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 ?
7755	(2^338242+2782)/2	101821	Stefano Morozzi	02/2021
7751	2^338240+81745	101821	Stefano Morozzi	02/2022
7752	2^338241-155551	101821	Stefano Morozzi	02/2022
7753	2^338242-108237	101821	Stefano Morozzi	04/2022
7754	2^338242+43045	101821	Stefano Morozzi	09/2022
7756	2^338238-126735	101820	Stefano Morozzi	12/2021
7757	2^338238+183855	101820	Stefano Morozzi	03/2022
7758	2^338238+141013	101820	Stefano Morozzi	06/2022
7759	2^338237+97227	101820	Stefano Morozzi	11/2022
7760	2^338238+48429	101820	Stefano Morozzi	11/2022
7761	2^338234-80925	101819	Stefano Morozzi	02/2022
7762	2^338234-154593	101819	Stefano Morozzi	02/2022
7763	2^338235-131787	101819	Stefano Morozzi	03/2022
7764	2^338233+89781	101819	Stefano Morozzi	05/2022
7765	2^338235+169971	101819	Stefano Morozzi	11/2022
7766	2^338233-113875	101819	Stefano Morozzi	12/2022
7773	(3*2^338236-1)/347	101818	Lelio R Paula	03/2014
7767	2^338232-175539	101818	Stefano Morozzi	12/2021
7768	2^338231+57345	101818	Stefano Morozzi	02/2022
7769	2^338232+36097	101818	Stefano Morozzi	03/2022
7770	2^338230+137403	101818	Stefano Morozzi	04/2022
7771	2^338231-59569	101818	Stefano Morozzi	04/2022
7772	2^338230-86633	101818	Stefano Morozzi	12/2022
7774	2^338228+159247	101817	Stefano Morozzi	03/2022
7775	2^338227-12631	101817	Stefano Morozzi	12/2022
7776	(34*10^101815+191)/9	101816	Robert Price	08/2021
7777	2^338224+185461	101816	Stefano Morozzi	03/2022
7778	2^338224+62295	101816	Stefano Morozzi	04/2022
7779	2^338225+162645	101816	Stefano Morozzi	04/2022
7780	2^338223+144209	101816	Stefano Morozzi	09/2022
7787	6^130841+103	101815	Lelio R Paula	10/2016
7781	2^338220+150405	101815	Stefano Morozzi	11/2021
7782	2^338219-4147	101815	Stefano Morozzi	01/2022
7783	2^338221+83391	101815	Stefano Morozzi	02/2022
7784	2^338221+62937	101815	Stefano Morozzi	04/2022
7785	2^338220-65697	101815	Stefano Morozzi	01/2023
7786	2^338220-139505	101815	Stefano Morozzi	01/2023
7788	2^338216+77473	101814	Stefano Morozzi	12/2021
7789	2^338218+155299	101814	Stefano Morozzi	01/2022
7790	2^338217-134745	101814	Stefano Morozzi	04/2022
7791	2^338218+73507	101814	Stefano Morozzi	11/2022
7792	2^338213-125631	101813	Stefano Morozzi	12/2021
7793	2^338215+25845	101813	Stefano Morozzi	12/2021
7794	2^338210-153537	101812	Stefano Morozzi	01/2022
7795	2^338209+60915	101812	Stefano Morozzi	03/2022
7796	2^338211-57297	101812	Stefano Morozzi	03/2022
7797	2^338211-110257	101812	Stefano Morozzi	06/2022
7798	2^338211+71549	101812	Stefano Morozzi	11/2022
7799	2^338208-178787	101811	Stefano Morozzi	01/2022
7800	2^338208+106153	101811	Stefano Morozzi	01/2022
7801	2^338207+16499	101811	Stefano Morozzi	06/2022
7802	2^338205+102471	101810	Stefano Morozzi	12/2021
7803	2^338199-176377	101809	Stefano Morozzi	12/2021
7804	2^338201-151233	101809	Stefano Morozzi	12/2021
7805	2^338202-152061	101809	Stefano Morozzi	12/2021
7806	2^338202+133785	101809	Stefano Morozzi	03/2022
7807	2^338200+135643	101809	Stefano Morozzi	03/2022
7808	2^338202+14169	101809	Stefano Morozzi	05/2022
7809	2^338202-85211	101809	Stefano Morozzi	06/2022
7810	2^338200+74265	101809	Stefano Morozzi	02/2023
7811	2^338196+121147	101808	Stefano Morozzi	11/2022
7812	2^338196+73551	101808	Stefano Morozzi	11/2022
7813	2^338194-175845	101807	Stefano Morozzi	12/2021
7814	2^338195+56771	101807	Stefano Morozzi	02/2022
7815	2^338195+162365	101807	Stefano Morozzi	04/2022
7816	2^338194+67497	101807	Stefano Morozzi	09/2022
7817	2^338193-116335	101807	Stefano Morozzi	01/2023
7818	2^338194-15585	101807	Stefano Morozzi	01/2023
7819	2^338192+130387	101806	Stefano Morozzi	01/2022
7820	2^338190+89359	101806	Stefano Morozzi	05/2022
7821	2^338189+144605	101806	Stefano Morozzi	09/2022
7822	2^338190-113537	101806	Stefano Morozzi	12/2022
7823	2^338186+127245	101805	Stefano Morozzi	12/2021
7824	2^338186-130013	101805	Stefano Morozzi	02/2022
7825	2^338186+39235	101805	Stefano Morozzi	05/2022
7826	2^338185+77315	101804	Stefano Morozzi	12/2021
7827	2^338185+102519	101804	Stefano Morozzi	12/2021
7828	2^338183-76539	101804	Stefano Morozzi	12/2021
7829	2^338185+104489	101804	Stefano Morozzi	01/2022
7830	2^338179+35361	101803	Stefano Morozzi	03/2022
7831	2^338181+64235	101803	Stefano Morozzi	05/2022
7832	2^338181+94047	101803	Stefano Morozzi	09/2022
7833	2^338180+146131	101803	Stefano Morozzi	11/2022
7834	2^338179+123399	101803	Stefano Morozzi	11/2022
7835	2^338182-42425	101803	Stefano Morozzi	02/2023
7836	2^338177+51807	101802	Stefano Morozzi	12/2021
7837	2^338177+107385	101802	Stefano Morozzi	02/2022
7838	2^338178+34287	101802	Stefano Morozzi	03/2022
7839	2^338178+184207	101802	Stefano Morozzi	03/2022
7840	2^338177-108901	101802	Stefano Morozzi	04/2022
7841	2^338177+141569	101802	Stefano Morozzi	06/2022
7842	2^338176+46221	101802	Stefano Morozzi	11/2022
7843	2^338175+25161	101801	Stefano Morozzi	11/2021
7844	2^338173-27901	101801	Stefano Morozzi	01/2022
7845	2^338174+23217	101801	Stefano Morozzi	11/2022
7846	2^338174+23793	101801	Stefano Morozzi	11/2022
7847	2^338173-36183	101801	Stefano Morozzi	12/2022
7848	2^338173-137053	101801	Stefano Morozzi	12/2022
7849	2^338174-36797	101801	Stefano Morozzi	12/2022
7850	2^338175-166509	101801	Stefano Morozzi	01/2023
7851	2^338169-155965	101800	Stefano Morozzi	02/2022
7852	2^338172+95797	101800	Stefano Morozzi	11/2022
7853	2^338171-117987	101800	Stefano Morozzi	02/2023
7854	2^338166+183237	101799	Stefano Morozzi	02/2022
7855	2^338168-157835	101799	Stefano Morozzi	03/2022
7856	2^338166+137107	101799	Stefano Morozzi	04/2022
7857	2^338166+22897	101799	Stefano Morozzi	11/2022
7858	2^338166-161123	101799	Stefano Morozzi	12/2022
7859	2^338165-152139	101798	Stefano Morozzi	12/2021
7860	2^338163-178947	101798	Stefano Morozzi	02/2022
7861	2^338164-64329	101798	Stefano Morozzi	01/2023
7862	2^338159-127575	101797	Stefano Morozzi	12/2021
7863	2^338161+154259	101797	Stefano Morozzi	01/2022
7864	2^338160+139947	101797	Stefano Morozzi	05/2022
7865	2^338160+191815	101797	Stefano Morozzi	09/2022
7866	2^338160+22207	101797	Stefano Morozzi	11/2022
7867	2^338161+196157	101797	Stefano Morozzi	11/2022
7868	2^338162-138635	101797	Stefano Morozzi	12/2022
7869	2^338156-75269	101796	Stefano Morozzi	12/2021
7870	2^338156-151247	101796	Stefano Morozzi	12/2021
7871	2^338156+103273	101796	Stefano Morozzi	01/2022
7872	2^338156+167053	101796	Stefano Morozzi	09/2022
7873	2^338158+69303	101796	Stefano Morozzi	09/2022
7874	2^338158+171189	101796	Stefano Morozzi	11/2022
7875	2^338157-188989	101796	Stefano Morozzi	12/2022
7876	2^338158-188711	101796	Stefano Morozzi	12/2022
7877	2^338155+132621	101795	Stefano Morozzi	02/2022
7878	2^338155-82605	101795	Stefano Morozzi	03/2022
7879	2^338155-182631	101795	Stefano Morozzi	03/2022
7880	2^338155+187755	101795	Stefano Morozzi	04/2022
7881	2^338154-83975	101795	Stefano Morozzi	04/2022
7882	2^338154+163759	101795	Stefano Morozzi	05/2022
7883	2^338152-25767	101794	Stefano Morozzi	12/2021
7884	2^338152+181927	101794	Stefano Morozzi	02/2022
7885	2^338151+60779	101794	Stefano Morozzi	03/2022
7886	2^338151+189149	101794	Stefano Morozzi	05/2022
7887	2^338152+45567	101794	Stefano Morozzi	11/2022
7888	2^338147+29343	101793	Stefano Morozzi	01/2022
7889	2^338148+130803	101793	Stefano Morozzi	01/2022
7890	2^338146+166167	101793	Stefano Morozzi	06/2022
7891	2^338149-185073	101793	Stefano Morozzi	06/2022
7892	2^338149+41757	101793	Stefano Morozzi	09/2022
7893	2^338149+125015	101793	Stefano Morozzi	02/2023
7894	2^338144+180697	101792	Stefano Morozzi	01/2022
7895	2^338143+8589	101792	Stefano Morozzi	02/2022
7896	2^338143-55611	101792	Stefano Morozzi	02/2022
7897	2^338143+60623	101792	Stefano Morozzi	03/2022
7898	2^338145-63609	101792	Stefano Morozzi	12/2022
7899	2^338141-77301	101791	Stefano Morozzi	12/2021
7900	2^338141+157145	101791	Stefano Morozzi	02/2022
7901	2^338140+84745	101791	Stefano Morozzi	03/2022
7902	2^338140+90073	101791	Stefano Morozzi	05/2022
7903	2^338142+96583	101791	Stefano Morozzi	11/2022
7904	2^338139-134719	101790	Stefano Morozzi	04/2022
7905	2^338138+95443	101790	Stefano Morozzi	11/2022
7906	2^338133+1445	101789	Stefano Morozzi	12/2021
7907	2^338133+172469	101789	Stefano Morozzi	11/2022
7908	2^338134+23235	101789	Stefano Morozzi	11/2022
7909	2^338132+105643	101788	Stefano Morozzi	01/2022
7910	2^338131+181871	101788	Stefano Morozzi	02/2022
7911	2^338132-184539	101788	Stefano Morozzi	04/2022
7912	2^338130+22383	101788	Stefano Morozzi	11/2022
7913	2^338132+170143	101788	Stefano Morozzi	11/2022
7914	2^338131-62599	101788	Stefano Morozzi	12/2022
7915	2^338128+128953	101787	Stefano Morozzi	01/2022
7916	2^338127+11021	101787	Stefano Morozzi	03/2022
7917	2^338127+192935	101787	Stefano Morozzi	09/2022
7918	2^338127+98621	101787	Stefano Morozzi	11/2022
7919	2^338128+98853	101787	Stefano Morozzi	02/2023
7920	2^338123-25959	101786	Stefano Morozzi	12/2021
7921	2^338124-180765	101786	Stefano Morozzi	02/2022
7922	2^338125-7129	101786	Stefano Morozzi	03/2022
7923	2^338125-40071	101786	Stefano Morozzi	01/2023
7927	2^338122-20117	101785	Enzo Doria	06/2013
7928	(2^338139+5)/905333	101785	Lelio R Paula	12/2013
7924	2^338122+32799	101785	Stefano Morozzi	02/2022
7925	2^338120+166411	101785	Stefano Morozzi	06/2022
7926	2^338122+90705	101785	Stefano Morozzi	06/2022
7929	2^338117+103761	101784	Stefano Morozzi	01/2022
7930	2^338118+53817	101784	Stefano Morozzi	01/2022
7931	2^338116+82585	101784	Stefano Morozzi	02/2022
7932	2^338118+39483	101784	Stefano Morozzi	05/2022
7933	2^338119+96659	101784	Stefano Morozzi	11/2022
7934	2^338115+61083	101783	Stefano Morozzi	03/2022
7935	2^338114+173287	101783	Stefano Morozzi	11/2022
7936	2^338113-139681	101783	Stefano Morozzi	01/2023
7937	2^338110-175365	101782	Stefano Morozzi	12/2021
7938	2^338110-3963	101782	Stefano Morozzi	01/2022
7939	2^338112+155061	101782	Stefano Morozzi	01/2022
7940	2^338112+137335	101782	Stefano Morozzi	04/2022
7941	2^338111-85627	101782	Stefano Morozzi	06/2022
7942	2^338111-90145	101782	Stefano Morozzi	01/2023
7951	35^65917-7092	101781	Enzo Doria	03/2013
7943	2^338107-1221	101781	Stefano Morozzi	12/2021
7944	2^338109+108539	101781	Stefano Morozzi	03/2022
7945	2^338109-7261	101781	Stefano Morozzi	03/2022
7946	2^338109-131961	101781	Stefano Morozzi	03/2022
7947	2^338108+39585	101781	Stefano Morozzi	05/2022
7948	2^338109+38147	101781	Stefano Morozzi	05/2022
7949	2^338108+17301	101781	Stefano Morozzi	09/2022
7950	2^338108-65859	101781	Stefano Morozzi	01/2023
7952	2^338105+79599	101780	Stefano Morozzi	01/2022
7953	2^338103-180675	101780	Stefano Morozzi	02/2022
7954	2^338103+19499	101780	Stefano Morozzi	09/2022
7955	2^338103-165319	101780	Stefano Morozzi	01/2023
7956	2^338100-100389	101779	Stefano Morozzi	12/2021
7957	2^338100+27595	101779	Stefano Morozzi	12/2021
7958	2^338101+101139	101779	Stefano Morozzi	12/2021
7959	2^338101+134985	101779	Stefano Morozzi	03/2022
7960	2^338102+186135	101779	Stefano Morozzi	03/2022
7961	2^338100+36885	101779	Stefano Morozzi	04/2022
7962	2^338102-8151	101779	Stefano Morozzi	04/2022
7963	2^338100+90637	101779	Stefano Morozzi	06/2022
7964	2^338101+68505	101779	Stefano Morozzi	09/2022
7965	2^338100-42867	101779	Stefano Morozzi	02/2023
7966	2^338097+100229	101778	Stefano Morozzi	11/2021
7967	2^338097-25695	101778	Stefano Morozzi	12/2021
7968	2^338098-110043	101778	Stefano Morozzi	06/2022
7969	2^338099-191389	101778	Stefano Morozzi	01/2023
7970	2^338093-128403	101777	Stefano Morozzi	01/2022
7971	2^338093+33051	101777	Stefano Morozzi	02/2022
7972	2^338094+135555	101777	Stefano Morozzi	03/2022
7973	2^338095-32395	101777	Stefano Morozzi	03/2022
7974	2^338090-175353	101776	Stefano Morozzi	12/2021
7975	2^338090+33277	101776	Stefano Morozzi	02/2022
7976	2^338091-105601	101776	Stefano Morozzi	02/2022
7977	2^338091-32127	101776	Stefano Morozzi	03/2022
7978	2^338092+12873	101776	Stefano Morozzi	04/2022
7979	2^338091-58485	101776	Stefano Morozzi	04/2022
7980	2^338086+177643	101775	Stefano Morozzi	12/2021
7981	2^338089+82905	101775	Stefano Morozzi	02/2022
7982	2^338088+87565	101775	Stefano Morozzi	04/2022
7983	2^338088-166205	101775	Stefano Morozzi	01/2023
7984	2^338089-140053	101775	Stefano Morozzi	01/2023
7985	2^338087+124935	101775	Stefano Morozzi	02/2023
7986	2^338085-3301	101774	Stefano Morozzi	01/2022
7987	2^338084+108691	101774	Stefano Morozzi	03/2022
7988	2^338083+164369	101774	Stefano Morozzi	05/2022
7989	2^338080+107521	101773	Stefano Morozzi	02/2022
7990	2^338080-156917	101773	Stefano Morozzi	03/2022
7991	2^338081+199775	101773	Stefano Morozzi	02/2023
7992	2^338076+62311	101772	Stefano Morozzi	04/2022
7993	2^338079+161745	101772	Stefano Morozzi	04/2022
7994	2^338078-60075	101772	Stefano Morozzi	06/2022
7995	2^338079+167079	101772	Stefano Morozzi	09/2022
7996	2^338076+122535	101772	Stefano Morozzi	11/2022
7997	2^338077+95619	101772	Stefano Morozzi	11/2022
7998	2^338078+20539	101772	Stefano Morozzi	11/2022
7999	2^338076-36813	101772	Stefano Morozzi	12/2022
8000	2^338078-64911	101772	Stefano Morozzi	01/2023

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Probable Primes Top 10000

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