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	2^983620+60451	296100	Phil Moore	03/2008
752	2^982721-2683	295829	Yves Minet	02/2016
753	(23*10^295581+7)/3	295582	Robert Price	05/2023
754	2^981298-2788421	295401	Enzo Doria	12/2015
755	2^981163-2790967	295360	Enzo Doria	12/2015
756	2^981016-15	295316	Stefano Morozzi	07/2022
757	8*10^295160-13	295161	Robert Price	08/2023
758	2^979594+1865839	294888	Enzo Doria	02/2016
759	2*10^294527-91	294528	Robert Price	02/2023
760	10^294475+49	294476	Robert Price	02/2023
761	(11*10^294308+91)/3	294309	Robert Price	03/2023
762	2^976760+1885021	294035	Enzo Doria	02/2017
763	3*2^976518+5	293962	Jon Grantham	07/2023
764	2^974441+1878407	293336	Enzo Doria	08/2016
765	2^974180+1876831	293258	Enzo Doria	07/2016
766	2^974170+453319	293255	Enzo Doria	01/2017
767	2^972744-114419	292826	Enzo Doria	03/2015
768	11^281143+6	292781	Paul Bourdelais	03/2021
769	(4*10^292619-91)/3	292620	Robert Price	12/2022
770	CopelandErdos(292447)	292447	Mark Rodenkirch	12/2015
771	3*10^292344-97	292345	Robert Price	01/2023
772	2^970911+1873373	292274	Enzo Doria	07/2016
773	2^970670+383059	292201	Enzo Doria	12/2016
774	2^970141-100363	292042	Enzo Doria	02/2014
775	2^969945+1874717	291983	Enzo Doria	06/2016
776	2^969384+1880701	291814	Enzo Doria	10/2016
777	(13*10^291721-43)/3	291722	Robert Price	08/2023
778	(3^611333-2^611333)/(99035947*87109884549431)	291659	Mike Oakes	02/2017
779	3*2^963892+5	290161	Jon Grantham	07/2023
780	(151*10^289877-1)/3	289879	Robert Price	07/2023
781	2^962194+60139	289650	Enzo Doria	02/2016
782	2^959307-1861507	288781	Enzo Doria	11/2015
783	(17*10^288692+31)/3	288693	Robert Price	04/2023
784	14^251797-3	288592	Paul Bourdelais	12/2020
785	(2*10^288371-23)/3	288371	Robert Price	10/2022
786	(31*10^288238-1)/3	288240	Robert Price	02/2023
787	(7^341063-2^341063)/5	288231	Jon Grantham	08/2023
788	2^957372+283531	288198	Enzo Doria	02/2017
789	2^957192-1864049	288144	Enzo Doria	01/2016
790	2^956446+1875199	287919	Enzo Doria	06/2016
791	7*10^287854+39	287855	Robert Price	01/2023
792	(17^233689+1)/18	287542	Paul Bourdelais	09/2013
793	2^955178+1883587	287538	Enzo Doria	12/2016
794	2^954127-954127^2	287221	Henri Lifchitz	01/2021
795	2^954001+1875257	287183	Enzo Doria	07/2016
796	2*10^287175-49	287176	Robert Price	05/2023
797	(22*10^287085-19)/3	287086	Robert Price	07/2023
798	2^953488+22411	287029	Enzo Doria	09/2023
799	(23891^65536+1)/2	286932	Serge Batalov	03/2018
800	5*3^601336-2^601336	286911	Jon Grantham	08/2023
801	2^952268+1878601	286662	Enzo Doria	09/2016
802	2^950801+81557	286220	Enzo Doria	08/2016
803	22845^65536+22844^65536	285658	Kellen Shenton	03/2021
804	(11*2^948635-13)/15	285568	Renaud Lifchitz	11/2011
805	(54^164839+1)/55	285565	Paul Bourdelais	07/2019
806	2^948510+782569	285530	Enzo Doria	10/2016
807	2^948374-114137	285490	Enzo Doria	01/2015
808	2^947739+1872923	285298	Enzo Doria	06/2016
809	7*10^284751+9	284752	Robert Price	04/2023
810	2^944561-21	284342	Stefano Morozzi	07/2022
811	(4*10^284330-31)/9	284330	Serge Batalov	11/2022
812	(32*10^283826-23)/9	283827	Serge Batalov	01/2023
813	2^942533+82067	283731	Enzo Doria	09/2016
814	2^941469+39	283411	Jon Grantham	08/2023
815	(10^283342-31)/3	283342	Robert Price	03/2023
816	2^940950+1874989	283255	Enzo Doria	06/2016
817	2^940426-2786141	283097	Enzo Doria	11/2015
818	(2*10^282948-11)/9	282948	Serge Batalov	11/2022
819	2^939881-114115	282933	Enzo Doria	12/2014
820	(14*10^282673-143)/3	282674	Robert Price	05/2023
821	10^282493+632551	282494	Patrick De Geest	02/2017
823	10^282493-9^282493	282493	Jean-Louis Charton	03/2007
822	10^282493-132327	282493	Patrick De Geest	02/2017
824	3^591827-2^591827	282374	Mike Oakes	08/2009
825	Tau(509^18946)	282048	Nik Lygeros / Olivier Rozier	05/2015
826	2^936716-1835519	281980	Enzo Doria	04/2015
827	2^936588+79411	281942	Enzo Doria	06/2016
828	2^936047+1877423	281779	Enzo Doria	08/2016
829	2^935713+1869377	281678	Enzo Doria	05/2016
830	2^933082+1877059	280886	Enzo Doria	08/2016
831	(5*10^280710+1)/3	280711	Serge Batalov	10/2014
832	2^931976+25	280553	Stefano Morozzi	05/2021
833	(42^172663+1)/43	280274	Paul Bourdelais	07/2019
834	(10^279978+11)/3	279978	Serge Batalov	07/2015
835	2^929524-1864829	279815	Enzo Doria	01/2016
836	2^929329+22697	279756	Enzo Doria	09/2023
837	2^929152+60181	279703	Enzo Doria	02/2016
838	2^928621-2787883	279543	Enzo Doria	11/2015
839	(2^927763+lucasV(-1,2,927763)+1)/2	279285	Mike Oakes	04/2017
840	2^927429+1882277	279184	Enzo Doria	12/2016
841	2^926766-11	278985	Stefano Morozzi	07/2022
842	(71^150697-1)/70	278978	Paul Bourdelais	07/2019
843	(33^183661-1)/32	278891	Paul Bourdelais	12/2018
844	(166*10^278633-7)/3	278635	Robert Price	02/2023
845	(2^925391+lucasV(-1,2,925391)+1)/2	278571	Mike Oakes	03/2017
846	2^925330-1301	278553	Yves Minet	06/2015
847	(299*10^278546+1)/3	278548	Robert Price	01/2023
848	(21^210599+1)/22	278457	Paul Bourdelais	08/2013
849	(266*10^278325+1)/3	278327	Robert Price	01/2023
850	2^923261-69175	277930	Enzo Doria	11/2015
851	757^96487-756^96487	277796	Jean-Louis Charton	12/2012
852	2^922301+57	277641	Stefano Morozzi	05/2021
853	7*10^277478-39	277479	Robert Price	07/2023
854	((((((((((((((291487327^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2	277369	Serge Batalov	07/2016
855	(5^396413-1)/4	277081	Paul Bourdelais	06/2010
856	2^920318+2792299	277044	Enzo Doria	02/2016
857	(16*10^276537-31)/3	276538	Robert Price	03/2023
858	2^918596-2786939	276525	Enzo Doria	11/2015
859	2^916639+60563	275936	Enzo Doria	04/2016
860	(2*10^275922+1)/3	275922	Serge Batalov	11/2022
861	2^916385-2786383	275860	Enzo Doria	11/2015
862	2^915928+82081	275722	Enzo Doria	09/2016
863	(4*10^275671+11)/3	275672	Tyler Busby	02/2023
864	2^915576-114137	275616	Enzo Doria	01/2015
865	2^914828+1876741	275391	Enzo Doria	07/2016
866	2^914757-2203	275370	Yves Minet	12/2015
867	7*10^275157-27	275158	Robert Price	11/2022
868	2^912744+20011	274764	Enzo Doria	06/2023
869	2^911900+1871245	274510	Enzo Doria	05/2016
870	(16*10^274251-91)/3	274252	Robert Price	11/2022
871	2^910999+9	274239	Stefano Morozzi	05/2021
872	(2^910869-7)/5	274199	Stefano Morozzi	08/2022
873	2^910490+283429	274085	Enzo Doria	01/2017
874	7*10^273983+39	273984	Robert Price	01/2023
875	2^909988-1862249	273934	Enzo Doria	12/2015
876	2^909297+1879157	273726	Enzo Doria	08/2016
877	2^909257-1864423	273714	Enzo Doria	01/2016
878	2^908739-7	273558	Stefano Morozzi	07/2022
879	2^908579-1861747	273510	Enzo Doria	12/2015
880	3*2^908005-5	273338	Jon Grantham	07/2023
881	2^907635-2791597	273226	Enzo Doria	01/2016
882	2^907059+211193	273052	Enzo Doria	08/2023
883	(53^158341+1)/54	273022	Paul Bourdelais	07/2019
884	2^906594-113201	272912	Enzo Doria	08/2014
885	9*10^272800+91	272801	Robert Price	05/2023
886	2*10^272710-49	272711	Robert Price	05/2023
887	2*10^272403-91	272404	Robert Price	02/2023
888	2^904773+1872167	272364	Enzo Doria	06/2016
889	6^349903+5	272278	Paul Bourdelais	02/2021
890	2^904149-1862473	272176	Enzo Doria	12/2015
891	(7*10^271757-61)/9	271757	Erik Branger	03/2012
892	2^902497+1880117	271679	Enzo Doria	09/2016
893	2^901858+77689	271487	Enzo Doria	06/2016
894	2^901372+1875301	271341	Enzo Doria	06/2016
895	(8*10^271039-77)/3	271040	Robert Price	04/2023
896	2^899999+1144031	270927	Norman Luhn	09/2023
897	2*10^270802-91	270803	Robert Price	02/2023
898	23*10^270799-7	270801	Robert Price	10/2022
899	2^899121-115033	270663	Enzo Doria	07/2015
900	2^898900+883021	270596	Enzo Doria	12/2016
901	2^898762-251511	270555	Enzo Doria	12/2013
902	2^898589+47	270503	Lelio R Paula	03/2016
903	187322*10^270343-187321	270349	Danilo Nitsche	09/2013
904	48358*10^270343-48357	270348	Danilo Nitsche	09/2013
905	(10^270343-1)/9	270343	Maksym Voznyy	07/2007
906	2^897867-3217	270285	Yves Minet	12/2016
907	2^897849-115273	270280	Enzo Doria	07/2015
908	2^896616-114179	269909	Enzo Doria	12/2014
909	(22*10^269517-19)/3	269518	Robert Price	07/2023
910	10^(2134739+1)-710^134739-1	269479	Robert Price	07/2023
911	2^894928+583561	269401	Enzo Doria	04/2017
912	2^894673-39343	269324	Enzo Doria	08/2015
913	F(1285607)	268676	Henri Lifchitz	11/2008
914	2^892234+22189	268590	Enzo Doria	09/2023
915	2^892112+187663	268553	Enzo Doria	08/2016
916	(266*10^268407-17)/3	268409	Robert Price	02/2023
917	(10^268207+1)/11	268206	Paul Bourdelais	02/2010
918	2^890957-69583	268205	Enzo Doria	12/2015
919	32841!^2+32840!^2+...+2!^2+1!^2	268128	Serge Batalov	07/2017
920	2^890122-351401	267954	Enzo Doria	07/2015
921	(19^209359-1)/18	267718	Paul Bourdelais	08/2010
922	(85^138647+1)/86	267507	Paul Bourdelais	07/2019
923	(485^99523-1)/484	267291	Michael Stocker	05/2020
924	2^886324+77791	266811	Enzo Doria	06/2016
925	7*10^266731+87	266732	Robert Price	11/2022
926	2^884714+1880527	266326	Enzo Doria	10/2016
927	7*10^266024-47	266025	Robert Price	08/2023
928	11^255426+255426^11	265999	Serge Batalov	05/2014
929	2^883462-343421	265949	Enzo Doria	07/2015
930	2^883442+1875019	265943	Enzo Doria	06/2016
931	2^883333-291583	265910	Enzo Doria	07/2015
932	10^265566+3593037	265567	Paul Bourdelais	08/2023
933	(2*10^265321-17)/3	265321	Serge Batalov	11/2022
934	(16*10^265052-91)/3	265053	Robert Price	11/2022
935	2^880411+1882673	265031	Enzo Doria	12/2016
936	(14*10^264791-11)/3	264792	Robert Price	08/2022
937	2^879530-2788031	264765	Enzo Doria	12/2015
938	(2*10^264539+61)/9	264539	Serge Batalov	11/2022
939	2^878118+2793079	264340	Enzo Doria	02/2016
940	(2^878073-7)/5	264326	Stefano Morozzi	08/2022
941	(37^168527-1)/36	264283	Paul Bourdelais	08/2019
942	5^377865+3^377865-1	264117	Jon Grantham	08/2023
943	(19*10^263971+131)/3	263972	Robert Price	08/2023
944	2^876202-17	263764	Stefano Morozzi	07/2022
945	(14*10^263720-11)/3	263721	Robert Price	08/2022
946	2^875748-461129	263627	Enzo Doria	07/2015
947	2^875518-15	263558	Stefano Morozzi	07/2022
948	(29*10^263523-17)/3	263524	Robert Price	01/2023
949	2^875181-2789923	263456	Enzo Doria	12/2015
950	2^875101-350083	263432	Enzo Doria	08/2015
951	2^874684+1883587	263307	Enzo Doria	01/2017
952	2^874616+1872211	263286	Enzo Doria	05/2016
953	3^551491+16	263129	Robert Price	04/2020
954	2^874073+2792957	263123	Enzo Doria	02/2016
955	2^873628+1878751	262989	Enzo Doria	08/2016
956	2^873497+20837	262949	Enzo Doria	08/2023
957	2^873288-269	262886	Yves Minet	01/2015
958	(2*10^262874+7)/9	262874	Rytis Slatkevicius	01/2023
959	(28*10^262655-43)/3	262656	Robert Price	04/2023
960	(2*10^262603-11)/9	262603	Serge Batalov	11/2022
961	2^871991-4207	262496	Yves Minet	03/2021
962	(23*10^262324+7)/3	262325	Robert Price	05/2023
963	2^871146-3173	262242	Yves Minet	07/2016
964	2^869601-163	261776	Yves Minet	01/2015
965	(2*10^261704+61)/9	261704	Serge Batalov	11/2022
966	2^869326+282859	261694	Enzo Doria	11/2016
967	2^869035-114181	261606	Enzo Doria	12/2014
968	4*10^261248+91	261249	Robert Price	11/2022
969	2^865715+80303	260607	Enzo Doria	07/2016
970	2^865048+1882411	260406	Enzo Doria	12/2016
971	2^864899-113871	260361	Enzo Doria	10/2014
972	(16*10^260256-91)/3	260257	Robert Price	11/2022
973	(7*10^260198-61)/9	260198	Erik Branger	11/2011
974	2^864298-2788421	260180	Enzo Doria	12/2015
975	2^864039-2791357	260102	Enzo Doria	01/2016
976	2^863621-113833	259976	Enzo Doria	10/2014
977	10^259945-11	259945	Mischa Rodermond	04/2023
978	(28*10^259897+113)/3	259898	Robert Price	06/2023
979	2^862837+75767	259740	Enzo Doria	05/2016
980	2^862637-31	259680	Jorge Menendez	05/2019
981	2^862088+1874941	259515	Enzo Doria	06/2016
982	2^861987-134557	259484	Hans Havermann	10/2018
983	(14*10^259431-143)/3	259432	Robert Price	05/2023
984	2^861516-1854029	259343	Enzo Doria	09/2015
985	2^860975-1853977	259180	Enzo Doria	09/2015
986	3^543128+16	259138	Robert Price	04/2020
987	2^860625-1858843	259074	Enzo Doria	10/2015
988	2^860110+77689	258919	Enzo Doria	05/2016
989	2^859600+1880371	258766	Enzo Doria	10/2016
990	2^859433+494711	258716	Makoto Morimoto	10/2013
991	(2^859433-44)/(2^2*3)	258715	Makoto Morimoto	08/2019
992	(2^859431-11)/3	258715	Stefano Morozzi	08/2022
993	(13*10^258710-43)/3	258711	Robert Price	08/2023
994	(2^859433+39899)/(73390746301)	258705	Makoto Morimoto	10/2016
995	2^859240+1875271	258658	Enzo Doria	06/2016
996	Tau(971^15738)	258571	Nik Lygeros / Olivier Rozier	05/2015
997	(23*10^258494-47)/3	258495	Robert Price	09/2023
998	(144^119671+1)/145	258292	Paul Bourdelais	08/2019
999	2^857608+105	258166	Stefano Morozzi	05/2021
1000	(11*2^857159-13)/15	258031	Renaud Lifchitz	08/2011

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Probable Primes Top 10000

(293510 PRPs in the top)