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 ?
751	(2*10^275922+1)/3	275922	Serge Batalov	11/2022
752	2^916385-2786383	275860	Enzo Doria	11/2015
753	2^915928+82081	275722	Enzo Doria	09/2016
754	(4*10^275671+11)/3	275672	Tyler Busby	02/2023
755	2^915576-114137	275616	Enzo Doria	01/2015
756	2^914828+1876741	275391	Enzo Doria	07/2016
757	2^914757-2203	275370	Yves Minet	12/2015
758	7*10^275157-27	275158	Robert Price	11/2022
759	2^911900+1871245	274510	Enzo Doria	05/2016
760	(16*10^274251-91)/3	274252	Robert Price	11/2022
761	2^910999+9	274239	Stefano Morozzi	05/2021
762	(2^910869-7)/5	274199	Stefano Morozzi	08/2022
763	2^910490+283429	274085	Enzo Doria	01/2017
764	7*10^273983+39	273984	Robert Price	01/2023
765	2^909988-1862249	273934	Enzo Doria	12/2015
766	2^909297+1879157	273726	Enzo Doria	08/2016
767	2^909257-1864423	273714	Enzo Doria	01/2016
768	2^908739-7	273558	Stefano Morozzi	07/2022
769	2^908579-1861747	273510	Enzo Doria	12/2015
770	2^907635-2791597	273226	Enzo Doria	01/2016
771	(53^158341+1)/54	273022	Paul Bourdelais	07/2019
772	2^906594-113201	272912	Enzo Doria	08/2014
773	2*10^272403-91	272404	Robert Price	02/2023
774	2^904773+1872167	272364	Enzo Doria	06/2016
775	6^349903+5	272278	Paul Bourdelais	02/2021
776	2^904149-1862473	272176	Enzo Doria	12/2015
777	(7*10^271757-61)/9	271757	Erik Branger	03/2012
778	2^902497+1880117	271679	Enzo Doria	09/2016
779	2^901858+77689	271487	Enzo Doria	06/2016
780	2^901372+1875301	271341	Enzo Doria	06/2016
781	2*10^270802-91	270803	Robert Price	02/2023
782	23*10^270799-7	270801	Robert Price	10/2022
783	2^899121-115033	270663	Enzo Doria	07/2015
784	2^898900+883021	270596	Enzo Doria	12/2016
785	2^898762-251511	270555	Enzo Doria	12/2013
786	2^898589+47	270503	Lelio R Paula	03/2016
787	187322*10^270343-187321	270349	Danilo Nitsche	09/2013
788	48358*10^270343-48357	270348	Danilo Nitsche	09/2013
789	(10^270343-1)/9	270343	Maksym Voznyy	07/2007
790	2^897867-3217	270285	Yves Minet	12/2016
791	2^897849-115273	270280	Enzo Doria	07/2015
792	2^896616-114179	269909	Enzo Doria	12/2014
793	2^894928+583561	269401	Enzo Doria	04/2017
794	2^894673-39343	269324	Enzo Doria	08/2015
795	F(1285607)	268676	Henri Lifchitz	11/2008
796	2^892112+187663	268553	Enzo Doria	08/2016
797	(266*10^268407-17)/3	268409	Robert Price	02/2023
798	(10^268207+1)/11	268206	Paul Bourdelais	02/2010
799	2^890957-69583	268205	Enzo Doria	12/2015
800	32841!^2+32840!^2+...+2!^2+1!^2	268128	Serge Batalov	07/2017
801	2^890122-351401	267954	Enzo Doria	07/2015
802	(19^209359-1)/18	267718	Paul Bourdelais	08/2010
803	(85^138647+1)/86	267507	Paul Bourdelais	07/2019
804	(485^99523-1)/484	267291	Michael Stocker	05/2020
805	2^886324+77791	266811	Enzo Doria	06/2016
806	7*10^266731+87	266732	Robert Price	11/2022
807	2^884714+1880527	266326	Enzo Doria	10/2016
808	11^255426+255426^11	265999	Serge Batalov	05/2014
809	2^883462-343421	265949	Enzo Doria	07/2015
810	2^883442+1875019	265943	Enzo Doria	06/2016
811	2^883333-291583	265910	Enzo Doria	07/2015
812	(2*10^265321-17)/3	265321	Serge Batalov	11/2022
813	(16*10^265052-91)/3	265053	Robert Price	11/2022
814	2^880411+1882673	265031	Enzo Doria	12/2016
815	(14*10^264791-11)/3	264792	Robert Price	08/2022
816	2^879530-2788031	264765	Enzo Doria	12/2015
817	(2*10^264539+61)/9	264539	Serge Batalov	11/2022
818	2^878118+2793079	264340	Enzo Doria	02/2016
819	(2^878073-7)/5	264326	Stefano Morozzi	08/2022
820	(37^168527-1)/36	264283	Paul Bourdelais	08/2019
821	2^876202-17	263764	Stefano Morozzi	07/2022
822	(14*10^263720-11)/3	263721	Robert Price	08/2022
823	2^875748-461129	263627	Enzo Doria	07/2015
824	2^875518-15	263558	Stefano Morozzi	07/2022
825	(29*10^263523-17)/3	263524	Robert Price	01/2023
826	2^875181-2789923	263456	Enzo Doria	12/2015
827	2^875101-350083	263432	Enzo Doria	08/2015
828	2^874684+1883587	263307	Enzo Doria	01/2017
829	2^874616+1872211	263286	Enzo Doria	05/2016
830	3^551491+16	263129	Robert Price	04/2020
831	2^874073+2792957	263123	Enzo Doria	02/2016
832	2^873628+1878751	262989	Enzo Doria	08/2016
833	2^873288-269	262886	Yves Minet	01/2015
834	(2*10^262874+7)/9	262874	Rytis Slatkevicius	01/2023
835	(2*10^262603-11)/9	262603	Serge Batalov	11/2022
836	2^871991-4207	262496	Yves Minet	03/2021
837	2^871146-3173	262242	Yves Minet	07/2016
838	2^869601-163	261776	Yves Minet	01/2015
839	(2*10^261704+61)/9	261704	Serge Batalov	11/2022
840	2^869326+282859	261694	Enzo Doria	11/2016
841	2^869035-114181	261606	Enzo Doria	12/2014
842	4*10^261248+91	261249	Robert Price	11/2022
843	2^865715+80303	260607	Enzo Doria	07/2016
844	2^865048+1882411	260406	Enzo Doria	12/2016
845	2^864899-113871	260361	Enzo Doria	10/2014
846	(16*10^260256-91)/3	260257	Robert Price	11/2022
847	(7*10^260198-61)/9	260198	Erik Branger	11/2011
848	2^864298-2788421	260180	Enzo Doria	12/2015
849	2^864039-2791357	260102	Enzo Doria	01/2016
850	2^863621-113833	259976	Enzo Doria	10/2014
851	2^862837+75767	259740	Enzo Doria	05/2016
852	2^862637-31	259680	Jorge Menendez	05/2019
853	2^862088+1874941	259515	Enzo Doria	06/2016
854	2^861987-134557	259484	Hans Havermann	10/2018
855	2^861516-1854029	259343	Enzo Doria	09/2015
856	2^860975-1853977	259180	Enzo Doria	09/2015
857	3^543128+16	259138	Robert Price	04/2020
858	2^860625-1858843	259074	Enzo Doria	10/2015
859	2^860110+77689	258919	Enzo Doria	05/2016
860	2^859600+1880371	258766	Enzo Doria	10/2016
861	2^859433+494711	258716	Makoto Morimoto	10/2013
862	(2^859433-44)/(2^2*3)	258715	Makoto Morimoto	08/2019
863	(2^859431-11)/3	258715	Stefano Morozzi	08/2022
864	(2^859433+39899)/(73390746301)	258705	Makoto Morimoto	10/2016
865	2^859240+1875271	258658	Enzo Doria	06/2016
866	Tau(971^15738)	258571	Nik Lygeros / Olivier Rozier	05/2015
867	(144^119671+1)/145	258292	Paul Bourdelais	08/2019
868	2^857608+105	258166	Stefano Morozzi	05/2021
869	(11*2^857159-13)/15	258031	Renaud Lifchitz	08/2011
870	2^857016-633113	257988	Enzo Doria	12/2013
871	2^855732-113969	257602	Enzo Doria	10/2014
872	2^853682-3911	256984	Enzo Doria	05/2014
873	11^246668-90	256879	Enzo Doria	12/2012
874	2^851904-113939	256449	Enzo Doria	10/2014
875	2^851725-851725^2	256395	Henri Lifchitz	03/2019
876	11^246167-90	256357	Enzo Doria	12/2012
877	(85*10^256301-1)/3	256303	Robert Price	12/2022
878	(10^256187+7)/63443/148782853	256175	Alfred Reich	10/2021
879	2^850700-569049	256087	Enzo Doria	11/2013
880	2^850675+153	256079	Stefano Morozzi	05/2021
881	21^193601-20^193601	255983	Jean-Louis Charton	02/2015
882	(37^163193+1)/38	255918	Paul Bourdelais	07/2019
883	(14*10^255805-83)/3	255806	Robert Price	11/2022
884	2^849177-114025	255628	Enzo Doria	12/2014
885	2^848502-3173	255425	Yves Minet	07/2016
886	2^848178-140291	255328	Enzo Doria	01/2014
887	7*10^255167+87	255168	Robert Price	11/2022
888	2^847622-2441	255160	Yves Minet	02/2016
889	2^847291+182843	255061	Enzo Doria	11/2016
890	2^847174+1879429	255025	Enzo Doria	09/2016
891	24*29^174239+13361	254809	Curtis Bright	04/2015
892	22*10^254639+7	254641	Robert Price	10/2022
893	2^845633-933075	254561	Paul Bourdelais	11/2021
894	2^845610-1868591	254554	Enzo Doria	04/2016
895	2^845484+81931	254517	Enzo Doria	08/2016
896	2^845402-114761	254492	Enzo Doria	05/2015
897	2^844334-2792441	254170	Enzo Doria	02/2016
898	(4*10^254107+11)/3	254108	Tyler Busby	02/2023
899	11^243796-90	253888	Enzo Doria	12/2012
900	(10^253891+7)/44777/79843/16940711	253875	Alfred Reich	10/2021
901	30^171733-29^171733	253671	Jean-Louis Charton	10/2018
902	2^842209+1876037	253531	Enzo Doria	07/2016
903	2^842123-59197	253505	Enzo Doria	10/2015
904	(8*10^253313-53)/9	253313	Serge Batalov	11/2022
905	2^840797-3	253106	Paul Bourdelais	06/2019
906	2^840716-2969	253081	Yves Minet	05/2016
907	2^840358-462491	252973	Enzo Doria	08/2015
908	2^840310+1878379	252959	Enzo Doria	08/2016
909	2^840203-21	252927	Stefano Morozzi	07/2022
910	11^242579-60	252620	Enzo Doria	10/2012
911	45^152659+2	252378	Robert Price	09/2015
912	(95^127583+1)/96	252322	Paul Bourdelais	07/2019
913	7*10^252209-17	252210	Robert Price	12/2022
914	2^837725+1869377	252181	Enzo Doria	05/2016
915	2^837536-311039	252124	Enzo Doria	06/2015
916	21^190632-2	252058	Robert Price	07/2015
917	2^837242+1873297	252035	Enzo Doria	06/2016
918	2^836656-2787929	251859	Enzo Doria	11/2015
919	2^836380+1875541	251776	Enzo Doria	07/2016
920	(359^98327-1)/358	251233	Alexander Zhirkov	11/2017
921	tau(41^28288)	250924	Nik Lygeros / Olivier Rozier	10/2013
922	2^832511-461197	250611	Enzo Doria	07/2015
923	2^832505+1881137	250609	Enzo Doria	11/2016
924	2^832363+583295	250567	Enzo Doria	12/2016
925	2^832244-403635	250531	Enzo Doria	01/2014
926	(14*10^250336-41)/9	250337	Serge Batalov	01/2023
927	2^831157+1880657	250204	Enzo Doria	11/2016
928	2^831088-7200899	250183	Enzo Doria	01/2015
929	2^830956-1349	250143	Yves Minet	07/2015
930	2^830037+282317	249867	Enzo Doria	09/2016
931	2^829589-113653	249732	Enzo Doria	09/2014
932	(4*10^249550-7)/3	249551	Serge Batalov	01/2023
933	2^828281-3193	249338	Yves Minet	08/2016
934	(2^828140-19)/3	249295	Stefano Morozzi	08/2022
935	2^828064-2785619	249273	Enzo Doria	10/2015
936	2^827602+60409	249134	Enzo Doria	03/2016
937	10^249010+348861	249011	Patrick De Geest	04/2016
938	10^249010-21	249010	Serge Batalov	12/2014
939	2^826733+1882907	248872	Enzo Doria	12/2016
940	2^825682+1876549	248556	Enzo Doria	07/2016
941	2^824991-114121	248348	Enzo Doria	12/2014
942	2^824642-362727	248242	Enzo Doria	12/2013
943	2^824565-114265	248219	Enzo Doria	01/2015
944	(73*10^248145-1)/9	248146	Robert Price	01/2015
945	(2^823337+1)/(3*362268281)	247841	Gord Palameta	08/2018
946	(2^822971-1)/6583769/28211445881/21255852651726486149207	247700	Robert Kinser	09/2016
947	2^822296+76501	247536	Enzo Doria	05/2016
948	2^821590-114167	247324	Enzo Doria	12/2014
949	2^821512-2790659	247300	Enzo Doria	12/2015
950	2^820077+382847	246868	Enzo Doria	11/2016
951	2^820001+81269	246845	Enzo Doria	07/2016
952	2^819463-59197	246683	Enzo Doria	10/2015
953	2^819296+80581	246633	Enzo Doria	07/2016
954	2^817160-350369	245990	Enzo Doria	06/2015
955	2^816039-19	245653	Stefano Morozzi	07/2022
956	(71*10^245558-17)/9	245559	Serge Batalov	01/2023
957	88093#+(653879#)/(88093#)	245374	Makoto Morimoto	11/2017
958	2^815111-113857	245373	Enzo Doria	10/2014
959	2^814914-4001	245314	Yves Minet	05/2017
960	846^83761-845^83761	245200	Jean-Louis Charton	12/2012
961	2^814356-2790449	245146	Enzo Doria	12/2015
962	2^814276-459029	245122	Enzo Doria	04/2015
963	2^814023+180923	245046	Enzo Doria	07/2016
964	(3^513059-2^513059)/(1026119*5430216457)	244776	Mike Oakes	03/2017
965	3^513007+16	244767	Robert Price	04/2020
966	2^811842-113675	244389	Enzo Doria	09/2014
967	2^811132-2787929	244176	Enzo Doria	11/2015
968	2^809746-2790971	243758	Enzo Doria	01/2016
969	2^808767-3295	243464	Yves Minet	12/2016
970	2^808621-113809	243420	Enzo Doria	09/2014
971	2^807724+1879621	243150	Enzo Doria	09/2016
972	2*10^242822-91	242823	Robert Price	02/2023
973	20^186554-3	242713	Paul Bourdelais	12/2020
974	2^805843-113611	242583	Enzo Doria	08/2014
975	2^805745-459763	242554	Enzo Doria	05/2015
976	2^805353+782687	242436	Enzo Doria	11/2016
977	6^311257+5	242206	Paul Bourdelais	02/2021
978	2^804277-417933	242112	Enzo Doria	01/2014
979	2^803468-269039	241868	Enzo Doria	10/2013
980	2^803172+80851	241779	Enzo Doria	07/2016
981	3^506233-2	241535	Robert Price	11/2013
982	2^802025-25999	241434	Enzo Doria	10/2013
983	(3^505823+3^252912+1)/7	241339	Serge Batalov	03/2014
984	2^801303+1872923	241217	Enzo Doria	05/2016
985	2^800579-1862947	240999	Enzo Doria	12/2015
986	3^504206+2	240568	Luke W. Richards	03/2018
987	2^798973-26283	240515	Enzo Doria	10/2013
988	2^798671-69487	240424	Enzo Doria	12/2015
989	2^797220+79831	239988	Enzo Doria	06/2016
990	2^796910-26001	239894	Enzo Doria	10/2013
991	2^796598+653119	239800	Enzo Doria	12/2016
992	2^796432-1859729	239750	Enzo Doria	11/2015
993	2^796002-1852211	239621	Enzo Doria	08/2015
994	2^795709+75767	239533	Enzo Doria	04/2016
995	2^795708+81721	239532	Enzo Doria	08/2016
996	2^795468-2786249	239460	Enzo Doria	10/2015
997	2^795442+80779	239452	Enzo Doria	07/2016
998	2^795075-1852057	239342	Enzo Doria	08/2015
999	(86^123677+1)/87	239252	Paul Bourdelais	01/2019
1000	2^794043+1875023	239031	Enzo Doria	06/2016

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PRP Records

Probable Primes Top 10000

(292102 PRPs in the top)