209	101816	Stefano Morozzi	09/2022
7500	6^130841+103	101815	Lelio R Paula	10/2016
7494	2^338220+150405	101815	Stefano Morozzi	11/2021
7495	2^338219-4147	101815	Stefano Morozzi	01/2022
7496	2^338221+83391	101815	Stefano Morozzi	02/2022
7497	2^338221+62937	101815	Stefano Morozzi	04/2022
7498	2^338220-65697	101815	Stefano Morozzi	01/2023
7499	2^338220-139505	101815	Stefano Morozzi	01/2023

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Probable Primes Top 10000

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