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 ?
7752	(2^338666+3154)/2	101949	Stefano Morozzi	09/2020
7751	2^338665+166637	101949	Stefano Morozzi	09/2022
7753	2^338662+31587	101948	Stefano Morozzi	02/2022
7754	2^338663-58375	101948	Stefano Morozzi	04/2022
7755	2^338663-107869	101948	Stefano Morozzi	04/2022
7756	2^338663+90435	101948	Stefano Morozzi	06/2022
7757	2^338661+70457	101948	Stefano Morozzi	11/2022
7758	2^338662+70519	101948	Stefano Morozzi	11/2022
7759	2^338663-39447	101948	Stefano Morozzi	01/2023
7760	2^338658-159191	101947	Stefano Morozzi	04/2022
7761	2^338659-159687	101947	Stefano Morozzi	04/2022
7762	2^338659+15543	101947	Stefano Morozzi	05/2022
7763	2^338658+44395	101947	Stefano Morozzi	09/2022
7764	2^338658+192537	101947	Stefano Morozzi	09/2022
7765	2^338659-90531	101947	Stefano Morozzi	01/2023
7766	2^338659-114759	101947	Stefano Morozzi	01/2023
7767	2^338659+124079	101947	Stefano Morozzi	02/2023
7768	2^338654+51027	101946	Stefano Morozzi	12/2021
7769	2^338656-152115	101946	Stefano Morozzi	12/2021
7770	2^338654+32415	101946	Stefano Morozzi	02/2022
7771	2^338654+39799	101946	Stefano Morozzi	05/2022
7772	2^338655+144579	101946	Stefano Morozzi	09/2022
7773	2^338657+97509	101946	Stefano Morozzi	11/2022
7774	2^338653+126629	101945	Stefano Morozzi	12/2021
7775	2^338653+33279	101945	Stefano Morozzi	02/2022
7776	2^338652-107097	101945	Stefano Morozzi	03/2022
7777	2^338653+94475	101945	Stefano Morozzi	09/2022
7778	2^338651+194073	101945	Stefano Morozzi	09/2022
7779	2^338652-89157	101945	Stefano Morozzi	01/2023
7780	2^338649-154663	101944	Stefano Morozzi	02/2022
7781	2^338650+61399	101944	Stefano Morozzi	04/2022
7782	2^338650-35655	101944	Stefano Morozzi	06/2022
7783	2^338650+169623	101944	Stefano Morozzi	09/2022
7784	2^338649-40743	101944	Stefano Morozzi	01/2023
7785	2^338645+150311	101943	Stefano Morozzi	11/2021
7786	2^338645+28481	101943	Stefano Morozzi	01/2022
7787	2^338647-77895	101943	Stefano Morozzi	01/2022
7788	2^338647-84607	101943	Stefano Morozzi	04/2022
7789	2^338647+164523	101943	Stefano Morozzi	05/2022
7790	2^338645+64845	101943	Stefano Morozzi	05/2022
7791	2^338644-35969	101943	Stefano Morozzi	12/2022
7792	2^338645-15715	101943	Stefano Morozzi	01/2023
7793	2^338641-152541	101942	Stefano Morozzi	12/2021
7794	2^338643-56487	101942	Stefano Morozzi	03/2022
7795	2^338642-186525	101942	Stefano Morozzi	12/2022
7796	2^338643-41715	101942	Stefano Morozzi	02/2023
7797	2^338638+100575	101941	Stefano Morozzi	12/2021
7798	2^338639-127461	101941	Stefano Morozzi	12/2021
7799	2^338640+187657	101941	Stefano Morozzi	04/2022
7800	2^338640+44431	101941	Stefano Morozzi	09/2022
7801	2^338635+1961	101940	Stefano Morozzi	12/2021
7802	2^338637+102125	101940	Stefano Morozzi	12/2021
7803	2^338636-135329	101940	Stefano Morozzi	06/2022
7804	2^338635+199485	101940	Stefano Morozzi	02/2023
7809	28594^3673+3673^28594	101939	Hans Havermann	02/2019
7805	2^338631+110741	101939	Stefano Morozzi	03/2022
7806	2^338631+112119	101939	Stefano Morozzi	04/2022
7807	2^338634-83097	101939	Stefano Morozzi	04/2022
7808	2^338633+139701	101939	Stefano Morozzi	05/2022
7810	2^338630-150341	101938	Stefano Morozzi	12/2021
7811	2^338630+12867	101938	Stefano Morozzi	04/2022
7812	2^338629+42147	101938	Stefano Morozzi	09/2022
7813	2^338628+121083	101938	Stefano Morozzi	11/2022
7814	2^338630+147235	101938	Stefano Morozzi	11/2022
7815	2^338628-37679	101938	Stefano Morozzi	12/2022
7816	2^338629-41383	101938	Stefano Morozzi	01/2023
7817	2^338628-91877	101938	Stefano Morozzi	02/2023
7818	2^338626-105875	101937	Stefano Morozzi	02/2022
7819	2^338625-111729	101937	Stefano Morozzi	12/2022
7820	2^338627+49299	101937	Stefano Morozzi	02/2023
7821	2^338621+33069	101936	Stefano Morozzi	02/2022
7822	2^338623-106405	101936	Stefano Morozzi	03/2022
7823	2^338621+61751	101936	Stefano Morozzi	04/2022
7824	2^338623-86577	101936	Stefano Morozzi	12/2022
7825	2^338620-150735	101935	Stefano Morozzi	12/2021
7826	2^338619-27765	101935	Stefano Morozzi	01/2022
7827	2^338619-77959	101935	Stefano Morozzi	01/2022
7828	2^338619-186367	101935	Stefano Morozzi	12/2022
7829	2^338618-64905	101935	Stefano Morozzi	01/2023
7830	2^338615+151655	101934	Stefano Morozzi	12/2021
7831	2^338616+5047	101934	Stefano Morozzi	01/2022
7832	2^338616+39705	101934	Stefano Morozzi	05/2022
7833	2^338617+149321	101934	Stefano Morozzi	02/2023
7834	2^338611+76659	101933	Stefano Morozzi	12/2021
7835	2^338613-109791	101933	Stefano Morozzi	04/2022
7836	2^338612+119583	101933	Stefano Morozzi	09/2022
7837	2^338611-140397	101933	Stefano Morozzi	01/2023
7838	2^338614-39653	101933	Stefano Morozzi	01/2023
7839	2^338609+130139	101932	Stefano Morozzi	01/2022
7840	2^338609+131327	101932	Stefano Morozzi	01/2022
7841	2^338608-155453	101932	Stefano Morozzi	02/2022
7842	2^338609+161721	101932	Stefano Morozzi	04/2022
7843	2^338609-10405	101932	Stefano Morozzi	06/2022
7844	2^338608+94017	101932	Stefano Morozzi	09/2022
7845	2^338610+170515	101932	Stefano Morozzi	11/2022
7846	2^338607+30611	101931	Stefano Morozzi	01/2022
7847	2^338607+106695	101931	Stefano Morozzi	02/2022
7848	2^338606-32291	101931	Stefano Morozzi	03/2022
7849	2^338606+15195	101931	Stefano Morozzi	05/2022
7850	2^338605+197789	101931	Stefano Morozzi	11/2022
7851	2^338607-90621	101931	Stefano Morozzi	01/2023
7852	2^338603-1195	101930	Stefano Morozzi	12/2021
7853	2^338601+108867	101930	Stefano Morozzi	03/2022
7854	2^338603+34311	101930	Stefano Morozzi	03/2022
7855	2^338598+57127	101929	Stefano Morozzi	02/2022
7856	2^338598+162645	101929	Stefano Morozzi	04/2022
7857	2^338599+43445	101929	Stefano Morozzi	09/2022
7858	2^338599+19485	101929	Stefano Morozzi	09/2022
7859	2^338598+46195	101929	Stefano Morozzi	11/2022
7860	2^338600-36393	101929	Stefano Morozzi	12/2022
7861	2^338596-1739	101928	Stefano Morozzi	12/2021
7862	2^338595-78687	101928	Stefano Morozzi	01/2022
7863	2^338595+181683	101928	Stefano Morozzi	02/2022
7864	2^338597-106045	101928	Stefano Morozzi	02/2022
7865	2^338595+119565	101928	Stefano Morozzi	09/2022
7866	2^338595+19623	101928	Stefano Morozzi	09/2022
7867	2^338595+21711	101928	Stefano Morozzi	11/2022
7868	2^338596-111129	101928	Stefano Morozzi	12/2022
7869	2^338591+53769	101927	Stefano Morozzi	01/2022
7870	2^338593+156989	101927	Stefano Morozzi	02/2022
7871	2^338592+36157	101927	Stefano Morozzi	03/2022
7872	2^338593+42099	101927	Stefano Morozzi	09/2022
7873	2^338591+46685	101927	Stefano Morozzi	11/2022
7874	2^338593+120437	101927	Stefano Morozzi	11/2022
7875	2^338591-165517	101927	Stefano Morozzi	01/2023
7876	2^338592-166107	101927	Stefano Morozzi	01/2023
7877	2^338592-189249	101927	Stefano Morozzi	01/2023
7878	2^338594-40493	101927	Stefano Morozzi	01/2023
7879	2^338590+182007	101926	Stefano Morozzi	02/2022
7880	2^338590+60747	101926	Stefano Morozzi	03/2022
7881	2^338588+62397	101926	Stefano Morozzi	04/2022
7882	2^338589-9685	101926	Stefano Morozzi	04/2022
7883	2^338588+73765	101926	Stefano Morozzi	02/2023
7884	2^338589-16915	101926	Stefano Morozzi	02/2023
7891	(2^338587+2306)/2	101925	Stefano Morozzi	02/2021
7885	2^338586+1153	101925	Stefano Morozzi	12/2021
7886	2^338587-51709	101925	Stefano Morozzi	12/2021
7887	2^338586+105303	101925	Stefano Morozzi	01/2022
7888	2^338585-131773	101925	Stefano Morozzi	03/2022
7889	2^338587+168039	101925	Stefano Morozzi	09/2022
7890	2^338585-140719	101925	Stefano Morozzi	01/2023
7892	2^338584+100771	101924	Stefano Morozzi	11/2021
7893	2^338581-150415	101924	Stefano Morozzi	12/2021
7894	2^338581-2349	101924	Stefano Morozzi	12/2021
7895	2^338582+42933	101924	Stefano Morozzi	09/2022
7896	2^338584+93267	101924	Stefano Morozzi	09/2022
7897	2^338582-86697	101924	Stefano Morozzi	12/2022
7898	2^338582-138035	101924	Stefano Morozzi	12/2022
7899	2^338584-115569	101924	Stefano Morozzi	01/2023
7900	2^338581-92793	101924	Stefano Morozzi	02/2023
7901	2^338578+67593	101923	Stefano Morozzi	09/2022
7902	2^338580+142201	101923	Stefano Morozzi	09/2022
7903	2^338579-14635	101923	Stefano Morozzi	01/2023
7904	2^338579-164985	101923	Stefano Morozzi	01/2023
7905	2^338575-28815	101922	Stefano Morozzi	01/2022
7906	2^338575-33645	101922	Stefano Morozzi	04/2022
7907	2^338577-92239	101922	Stefano Morozzi	02/2023
7908	2^338573-156693	101921	Stefano Morozzi	03/2022
7909	2^338572+193305	101921	Stefano Morozzi	09/2022
7910	2^338573+173751	101921	Stefano Morozzi	02/2023
7911	2^338574+73707	101921	Stefano Morozzi	02/2023
7916	2^338568+37	101920	Lelio R Paula	07/2011
7912	2^338570-53933	101920	Stefano Morozzi	02/2022
7913	2^338569+87201	101920	Stefano Morozzi	04/2022
7914	2^338570-36897	101920	Stefano Morozzi	12/2022
7915	2^338570-61157	101920	Stefano Morozzi	12/2022
7917	2^338567-9619	101919	Stefano Morozzi	04/2022
7918	2^338565-141589	101919	Stefano Morozzi	01/2023
7919	2^338565+148821	101919	Stefano Morozzi	02/2023
7920	2^338564-56763	101918	Stefano Morozzi	03/2022
7921	2^338561+112007	101918	Stefano Morozzi	04/2022
7922	2^338561-9315	101918	Stefano Morozzi	04/2022
7923	2^338564+41965	101918	Stefano Morozzi	09/2022
7924	2^338561+121139	101918	Stefano Morozzi	11/2022
7925	2^338562+21799	101918	Stefano Morozzi	11/2022
7933	2^338559-1858777	101917	Enzo Doria	04/2016
7926	2^338558+4825	101917	Stefano Morozzi	01/2022
7927	2^338559-127935	101917	Stefano Morozzi	01/2022
7928	2^338560+154891	101917	Stefano Morozzi	01/2022
7929	2^338559+131885	101917	Stefano Morozzi	02/2022
7930	2^338558+93735	101917	Stefano Morozzi	09/2022
7931	2^338559-90957	101917	Stefano Morozzi	01/2023
7932	2^338559-190761	101917	Stefano Morozzi	01/2023
7934	2^338555+189981	101916	Stefano Morozzi	05/2022
7935	2^338553-125383	101915	Stefano Morozzi	12/2021
7936	2^338554-82821	101915	Stefano Morozzi	03/2022
7937	2^338548+76923	101914	Stefano Morozzi	12/2021
7938	2^338549+158517	101914	Stefano Morozzi	03/2022
7939	2^338549+85397	101914	Stefano Morozzi	03/2022
7940	2^338548+138121	101914	Stefano Morozzi	05/2022
7941	2^338550-110301	101914	Stefano Morozzi	06/2022
7942	2^338547+129321	101913	Stefano Morozzi	01/2022
7943	2^338547-153481	101913	Stefano Morozzi	01/2022
7944	2^338545-11059	101913	Stefano Morozzi	12/2022
7945	2^338544+107853	101912	Stefano Morozzi	02/2022
7946	2^338542+172813	101912	Stefano Morozzi	11/2022
7947	2^338544-12687	101912	Stefano Morozzi	12/2022
7948	2^338543-140677	101912	Stefano Morozzi	01/2023
7949	2^338541+152721	101911	Stefano Morozzi	01/2022
7950	2^338539+60825	101911	Stefano Morozzi	03/2022
7951	2^338539+160881	101911	Stefano Morozzi	03/2022
7952	2^338541-182523	101911	Stefano Morozzi	03/2022
7953	2^338540+87645	101911	Stefano Morozzi	04/2022
7954	2^338541+148305	101911	Stefano Morozzi	11/2022
7955	2^338541-163075	101911	Stefano Morozzi	12/2022
7956	2^338536-100785	101910	Stefano Morozzi	12/2021
7957	2^338535-51837	101910	Stefano Morozzi	12/2021
7958	2^338535-158745	101910	Stefano Morozzi	04/2022
7959	2^338536-189977	101910	Stefano Morozzi	01/2023
7960	2^338537-65623	101910	Stefano Morozzi	01/2023
7961	2^338532+39445	101909	Stefano Morozzi	05/2022
7962	2^338532+141415	101909	Stefano Morozzi	06/2022
7963	2^338532-136037	101909	Stefano Morozzi	06/2022
7964	2^338531+81081	101908	Stefano Morozzi	01/2022
7965	2^338530+59835	101908	Stefano Morozzi	03/2022
7966	2^338529+186551	101908	Stefano Morozzi	04/2022
7967	2^338531+61313	101908	Stefano Morozzi	04/2022
7968	2^338531-9277	101908	Stefano Morozzi	04/2022
7969	2^338528-92727	101908	Stefano Morozzi	02/2023
7970	2^338527+191205	101907	Stefano Morozzi	06/2022
7971	2^338525+99621	101907	Stefano Morozzi	02/2023
7972	2^338524+54421	101906	Stefano Morozzi	01/2022
7973	2^338522-155811	101906	Stefano Morozzi	02/2022
7974	2^338523-16291	101906	Stefano Morozzi	01/2023
7975	2^338522-142137	101906	Stefano Morozzi	02/2023
7976	2^338521+183131	101905	Stefano Morozzi	02/2022
7977	2^338520+34945	101905	Stefano Morozzi	03/2022
7978	2^338518-182885	101905	Stefano Morozzi	04/2022
7979	2^338518+114633	101905	Stefano Morozzi	05/2022
7980	2^338518-12621	101905	Stefano Morozzi	12/2022
7981	2^338518-187325	101905	Stefano Morozzi	12/2022
7989	(9*2^338520+1)/365	101904	Lelio R Paula	12/2013
7982	2^338517-125955	101904	Stefano Morozzi	12/2021
7983	2^338517+126437	101904	Stefano Morozzi	12/2021
7984	2^338517-53499	101904	Stefano Morozzi	01/2022
7985	2^338515+30369	101904	Stefano Morozzi	01/2022
7986	2^338517-184623	101904	Stefano Morozzi	04/2022
7987	2^338515+89333	101904	Stefano Morozzi	05/2022
7988	2^338515+198813	101904	Stefano Morozzi	02/2023
7992	24502^14419+14419^24502	101903	Hans Havermann	01/2019
7990	2^338512-827	101903	Stefano Morozzi	12/2021
7991	2^338514-6611	101903	Stefano Morozzi	03/2022
7993	2^338509+5139	101902	Stefano Morozzi	01/2022
7994	2^338509+40205	101902	Stefano Morozzi	06/2022
7995	2^338511+19959	101902	Stefano Morozzi	09/2022
7996	2^338510-37877	101902	Stefano Morozzi	12/2022
7997	2^338507-188655	101901	Stefano Morozzi	12/2022
7998	2^338507-114457	101901	Stefano Morozzi	01/2023
7999	2^338504-152615	101900	Stefano Morozzi	01/2022
8000	2^338502-4587	101900	Stefano Morozzi	02/2022

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Probable Primes Top 10000

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