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) !!!

Submit your PRPs

See the Top discoverers
See the Latest PRPs
Search by form


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	(53^158341+1)/54	273022	Paul Bourdelais	07/2019
752	2^906594-113201	272912	Enzo Doria	08/2014
753	2^904773+1872167	272364	Enzo Doria	06/2016
754	6^349903+5	272278	Paul Bourdelais	02/2021
755	2^904149-1862473	272176	Enzo Doria	12/2015
756	(7*10^271757-61)/9	271757	Erik Branger	03/2012
757	2^902497+1880117	271679	Enzo Doria	09/2016
758	2^901858+77689	271487	Enzo Doria	06/2016
759	2^901372+1875301	271341	Enzo Doria	06/2016
760	23*10^270799-7	270801	Robert Price	10/2022
761	2^899121-115033	270663	Enzo Doria	07/2015
762	2^898900+883021	270596	Enzo Doria	12/2016
763	2^898762-251511	270555	Enzo Doria	12/2013
764	2^898589+47	270503	Lelio R Paula	03/2016
765	187322*10^270343-187321	270349	Danilo Nitsche	09/2013
766	48358*10^270343-48357	270348	Danilo Nitsche	09/2013
767	(10^270343-1)/9	270343	Maksym Voznyy	07/2007
768	2^897867-3217	270285	Yves Minet	12/2016
769	2^897849-115273	270280	Enzo Doria	07/2015
770	2^896616-114179	269909	Enzo Doria	12/2014
771	2^894928+583561	269401	Enzo Doria	04/2017
772	2^894673-39343	269324	Enzo Doria	08/2015
773	F(1285607)	268676	Henri Lifchitz	11/2008
774	2^892112+187663	268553	Enzo Doria	08/2016
775	(10^268207+1)/11	268206	Paul Bourdelais	02/2010
776	2^890957-69583	268205	Enzo Doria	12/2015
777	32841!^2+32840!^2+...+2!^2+1!^2	268128	Serge Batalov	07/2017
778	2^890122-351401	267954	Enzo Doria	07/2015
779	(19^209359-1)/18	267718	Paul Bourdelais	08/2010
780	(85^138647+1)/86	267507	Paul Bourdelais	07/2019
781	(485^99523-1)/484	267291	Michael Stocker	05/2020
782	2^886324+77791	266811	Enzo Doria	06/2016
783	7*10^266731+87	266732	Robert Price	11/2022
784	2^884714+1880527	266326	Enzo Doria	10/2016
785	11^255426+255426^11	265999	Serge Batalov	05/2014
786	2^883462-343421	265949	Enzo Doria	07/2015
787	2^883442+1875019	265943	Enzo Doria	06/2016
788	2^883333-291583	265910	Enzo Doria	07/2015
789	(2*10^265321-17)/3	265321	Serge Batalov	11/2022
790	(16*10^265052-91)/3	265053	Robert Price	11/2022
791	2^880411+1882673	265031	Enzo Doria	12/2016
792	(14*10^264791-11)/3	264792	Robert Price	08/2022
793	2^879530-2788031	264765	Enzo Doria	12/2015
794	(2*10^264539+61)/9	264539	Serge Batalov	11/2022
795	2^878118+2793079	264340	Enzo Doria	02/2016
796	(2^878073-7)/5	264326	Stefano Morozzi	08/2022
797	(37^168527-1)/36	264283	Paul Bourdelais	08/2019
798	2^876202-17	263764	Stefano Morozzi	07/2022
799	(14*10^263720-11)/3	263721	Robert Price	08/2022
800	2^875748-461129	263627	Enzo Doria	07/2015
801	2^875518-15	263558	Stefano Morozzi	07/2022
802	(29*10^263523-17)/3	263524	Robert Price	01/2023
803	2^875181-2789923	263456	Enzo Doria	12/2015
804	2^875101-350083	263432	Enzo Doria	08/2015
805	2^874684+1883587	263307	Enzo Doria	01/2017
806	2^874616+1872211	263286	Enzo Doria	05/2016
807	3^551491+16	263129	Robert Price	04/2020
808	2^874073+2792957	263123	Enzo Doria	02/2016
809	2^873628+1878751	262989	Enzo Doria	08/2016
810	2^873288-269	262886	Yves Minet	01/2015
811	(2*10^262874+7)/9	262874	Rytis Slatkevicius	01/2023
812	(2*10^262603-11)/9	262603	Serge Batalov	11/2022
813	2^871991-4207	262496	Yves Minet	03/2021
814	2^871146-3173	262242	Yves Minet	07/2016
815	2^869601-163	261776	Yves Minet	01/2015
816	(2*10^261704+61)/9	261704	Serge Batalov	11/2022
817	2^869326+282859	261694	Enzo Doria	11/2016
818	2^869035-114181	261606	Enzo Doria	12/2014
819	4*10^261248+91	261249	Robert Price	11/2022
820	2^865715+80303	260607	Enzo Doria	07/2016
821	2^865048+1882411	260406	Enzo Doria	12/2016
822	2^864899-113871	260361	Enzo Doria	10/2014
823	(16*10^260256-91)/3	260257	Robert Price	11/2022
824	(7*10^260198-61)/9	260198	Erik Branger	11/2011
825	2^864298-2788421	260180	Enzo Doria	12/2015
826	2^864039-2791357	260102	Enzo Doria	01/2016
827	2^863621-113833	259976	Enzo Doria	10/2014
828	2^862837+75767	259740	Enzo Doria	05/2016
829	2^862637-31	259680	Jorge Menendez	05/2019
830	2^862088+1874941	259515	Enzo Doria	06/2016
831	2^861987-134557	259484	Hans Havermann	10/2018
832	2^861516-1854029	259343	Enzo Doria	09/2015
833	2^860975-1853977	259180	Enzo Doria	09/2015
834	3^543128+16	259138	Robert Price	04/2020
835	2^860625-1858843	259074	Enzo Doria	10/2015
836	2^860110+77689	258919	Enzo Doria	05/2016
837	2^859600+1880371	258766	Enzo Doria	10/2016
838	2^859433+494711	258716	Makoto Morimoto	10/2013
839	(2^859433-44)/(2^2*3)	258715	Makoto Morimoto	08/2019
840	(2^859431-11)/3	258715	Stefano Morozzi	08/2022
841	(2^859433+39899)/(73390746301)	258705	Makoto Morimoto	10/2016
842	2^859240+1875271	258658	Enzo Doria	06/2016
843	Tau(971^15738)	258571	Nik Lygeros / Olivier Rozier	05/2015
844	(144^119671+1)/145	258292	Paul Bourdelais	08/2019
845	2^857608+105	258166	Stefano Morozzi	05/2021
846	(11*2^857159-13)/15	258031	Renaud Lifchitz	08/2011
847	2^857016-633113	257988	Enzo Doria	12/2013
848	2^855732-113969	257602	Enzo Doria	10/2014
849	2^853682-3911	256984	Enzo Doria	05/2014
850	11^246668-90	256879	Enzo Doria	12/2012
851	2^851904-113939	256449	Enzo Doria	10/2014
852	2^851725-851725^2	256395	Henri Lifchitz	03/2019
853	11^246167-90	256357	Enzo Doria	12/2012
854	(85*10^256301-1)/3	256303	Robert Price	12/2022
855	(10^256187+7)/63443/148782853	256175	Alfred Reich	10/2021
856	2^850700-569049	256087	Enzo Doria	11/2013
857	2^850675+153	256079	Stefano Morozzi	05/2021
858	21^193601-20^193601	255983	Jean-Louis Charton	02/2015
859	(37^163193+1)/38	255918	Paul Bourdelais	07/2019
860	(14*10^255805-83)/3	255806	Robert Price	11/2022
861	2^849177-114025	255628	Enzo Doria	12/2014
862	2^848502-3173	255425	Yves Minet	07/2016
863	2^848178-140291	255328	Enzo Doria	01/2014
864	7*10^255167+87	255168	Robert Price	11/2022
865	2^847622-2441	255160	Yves Minet	02/2016
866	2^847291+182843	255061	Enzo Doria	11/2016
867	2^847174+1879429	255025	Enzo Doria	09/2016
868	24*29^174239+13361	254809	Curtis Bright	04/2015
869	22*10^254639+7	254641	Robert Price	10/2022
870	2^845633-933075	254561	Paul Bourdelais	11/2021
871	2^845610-1868591	254554	Enzo Doria	04/2016
872	2^845484+81931	254517	Enzo Doria	08/2016
873	2^845402-114761	254492	Enzo Doria	05/2015
874	2^844334-2792441	254170	Enzo Doria	02/2016
875	11^243796-90	253888	Enzo Doria	12/2012
876	(10^253891+7)/44777/79843/16940711	253875	Alfred Reich	10/2021
877	30^171733-29^171733	253671	Jean-Louis Charton	10/2018
878	2^842209+1876037	253531	Enzo Doria	07/2016
879	2^842123-59197	253505	Enzo Doria	10/2015
880	(8*10^253313-53)/9	253313	Serge Batalov	11/2022
881	2^840797-3	253106	Paul Bourdelais	06/2019
882	2^840716-2969	253081	Yves Minet	05/2016
883	2^840358-462491	252973	Enzo Doria	08/2015
884	2^840310+1878379	252959	Enzo Doria	08/2016
885	2^840203-21	252927	Stefano Morozzi	07/2022
886	11^242579-60	252620	Enzo Doria	10/2012
887	45^152659+2	252378	Robert Price	09/2015
888	(95^127583+1)/96	252322	Paul Bourdelais	07/2019
889	7*10^252209-17	252210	Robert Price	12/2022
890	2^837725+1869377	252181	Enzo Doria	05/2016
891	2^837536-311039	252124	Enzo Doria	06/2015
892	21^190632-2	252058	Robert Price	07/2015
893	2^837242+1873297	252035	Enzo Doria	06/2016
894	2^836656-2787929	251859	Enzo Doria	11/2015
895	2^836380+1875541	251776	Enzo Doria	07/2016
896	(359^98327-1)/358	251233	Alexander Zhirkov	11/2017
897	tau(41^28288)	250924	Nik Lygeros / Olivier Rozier	10/2013
898	2^832511-461197	250611	Enzo Doria	07/2015
899	2^832505+1881137	250609	Enzo Doria	11/2016
900	2^832363+583295	250567	Enzo Doria	12/2016
901	2^832244-403635	250531	Enzo Doria	01/2014
902	(14*10^250336-41)/9	250337	Serge Batalov	01/2023
903	2^831157+1880657	250204	Enzo Doria	11/2016
904	2^831088-7200899	250183	Enzo Doria	01/2015
905	2^830956-1349	250143	Yves Minet	07/2015
906	2^830037+282317	249867	Enzo Doria	09/2016
907	2^829589-113653	249732	Enzo Doria	09/2014
908	(4*10^249550-7)/3	249551	Serge Batalov	01/2023
909	2^828281-3193	249338	Yves Minet	08/2016
910	(2^828140-19)/3	249295	Stefano Morozzi	08/2022
911	2^828064-2785619	249273	Enzo Doria	10/2015
912	2^827602+60409	249134	Enzo Doria	03/2016
913	10^249010+348861	249011	Patrick De Geest	04/2016
914	10^249010-21	249010	Serge Batalov	12/2014
915	2^826733+1882907	248872	Enzo Doria	12/2016
916	2^825682+1876549	248556	Enzo Doria	07/2016
917	2^824991-114121	248348	Enzo Doria	12/2014
918	2^824642-362727	248242	Enzo Doria	12/2013
919	2^824565-114265	248219	Enzo Doria	01/2015
920	(73*10^248145-1)/9	248146	Robert Price	01/2015
921	(2^823337+1)/(3*362268281)	247841	Gord Palameta	08/2018
922	(2^822971-1)/6583769/28211445881/21255852651726486149207	247700	Robert Kinser	09/2016
923	2^822296+76501	247536	Enzo Doria	05/2016
924	2^821590-114167	247324	Enzo Doria	12/2014
925	2^821512-2790659	247300	Enzo Doria	12/2015
926	2^820077+382847	246868	Enzo Doria	11/2016
927	2^820001+81269	246845	Enzo Doria	07/2016
928	2^819463-59197	246683	Enzo Doria	10/2015
929	2^819296+80581	246633	Enzo Doria	07/2016
930	2^817160-350369	245990	Enzo Doria	06/2015
931	2^816039-19	245653	Stefano Morozzi	07/2022
932	(71*10^245558-17)/9	245559	Serge Batalov	01/2023
933	88093#+(653879#)/(88093#)	245374	Makoto Morimoto	11/2017
934	2^815111-113857	245373	Enzo Doria	10/2014
935	2^814914-4001	245314	Yves Minet	05/2017
936	846^83761-845^83761	245200	Jean-Louis Charton	12/2012
937	2^814356-2790449	245146	Enzo Doria	12/2015
938	2^814276-459029	245122	Enzo Doria	04/2015
939	2^814023+180923	245046	Enzo Doria	07/2016
940	(3^513059-2^513059)/(1026119*5430216457)	244776	Mike Oakes	03/2017
941	3^513007+16	244767	Robert Price	04/2020
942	2^811842-113675	244389	Enzo Doria	09/2014
943	2^811132-2787929	244176	Enzo Doria	11/2015
944	2^809746-2790971	243758	Enzo Doria	01/2016
945	2^808767-3295	243464	Yves Minet	12/2016
946	2^808621-113809	243420	Enzo Doria	09/2014
947	2^807724+1879621	243150	Enzo Doria	09/2016
948	20^186554-3	242713	Paul Bourdelais	12/2020
949	2^805843-113611	242583	Enzo Doria	08/2014
950	2^805745-459763	242554	Enzo Doria	05/2015
951	2^805353+782687	242436	Enzo Doria	11/2016
952	6^311257+5	242206	Paul Bourdelais	02/2021
953	2^804277-417933	242112	Enzo Doria	01/2014
954	2^803468-269039	241868	Enzo Doria	10/2013
955	2^803172+80851	241779	Enzo Doria	07/2016
956	3^506233-2	241535	Robert Price	11/2013
957	2^802025-25999	241434	Enzo Doria	10/2013
958	(3^505823+3^252912+1)/7	241339	Serge Batalov	03/2014
959	2^801303+1872923	241217	Enzo Doria	05/2016
960	2^800579-1862947	240999	Enzo Doria	12/2015
961	3^504206+2	240568	Luke W. Richards	03/2018
962	2^798973-26283	240515	Enzo Doria	10/2013
963	2^798671-69487	240424	Enzo Doria	12/2015
964	2^797220+79831	239988	Enzo Doria	06/2016
965	2^796910-26001	239894	Enzo Doria	10/2013
966	2^796598+653119	239800	Enzo Doria	12/2016
967	2^796432-1859729	239750	Enzo Doria	11/2015
968	2^796002-1852211	239621	Enzo Doria	08/2015
969	2^795709+75767	239533	Enzo Doria	04/2016
970	2^795708+81721	239532	Enzo Doria	08/2016
971	2^795468-2786249	239460	Enzo Doria	10/2015
972	2^795442+80779	239452	Enzo Doria	07/2016
973	2^795075-1852057	239342	Enzo Doria	08/2015
974	(86^123677+1)/87	239252	Paul Bourdelais	01/2019
975	2^794043+1875023	239031	Enzo Doria	06/2016
976	2^793347-69577	238822	Enzo Doria	01/2016
977	2^792988-344429	238714	Enzo Doria	08/2015
978	2^792700-2786369	238627	Enzo Doria	11/2015
979	2^792663-1844797	238616	Enzo Doria	06/2015
980	2^792605-291943	238598	Enzo Doria	07/2015
981	(2^792061-2^396031+1)/5	238434	Thomas Ritschel	03/2014
982	4*10^238163+21	238164	Robert Price	12/2022
983	2^789373+1869377	237625	Enzo Doria	05/2016
984	((10^59387+1)^3(10^59387+1+10^29694)-(10^118774+10^59387)(10^29694-1)+10^178161)/27961	237544	Serge Batalov	04/2015
985	2^788942+1866409	237496	Enzo Doria	02/2016
986	2^788844-114329	237466	Enzo Doria	01/2015
987	2^788705-1859713	237424	Enzo Doria	11/2015
988	2^786180+1871971	236664	Enzo Doria	05/2016
989	11^227092-90	236492	Enzo Doria	11/2012
990	2^785260+1866361	236387	Enzo Doria	02/2016
991	2^785220+1880611	236375	Enzo Doria	10/2016
992	(2^784689-15)/7	236215	Stefano Morozzi	08/2022
993	19^184650-2	236122	Robert Price	10/2014
994	10^236059+216513	236060	Patrick De Geest	04/2016
995	10^236059-20909	236059	Robert Price	09/2015
996	2^783893-21	235976	Stefano Morozzi	07/2022
997	(87^121487-1)/86	235625	Paul Bourdelais	12/2018
998	2^782634-113981	235597	Enzo Doria	11/2014
999	2^782423+1879733	235533	Enzo Doria	09/2016
1000	2^781682-2789543	235310	Enzo Doria	12/2015

Find by discoverer :

PRP Records

Probable Primes Top 10000

(291910 PRPs in the top)