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 ?
8001	2^338672-182063	101951	Stefano Morozzi	03/2022
8002	2^338672+36667	101951	Stefano Morozzi	04/2022
8003	2^338668+2583	101950	Stefano Morozzi	12/2021
8004	2^338670-157001	101950	Stefano Morozzi	03/2022
8005	2^338669-8353	101950	Stefano Morozzi	04/2022
8006	2^338670+40635	101950	Stefano Morozzi	06/2022
8014	(2^338666+3154)/2	101949	Stefano Morozzi	09/2020
8007	2^338665+1577	101949	Stefano Morozzi	12/2021
8008	2^338665-51133	101949	Stefano Morozzi	12/2021
8009	2^338664+4345	101949	Stefano Morozzi	01/2022
8010	2^338666-128943	101949	Stefano Morozzi	01/2022
8011	2^338664+131535	101949	Stefano Morozzi	01/2022
8012	2^338667+14943	101949	Stefano Morozzi	05/2022
8013	2^338665+166637	101949	Stefano Morozzi	09/2022
8015	2^338662+31587	101948	Stefano Morozzi	02/2022
8016	2^338663-58375	101948	Stefano Morozzi	04/2022
8017	2^338663-107869	101948	Stefano Morozzi	04/2022
8018	2^338663+90435	101948	Stefano Morozzi	06/2022
8019	2^338661+70457	101948	Stefano Morozzi	11/2022
8020	2^338662+70519	101948	Stefano Morozzi	11/2022
8021	2^338663-39447	101948	Stefano Morozzi	01/2023
8022	2^338658-159191	101947	Stefano Morozzi	04/2022
8023	2^338659-159687	101947	Stefano Morozzi	04/2022
8024	2^338659+15543	101947	Stefano Morozzi	05/2022
8025	2^338658+44395	101947	Stefano Morozzi	09/2022
8026	2^338658+192537	101947	Stefano Morozzi	09/2022
8027	2^338659-90531	101947	Stefano Morozzi	01/2023
8028	2^338659-114759	101947	Stefano Morozzi	01/2023
8029	2^338659+124079	101947	Stefano Morozzi	02/2023
8030	2^338654+51027	101946	Stefano Morozzi	12/2021
8031	2^338656-152115	101946	Stefano Morozzi	12/2021
8032	2^338654+32415	101946	Stefano Morozzi	02/2022
8033	2^338654+39799	101946	Stefano Morozzi	05/2022
8034	2^338655+144579	101946	Stefano Morozzi	09/2022
8035	2^338657+97509	101946	Stefano Morozzi	11/2022
8036	2^338653+126629	101945	Stefano Morozzi	12/2021
8037	2^338653+33279	101945	Stefano Morozzi	02/2022
8038	2^338652-107097	101945	Stefano Morozzi	03/2022
8039	2^338653+94475	101945	Stefano Morozzi	09/2022
8040	2^338651+194073	101945	Stefano Morozzi	09/2022
8041	2^338652-89157	101945	Stefano Morozzi	01/2023
8042	2^338649-154663	101944	Stefano Morozzi	02/2022
8043	2^338650+61399	101944	Stefano Morozzi	04/2022
8044	2^338650-35655	101944	Stefano Morozzi	06/2022
8045	2^338650+169623	101944	Stefano Morozzi	09/2022
8046	2^338649-40743	101944	Stefano Morozzi	01/2023
8047	2^338645+150311	101943	Stefano Morozzi	11/2021
8048	2^338645+28481	101943	Stefano Morozzi	01/2022
8049	2^338647-77895	101943	Stefano Morozzi	01/2022
8050	2^338647-84607	101943	Stefano Morozzi	04/2022
8051	2^338647+164523	101943	Stefano Morozzi	05/2022
8052	2^338645+64845	101943	Stefano Morozzi	05/2022
8053	2^338644-35969	101943	Stefano Morozzi	12/2022
8054	2^338645-15715	101943	Stefano Morozzi	01/2023
8055	2^338641-152541	101942	Stefano Morozzi	12/2021
8056	2^338643-56487	101942	Stefano Morozzi	03/2022
8057	2^338642-186525	101942	Stefano Morozzi	12/2022
8058	2^338643-41715	101942	Stefano Morozzi	02/2023
8059	2^338638+100575	101941	Stefano Morozzi	12/2021
8060	2^338639-127461	101941	Stefano Morozzi	12/2021
8061	2^338640+187657	101941	Stefano Morozzi	04/2022
8062	2^338640+44431	101941	Stefano Morozzi	09/2022
8063	2^338635+1961	101940	Stefano Morozzi	12/2021
8064	2^338637+102125	101940	Stefano Morozzi	12/2021
8065	2^338636-135329	101940	Stefano Morozzi	06/2022
8066	2^338635+199485	101940	Stefano Morozzi	02/2023
8071	28594^3673+3673^28594	101939	Hans Havermann	02/2019
8067	2^338631+110741	101939	Stefano Morozzi	03/2022
8068	2^338631+112119	101939	Stefano Morozzi	04/2022
8069	2^338634-83097	101939	Stefano Morozzi	04/2022
8070	2^338633+139701	101939	Stefano Morozzi	05/2022
8072	2^338630-150341	101938	Stefano Morozzi	12/2021
8073	2^338630+12867	101938	Stefano Morozzi	04/2022
8074	2^338629+42147	101938	Stefano Morozzi	09/2022
8075	2^338628+121083	101938	Stefano Morozzi	11/2022
8076	2^338630+147235	101938	Stefano Morozzi	11/2022
8077	2^338628-37679	101938	Stefano Morozzi	12/2022
8078	2^338629-41383	101938	Stefano Morozzi	01/2023
8079	2^338628-91877	101938	Stefano Morozzi	02/2023
8080	2^338626-105875	101937	Stefano Morozzi	02/2022
8081	2^338625-111729	101937	Stefano Morozzi	12/2022
8082	2^338627+49299	101937	Stefano Morozzi	02/2023
8083	2^338621+33069	101936	Stefano Morozzi	02/2022
8084	2^338623-106405	101936	Stefano Morozzi	03/2022
8085	2^338621+61751	101936	Stefano Morozzi	04/2022
8086	2^338623-86577	101936	Stefano Morozzi	12/2022
8087	2^338620-150735	101935	Stefano Morozzi	12/2021
8088	2^338619-27765	101935	Stefano Morozzi	01/2022
8089	2^338619-77959	101935	Stefano Morozzi	01/2022
8090	2^338619-186367	101935	Stefano Morozzi	12/2022
8091	2^338618-64905	101935	Stefano Morozzi	01/2023
8092	2^338615+151655	101934	Stefano Morozzi	12/2021
8093	2^338616+5047	101934	Stefano Morozzi	01/2022
8094	2^338616+39705	101934	Stefano Morozzi	05/2022
8095	2^338617+149321	101934	Stefano Morozzi	02/2023
8096	2^338611+76659	101933	Stefano Morozzi	12/2021
8097	2^338613-109791	101933	Stefano Morozzi	04/2022
8098	2^338612+119583	101933	Stefano Morozzi	09/2022
8099	2^338611-140397	101933	Stefano Morozzi	01/2023
8100	2^338614-39653	101933	Stefano Morozzi	01/2023
8101	2^338609+130139	101932	Stefano Morozzi	01/2022
8102	2^338609+131327	101932	Stefano Morozzi	01/2022
8103	2^338608-155453	101932	Stefano Morozzi	02/2022
8104	2^338609+161721	101932	Stefano Morozzi	04/2022
8105	2^338609-10405	101932	Stefano Morozzi	06/2022
8106	2^338608+94017	101932	Stefano Morozzi	09/2022
8107	2^338610+170515	101932	Stefano Morozzi	11/2022
8108	2^338607+30611	101931	Stefano Morozzi	01/2022
8109	2^338607+106695	101931	Stefano Morozzi	02/2022
8110	2^338606-32291	101931	Stefano Morozzi	03/2022
8111	2^338606+15195	101931	Stefano Morozzi	05/2022
8112	2^338605+197789	101931	Stefano Morozzi	11/2022
8113	2^338607-90621	101931	Stefano Morozzi	01/2023
8114	2^338603-1195	101930	Stefano Morozzi	12/2021
8115	2^338601+108867	101930	Stefano Morozzi	03/2022
8116	2^338603+34311	101930	Stefano Morozzi	03/2022
8117	2^338598+57127	101929	Stefano Morozzi	02/2022
8118	2^338598+162645	101929	Stefano Morozzi	04/2022
8119	2^338599+43445	101929	Stefano Morozzi	09/2022
8120	2^338599+19485	101929	Stefano Morozzi	09/2022
8121	2^338598+46195	101929	Stefano Morozzi	11/2022
8122	2^338600-36393	101929	Stefano Morozzi	12/2022
8123	2^338596-1739	101928	Stefano Morozzi	12/2021
8124	2^338595-78687	101928	Stefano Morozzi	01/2022
8125	2^338595+181683	101928	Stefano Morozzi	02/2022
8126	2^338597-106045	101928	Stefano Morozzi	02/2022
8127	2^338595+119565	101928	Stefano Morozzi	09/2022
8128	2^338595+19623	101928	Stefano Morozzi	09/2022
8129	2^338595+21711	101928	Stefano Morozzi	11/2022
8130	2^338596-111129	101928	Stefano Morozzi	12/2022
8131	2^338591+53769	101927	Stefano Morozzi	01/2022
8132	2^338593+156989	101927	Stefano Morozzi	02/2022
8133	2^338592+36157	101927	Stefano Morozzi	03/2022
8134	2^338593+42099	101927	Stefano Morozzi	09/2022
8135	2^338591+46685	101927	Stefano Morozzi	11/2022
8136	2^338593+120437	101927	Stefano Morozzi	11/2022
8137	2^338591-165517	101927	Stefano Morozzi	01/2023
8138	2^338592-166107	101927	Stefano Morozzi	01/2023
8139	2^338592-189249	101927	Stefano Morozzi	01/2023
8140	2^338594-40493	101927	Stefano Morozzi	01/2023
8141	2^338590+182007	101926	Stefano Morozzi	02/2022
8142	2^338590+60747	101926	Stefano Morozzi	03/2022
8143	2^338588+62397	101926	Stefano Morozzi	04/2022
8144	2^338589-9685	101926	Stefano Morozzi	04/2022
8145	2^338588+73765	101926	Stefano Morozzi	02/2023
8146	2^338589-16915	101926	Stefano Morozzi	02/2023
8153	(2^338587+2306)/2	101925	Stefano Morozzi	02/2021
8147	2^338586+1153	101925	Stefano Morozzi	12/2021
8148	2^338587-51709	101925	Stefano Morozzi	12/2021
8149	2^338586+105303	101925	Stefano Morozzi	01/2022
8150	2^338585-131773	101925	Stefano Morozzi	03/2022
8151	2^338587+168039	101925	Stefano Morozzi	09/2022
8152	2^338585-140719	101925	Stefano Morozzi	01/2023
8154	2^338584+100771	101924	Stefano Morozzi	11/2021
8155	2^338581-150415	101924	Stefano Morozzi	12/2021
8156	2^338581-2349	101924	Stefano Morozzi	12/2021
8157	2^338582+42933	101924	Stefano Morozzi	09/2022
8158	2^338584+93267	101924	Stefano Morozzi	09/2022
8159	2^338582-86697	101924	Stefano Morozzi	12/2022
8160	2^338582-138035	101924	Stefano Morozzi	12/2022
8161	2^338584-115569	101924	Stefano Morozzi	01/2023
8162	2^338581-92793	101924	Stefano Morozzi	02/2023
8163	2^338578+67593	101923	Stefano Morozzi	09/2022
8164	2^338580+142201	101923	Stefano Morozzi	09/2022
8165	2^338579-14635	101923	Stefano Morozzi	01/2023
8166	2^338579-164985	101923	Stefano Morozzi	01/2023
8167	2^338575-28815	101922	Stefano Morozzi	01/2022
8168	2^338575-33645	101922	Stefano Morozzi	04/2022
8169	2^338577-92239	101922	Stefano Morozzi	02/2023
8170	2^338573-156693	101921	Stefano Morozzi	03/2022
8171	2^338572+193305	101921	Stefano Morozzi	09/2022
8172	2^338573+173751	101921	Stefano Morozzi	02/2023
8173	2^338574+73707	101921	Stefano Morozzi	02/2023
8178	2^338568+37	101920	Lelio R Paula	07/2011
8174	2^338570-53933	101920	Stefano Morozzi	02/2022
8175	2^338569+87201	101920	Stefano Morozzi	04/2022
8176	2^338570-36897	101920	Stefano Morozzi	12/2022
8177	2^338570-61157	101920	Stefano Morozzi	12/2022
8179	2^338567-9619	101919	Stefano Morozzi	04/2022
8180	2^338565-141589	101919	Stefano Morozzi	01/2023
8181	2^338565+148821	101919	Stefano Morozzi	02/2023
8182	2^338564-56763	101918	Stefano Morozzi	03/2022
8183	2^338561+112007	101918	Stefano Morozzi	04/2022
8184	2^338561-9315	101918	Stefano Morozzi	04/2022
8185	2^338564+41965	101918	Stefano Morozzi	09/2022
8186	2^338561+121139	101918	Stefano Morozzi	11/2022
8187	2^338562+21799	101918	Stefano Morozzi	11/2022
8195	2^338559-1858777	101917	Enzo Doria	04/2016
8188	2^338558+4825	101917	Stefano Morozzi	01/2022
8189	2^338559-127935	101917	Stefano Morozzi	01/2022
8190	2^338560+154891	101917	Stefano Morozzi	01/2022
8191	2^338559+131885	101917	Stefano Morozzi	02/2022
8192	2^338558+93735	101917	Stefano Morozzi	09/2022
8193	2^338559-90957	101917	Stefano Morozzi	01/2023
8194	2^338559-190761	101917	Stefano Morozzi	01/2023
8196	2^338555+189981	101916	Stefano Morozzi	05/2022
8197	2^338553-125383	101915	Stefano Morozzi	12/2021
8198	2^338554-82821	101915	Stefano Morozzi	03/2022
8199	2^338548+76923	101914	Stefano Morozzi	12/2021
8200	2^338549+158517	101914	Stefano Morozzi	03/2022
8201	2^338549+85397	101914	Stefano Morozzi	03/2022
8202	2^338548+138121	101914	Stefano Morozzi	05/2022
8203	2^338550-110301	101914	Stefano Morozzi	06/2022
8204	2^338547+129321	101913	Stefano Morozzi	01/2022
8205	2^338547-153481	101913	Stefano Morozzi	01/2022
8206	2^338545-11059	101913	Stefano Morozzi	12/2022
8207	2^338544+107853	101912	Stefano Morozzi	02/2022
8208	2^338542+172813	101912	Stefano Morozzi	11/2022
8209	2^338544-12687	101912	Stefano Morozzi	12/2022
8210	2^338543-140677	101912	Stefano Morozzi	01/2023
8211	2^338541+152721	101911	Stefano Morozzi	01/2022
8212	2^338539+60825	101911	Stefano Morozzi	03/2022
8213	2^338539+160881	101911	Stefano Morozzi	03/2022
8214	2^338541-182523	101911	Stefano Morozzi	03/2022
8215	2^338540+87645	101911	Stefano Morozzi	04/2022
8216	2^338541+148305	101911	Stefano Morozzi	11/2022
8217	2^338541-163075	101911	Stefano Morozzi	12/2022
8218	2^338536-100785	101910	Stefano Morozzi	12/2021
8219	2^338535-51837	101910	Stefano Morozzi	12/2021
8220	2^338535-158745	101910	Stefano Morozzi	04/2022
8221	2^338536-189977	101910	Stefano Morozzi	01/2023
8222	2^338537-65623	101910	Stefano Morozzi	01/2023
8223	2^338532+39445	101909	Stefano Morozzi	05/2022
8224	2^338532+141415	101909	Stefano Morozzi	06/2022
8225	2^338532-136037	101909	Stefano Morozzi	06/2022
8226	2^338531+81081	101908	Stefano Morozzi	01/2022
8227	2^338530+59835	101908	Stefano Morozzi	03/2022
8228	2^338529+186551	101908	Stefano Morozzi	04/2022
8229	2^338531+61313	101908	Stefano Morozzi	04/2022
8230	2^338531-9277	101908	Stefano Morozzi	04/2022
8231	2^338528-92727	101908	Stefano Morozzi	02/2023
8232	2^338527+191205	101907	Stefano Morozzi	06/2022
8233	2^338525+99621	101907	Stefano Morozzi	02/2023
8234	2^338524+54421	101906	Stefano Morozzi	01/2022
8235	2^338522-155811	101906	Stefano Morozzi	02/2022
8236	2^338523-16291	101906	Stefano Morozzi	01/2023
8237	2^338522-142137	101906	Stefano Morozzi	02/2023
8238	2^338521+183131	101905	Stefano Morozzi	02/2022
8239	2^338520+34945	101905	Stefano Morozzi	03/2022
8240	2^338518-182885	101905	Stefano Morozzi	04/2022
8241	2^338518+114633	101905	Stefano Morozzi	05/2022
8242	2^338518-12621	101905	Stefano Morozzi	12/2022
8243	2^338518-187325	101905	Stefano Morozzi	12/2022
8244	2^338517-125955	101904	Stefano Morozzi	12/2021
8245	2^338517+126437	101904	Stefano Morozzi	12/2021
8246	2^338517-53499	101904	Stefano Morozzi	01/2022
8247	2^338515+30369	101904	Stefano Morozzi	01/2022
8248	2^338517-184623	101904	Stefano Morozzi	04/2022
8249	2^338515+89333	101904	Stefano Morozzi	05/2022
8250	2^338515+198813	101904	Stefano Morozzi	02/2023

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Probable Primes Top 10000

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