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 ?
7751	2^338843-127261	102002	Stefano Morozzi	12/2021
7752	2^338843+107205	102002	Stefano Morozzi	02/2022
7753	2^338842-33185	102002	Stefano Morozzi	04/2022
7754	2^338842+14227	102002	Stefano Morozzi	05/2022
7755	2^338842+147973	102002	Stefano Morozzi	11/2022
7763	8*10^102000+51	102001	Robert Price	08/2019
7756	2^338838+150837	102001	Stefano Morozzi	11/2021
7757	2^338838+141397	102001	Stefano Morozzi	06/2022
7758	2^338839+194363	102001	Stefano Morozzi	09/2022
7759	2^338838+95637	102001	Stefano Morozzi	11/2022
7760	2^338839+171545	102001	Stefano Morozzi	11/2022
7761	2^338837-40071	102001	Stefano Morozzi	01/2023
7762	2^338838-90251	102001	Stefano Morozzi	01/2023
7764	2^338835-150625	102000	Stefano Morozzi	12/2021
7765	2^338834-32877	102000	Stefano Morozzi	04/2022
7769	(2^338832+642)/2	101999	Stefano Morozzi	09/2020
7766	2^338833-100905	101999	Stefano Morozzi	12/2021
7767	2^338831+54419	101999	Stefano Morozzi	01/2022
7768	2^338831-63687	101999	Stefano Morozzi	12/2022
7777	2^338829-113239	101998	Enzo Doria	07/2014
7778	2^338828-113297	101998	Enzo Doria	07/2014
7770	2^338830+25017	101998	Stefano Morozzi	11/2021
7771	2^338831+321	101998	Stefano Morozzi	11/2021
7772	2^338827-26197	101998	Stefano Morozzi	12/2021
7773	2^338829+52727	101998	Stefano Morozzi	01/2022
7774	2^338827-55461	101998	Stefano Morozzi	02/2022
7775	2^338828-65859	101998	Stefano Morozzi	01/2023
7776	2^338829+99365	101998	Stefano Morozzi	02/2023
7779	2^338825-27453	101997	Stefano Morozzi	12/2021
7780	2^338824+89355	101997	Stefano Morozzi	05/2022
7781	2^338825-10995	101997	Stefano Morozzi	06/2022
7782	2^338824+149865	101997	Stefano Morozzi	02/2023
7783	2^338822+111175	101996	Stefano Morozzi	03/2022
7784	2^338822+187819	101996	Stefano Morozzi	04/2022
7785	2^338823+139545	101996	Stefano Morozzi	05/2022
7786	2^338823-184905	101996	Stefano Morozzi	06/2022
7787	2^338821-38919	101996	Stefano Morozzi	12/2022
7788	2^338820+41317	101995	Stefano Morozzi	06/2022
7789	2^338817+46019	101995	Stefano Morozzi	11/2022
7790	2^338820+148083	101995	Stefano Morozzi	11/2022
7791	2^338817-163251	101995	Stefano Morozzi	12/2022
7792	2^338819-63705	101995	Stefano Morozzi	12/2022
7793	2^338817-92509	101995	Stefano Morozzi	02/2023
7794	2^338815+151175	101994	Stefano Morozzi	12/2021
7795	2^338814-30011	101994	Stefano Morozzi	02/2022
7796	2^338814+12309	101994	Stefano Morozzi	04/2022
7797	2^338816-60647	101994	Stefano Morozzi	06/2022
7798	2^338816+171043	101994	Stefano Morozzi	11/2022
7799	2^338814-11513	101994	Stefano Morozzi	12/2022
7800	2^338811-126999	101993	Stefano Morozzi	12/2021
7801	2^338811+131621	101993	Stefano Morozzi	02/2022
7802	2^338812-107637	101993	Stefano Morozzi	03/2022
7803	2^338813+192725	101993	Stefano Morozzi	09/2022
7804	2^338812+94731	101993	Stefano Morozzi	11/2022
7805	2^338813+49205	101993	Stefano Morozzi	02/2023
7806	2^338809-152755	101992	Stefano Morozzi	01/2022
7807	2^338808+156531	101992	Stefano Morozzi	01/2022
7808	2^338808+7885	101992	Stefano Morozzi	02/2022
7809	2^338808-105797	101992	Stefano Morozzi	02/2022
7810	2^338807-35899	101992	Stefano Morozzi	06/2022
7811	2^338808-89175	101992	Stefano Morozzi	01/2023
7812	2^338808-91475	101992	Stefano Morozzi	01/2023
7813	2^338805+29879	101991	Stefano Morozzi	01/2022
7814	2^338805+157925	101991	Stefano Morozzi	02/2022
7815	2^338804-6809	101991	Stefano Morozzi	03/2022
7816	2^338806-157095	101991	Stefano Morozzi	03/2022
7817	2^338804-133173	101991	Stefano Morozzi	04/2022
7818	2^338805-115189	101991	Stefano Morozzi	01/2023
7819	2^338802+150403	101990	Stefano Morozzi	11/2021
7820	2^338801+154587	101990	Stefano Morozzi	01/2022
7821	2^338802-180603	101990	Stefano Morozzi	02/2022
7822	2^338803-31921	101990	Stefano Morozzi	03/2022
7823	2^338803-81735	101990	Stefano Morozzi	03/2022
7824	2^338803+195141	101990	Stefano Morozzi	11/2022
7825	2^338800+160141	101989	Stefano Morozzi	03/2022
7826	2^338797-82489	101989	Stefano Morozzi	03/2022
7831	2^338796+93	101988	Donovan Johnson	06/2008
7827	2^338795+455	101988	Stefano Morozzi	11/2021
7828	2^338795-102075	101988	Stefano Morozzi	12/2021
7829	2^338794-3483	101988	Stefano Morozzi	01/2022
7830	2^338796+179641	101988	Stefano Morozzi	01/2022
7832	2^338793-5155	101987	Stefano Morozzi	02/2022
7833	2^338793+111107	101987	Stefano Morozzi	03/2022
7834	2^338791+112083	101987	Stefano Morozzi	04/2022
7835	2^338792-85097	101987	Stefano Morozzi	06/2022
7836	(61*10^101986+47)/9	101987	Robert Price	07/2022
7837	2^338787+53309	101986	Stefano Morozzi	01/2022
7838	2^338787-153817	101986	Stefano Morozzi	01/2022
7839	2^338789+56229	101986	Stefano Morozzi	01/2022
7840	2^338790+6429	101986	Stefano Morozzi	01/2022
7841	2^338788+131701	101986	Stefano Morozzi	02/2022
7842	2^338785+104639	101985	Stefano Morozzi	01/2022
7843	2^338784+37591	101985	Stefano Morozzi	04/2022
7844	2^338786-9831	101985	Stefano Morozzi	04/2022
7845	2^338783+109065	101984	Stefano Morozzi	03/2022
7846	2^338779+86711	101983	Stefano Morozzi	04/2022
7847	2^338778+113589	101983	Stefano Morozzi	05/2022
7848	2^338775-30369	101982	Stefano Morozzi	02/2022
7849	2^338774+159135	101982	Stefano Morozzi	03/2022
7850	2^338776+113001	101982	Stefano Morozzi	04/2022
7851	2^338774+117039	101982	Stefano Morozzi	09/2022
7852	2^338775+167109	101982	Stefano Morozzi	09/2022
7853	2^338774+147595	101982	Stefano Morozzi	11/2022
7854	2^338772+42733	101981	Stefano Morozzi	09/2022
7855	2^338771-138805	101981	Stefano Morozzi	12/2022
7856	2^338768-181007	101980	Stefano Morozzi	02/2022
7857	2^338768+108807	101980	Stefano Morozzi	03/2022
7858	2^338767+169155	101980	Stefano Morozzi	09/2022
7859	2^338769+95369	101980	Stefano Morozzi	11/2022
7860	2^338769+195965	101980	Stefano Morozzi	11/2022
7861	2^338770-12725	101980	Stefano Morozzi	12/2022
7862	2^338768-140843	101980	Stefano Morozzi	01/2023
7863	2^338764+138013	101979	Stefano Morozzi	04/2022
7864	2^338765-160323	101979	Stefano Morozzi	06/2022
7865	2^338765+124545	101979	Stefano Morozzi	02/2023
7871	lucasU(1373,1,32502)-lucasU(1373,1,32501)	101978	Mike Oakes	05/2009
7866	2^338761+103671	101978	Stefano Morozzi	01/2022
7867	2^338763-7651	101978	Stefano Morozzi	03/2022
7868	2^338763+65591	101978	Stefano Morozzi	06/2022
7869	2^338762-111875	101978	Stefano Morozzi	12/2022
7870	2^338762-192237	101978	Stefano Morozzi	02/2023
7872	2^338757-5151	101977	Stefano Morozzi	02/2022
7873	2^338760-79037	101977	Stefano Morozzi	02/2022
7874	2^338757-82143	101977	Stefano Morozzi	03/2022
7875	2^338757+137007	101977	Stefano Morozzi	04/2022
7876	2^338755+158531	101976	Stefano Morozzi	03/2022
7877	2^338755+74081	101976	Stefano Morozzi	02/2023
7878	2^338752-153353	101975	Stefano Morozzi	01/2022
7879	2^338751+8001	101975	Stefano Morozzi	02/2022
7880	2^338752+32977	101975	Stefano Morozzi	02/2022
7881	2^338753-79233	101975	Stefano Morozzi	02/2022
7882	2^338752-88157	101975	Stefano Morozzi	12/2022
7883	2^338750-175625	101974	Stefano Morozzi	12/2021
7884	2^338747-2731	101974	Stefano Morozzi	12/2021
7885	2^338750-29597	101974	Stefano Morozzi	02/2022
7886	2^338748+35095	101974	Stefano Morozzi	03/2022
7887	2^338747+137475	101974	Stefano Morozzi	04/2022
7888	2^338747+162005	101974	Stefano Morozzi	04/2022
7889	2^338750+162237	101974	Stefano Morozzi	04/2022
7890	2^338747-184365	101974	Stefano Morozzi	04/2022
7891	2^338748+64341	101974	Stefano Morozzi	05/2022
7892	2^338750+24445	101974	Stefano Morozzi	02/2023
7893	2^338746+59577	101973	Stefano Morozzi	03/2022
7894	2^338746+62055	101973	Stefano Morozzi	04/2022
7895	2^338744+194065	101973	Stefano Morozzi	09/2022
7896	2^338741+25359	101972	Stefano Morozzi	12/2021
7897	2^338743+176981	101972	Stefano Morozzi	12/2021
7898	2^338741+183029	101972	Stefano Morozzi	02/2022
7899	2^338743-130309	101972	Stefano Morozzi	02/2022
7900	2^338741+86349	101972	Stefano Morozzi	04/2022
7901	2^338741+111561	101972	Stefano Morozzi	04/2022
7902	2^338743+172301	101972	Stefano Morozzi	11/2022
7903	2^338741-189969	101972	Stefano Morozzi	01/2023
7904	2^338739+76959	101971	Stefano Morozzi	12/2021
7905	2^338739-105957	101971	Stefano Morozzi	02/2022
7906	2^338739+190149	101971	Stefano Morozzi	05/2022
7907	2^338738+64947	101971	Stefano Morozzi	05/2022
7908	2^338740+119947	101971	Stefano Morozzi	11/2022
7909	2^338740-186837	101971	Stefano Morozzi	12/2022
7910	2^338737+127547	101970	Stefano Morozzi	12/2021
7911	2^338737+128591	101970	Stefano Morozzi	01/2022
7912	2^338735-153165	101970	Stefano Morozzi	01/2022
7913	2^338734+13719	101970	Stefano Morozzi	05/2022
7914	2^338734-138225	101970	Stefano Morozzi	12/2022
7915	2^338735-186129	101970	Stefano Morozzi	12/2022
7921	25295^10744+10744^25295	101969	Hans Havermann	01/2019
7922	25712^9243+9243^25712	101969	Hans Havermann	01/2019
7916	2^338731-150895	101969	Stefano Morozzi	12/2021
7917	2^338731+54911	101969	Stefano Morozzi	01/2022
7918	2^338731+85863	101969	Stefano Morozzi	03/2022
7919	2^338732+185047	101969	Stefano Morozzi	03/2022
7920	2^338733+193791	101969	Stefano Morozzi	09/2022
7923	2^338729+69221	101968	Stefano Morozzi	09/2022
7924	2^338728+123355	101968	Stefano Morozzi	11/2022
7925	2^338730-87063	101968	Stefano Morozzi	12/2022
7926	2^338726+128199	101967	Stefano Morozzi	01/2022
7927	2^338727+127745	101967	Stefano Morozzi	01/2022
7928	2^338724+32971	101967	Stefano Morozzi	02/2022
7929	2^338727+189683	101967	Stefano Morozzi	05/2022
7930	2^338727+118293	101967	Stefano Morozzi	09/2022
7931	2^338723-76651	101966	Stefano Morozzi	12/2021
7932	2^338721+79037	101966	Stefano Morozzi	01/2022
7933	2^338723-132621	101966	Stefano Morozzi	03/2022
7934	2^338722+137313	101966	Stefano Morozzi	04/2022
7935	2^338722+162915	101966	Stefano Morozzi	04/2022
7936	2^338723+199161	101966	Stefano Morozzi	02/2023
7937	2^338718-126861	101965	Stefano Morozzi	12/2021
7938	2^338718-109127	101965	Stefano Morozzi	04/2022
7943	(71^55079-1)/70	101964	Paul Bourdelais	08/2017
7939	2^338714+30835	101964	Stefano Morozzi	01/2022
7940	2^338714+156715	101964	Stefano Morozzi	02/2022
7941	2^338715+19923	101964	Stefano Morozzi	09/2022
7942	2^338716+173253	101964	Stefano Morozzi	11/2022
7944	2^338711+125399	101963	Stefano Morozzi	12/2021
7945	2^338713-30895	101963	Stefano Morozzi	02/2022
7946	2^338712-132545	101963	Stefano Morozzi	03/2022
7947	2^338713+87825	101963	Stefano Morozzi	04/2022
7948	2^338712+190333	101963	Stefano Morozzi	06/2022
7949	2^338709-154429	101962	Stefano Morozzi	02/2022
7950	2^338710+140545	101962	Stefano Morozzi	06/2022
7951	2^338706-102917	101961	Stefano Morozzi	01/2022
7952	2^338705+34727	101961	Stefano Morozzi	03/2022
7953	2^338706-165633	101961	Stefano Morozzi	01/2023
7954	2^338707-116115	101961	Stefano Morozzi	01/2023
7955	2^338698+104083	101959	Stefano Morozzi	01/2022
7956	2^338700-184565	101959	Stefano Morozzi	04/2022
7957	2^338700+189777	101959	Stefano Morozzi	05/2022
7958	2^338698+41779	101959	Stefano Morozzi	09/2022
7959	2^338699+148533	101959	Stefano Morozzi	11/2022
7960	2^338700+97381	101959	Stefano Morozzi	11/2022
7961	2^338698-142181	101959	Stefano Morozzi	02/2023
7962	2^338696+181671	101958	Stefano Morozzi	02/2022
7963	2^338697+146651	101958	Stefano Morozzi	11/2022
7964	2^338695-116977	101958	Stefano Morozzi	02/2023
7965	2^338692+106297	101957	Stefano Morozzi	01/2022
7966	2^338692+33195	101957	Stefano Morozzi	02/2022
7967	2^338692+110505	101957	Stefano Morozzi	03/2022
7968	2^338692+190093	101957	Stefano Morozzi	05/2022
7969	2^338692+173343	101957	Stefano Morozzi	11/2022
7970	2^338693+144975	101957	Stefano Morozzi	11/2022
7971	2^338692+149281	101957	Stefano Morozzi	02/2023
7972	2^338688+82203	101956	Stefano Morozzi	02/2022
7973	2^338689+82365	101956	Stefano Morozzi	02/2022
7974	2^338688-92159	101956	Stefano Morozzi	02/2023
7975	2^338686-81303	101955	Stefano Morozzi	03/2022
7976	2^338687+40461	101955	Stefano Morozzi	06/2022
7977	2^338687+65283	101955	Stefano Morozzi	06/2022
7983	2^338682-19865	101954	Enzo Doria	06/2013
7984	(2^(112895*3+1)+243)/7	101954	Kevin Acres	12/2013
7978	(8*10^101954-269)/9	101954	Robert Price	09/2021
7979	2^338683+50303	101954	Stefano Morozzi	11/2021
7980	2^338682-107205	101954	Stefano Morozzi	03/2022
7981	2^338682+13839	101954	Stefano Morozzi	05/2022
7982	2^338683-42837	101954	Stefano Morozzi	02/2023
7985	2^338678-180005	101953	Stefano Morozzi	02/2022
7986	2^338680+15855	101953	Stefano Morozzi	06/2022
7987	2^338678+93175	101953	Stefano Morozzi	09/2022
7988	2^338680+99217	101953	Stefano Morozzi	02/2023
7989	2^338674-175967	101952	Stefano Morozzi	12/2021
7990	2^338677-177373	101952	Stefano Morozzi	12/2021
7991	2^338677+102999	101952	Stefano Morozzi	01/2022
7992	2^338676+33381	101952	Stefano Morozzi	03/2022
7993	2^338677-82699	101952	Stefano Morozzi	03/2022
7994	2^338676-34299	101952	Stefano Morozzi	04/2022
7995	2^338675+188445	101952	Stefano Morozzi	05/2022
7996	2^338676+165271	101952	Stefano Morozzi	06/2022
7997	2^338674-187551	101952	Stefano Morozzi	12/2022
7998	2^338676-42243	101952	Stefano Morozzi	02/2023
7999	2^338671-55041	101951	Stefano Morozzi	02/2022
8000	2^338673-80203	101951	Stefano Morozzi	02/2022

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PRP Records

Probable Primes Top 10000

(295765 PRPs in the top)