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	(19*10^353884-91)/9	353885	Alfred Reich	02/2023
752	(10^353884*19-91)/9	353885	Alfred Reich	10/2023
753	20^271951+3	353817	Paul Bourdelais	01/2021
754	72722^72722+7^7	353551	Serge Batalov	04/2024
755	2^1173095+21	353137	Stefano Morozzi	10/2022
756	2^1170959+218945	352494	Enzo Doria	03/2024
757	(63^195893-1)/62	352477	Paul Bourdelais	08/2020
758	2^1170331+27293	352305	Enzo Doria	01/2024
759	2^1170326+7	352304	Stefano Morozzi	10/2022
760	numbpart(100000135540)	352269	Serge Batalov	04/2017
761	(10^352237-1)/9/10567111/950335427	352221	Maksym Voznyy	01/2015
762	5*3^737931-2^737931	352084	Jon Grantham	08/2023
763	2^1168851+223613	351860	Enzo Doria	06/2024
764	2^1168554+783529	351770	Enzo Doria	01/2017
765	(2^1168183-1)/54763676838381762583	351639	Matthias Wurtinger	01/2011
766	2^1166950+30409	351287	Enzo Doria	03/2024
767	2^1166563+223103	351171	Enzo Doria	05/2024
768	2^1166152+1882411	351047	Enzo Doria	12/2016
769	2^1163972+20971	350391	Enzo Doria	08/2023
770	2^1163272+22411	350180	Enzo Doria	10/2023
771	10^350071+7	350072	Alfred Reich	05/2021
772	2^1162154+1890207	349844	Enzo Doria	08/2017
773	(7*10^348724-61)/9	348724	Erik Branger	09/2016
774	(4*10^348453+41)/9	348453	Serge Batalov	11/2022
775	(127^165601-1)/126	348390	Alexander Zhirkov	09/2015
776	2^1155085+213377	347716	Enzo Doria	09/2023
777	2^1153083+1883693	347113	Enzo Doria	04/2017
778	(2^1148729+2^574365+1)/5	345802	Borys Jaworski	03/2007
779	2^1145882+80779	344945	Enzo Doria	09/2016
780	2^1143425+221177	344206	Enzo Doria	03/2024
781	2^1141813+27047	343720	Enzo Doria	12/2023
782	2^1141114+221869	343510	Enzo Doria	04/2024
783	2^1138296+27541	342662	Enzo Doria	01/2024
784	2^1136462+1887289	342110	Enzo Doria	05/2017
785	F(1636007)	341905	Henri Lifchitz	03/2009
786	(2^1135567+13)/3	341840	Stefano Morozzi	09/2022
787	2^1134873+223637	341631	Enzo Doria	06/2024
788	2^1133678+782569	341272	Enzo Doria	11/2016
789	(11^327001+1)/12	340536	Paul Bourdelais	09/2013
790	2^1129965+223667	340154	Enzo Doria	06/2024
791	2^1129361+221597	339972	Enzo Doria	04/2024
792	2^1128621+25919	339749	Enzo Doria	12/2023
793	(2^1127239+2^563620+1)/5	339333	Borys Jaworski	11/2006
794	Tau(907^20848)	339132	Nik Lygeros / Olivier Rozier	01/2016
795	2^1126380-3	339075	Paul Bourdelais	06/2019
796	2^1125784+24331	338895	Enzo Doria	10/2023
797	2^1125446+1885099	338794	Enzo Doria	08/2017
798	(63^188147+1)/64	338539	Paul Bourdelais	12/2020
799	2^1124549+143807	338523	Enzo Doria	10/2016
800	(4*10^338476+23)/9	338476	Serge Batalov	11/2022
801	2^1121187+1886783	337511	Enzo Doria	04/2017
802	(48^200443-1)/47	336992	Paul Bourdelais	08/2020
803	(2*10^336405+43)/9	336405	Rytis Slatkevicius	01/2023
804	(94^170371-1)/93	336162	Paul Bourdelais	09/2020
805	2^1116184+1883521	336005	Enzo Doria	02/2017
806	2^1115727+27683	335868	Enzo Doria	01/2024
807	2^1114974+28759	335641	Enzo Doria	02/2024
808	2^1114517+1880087	335504	Enzo Doria	10/2016
809	(5*10^335480+31)/9	335480	Serge Batalov	11/2022
810	5*3^701688+2^701688	334791	Jon Grantham	08/2023
811	(101^166849+1)/102	334418	Paul Bourdelais	12/2020
812	(3^700897+1)/4	334413	Paul Bourdelais	04/2010
813	2^1109200+223201	333903	Enzo Doria	05/2024
814	2^1108463+32513	333681	Enzo Doria	05/2024
815	2^1104500+22411	332488	Enzo Doria	10/2023
816	2^1104408-114539	332460	Enzo Doria	03/2015
817	2^1101921+82085	331712	Enzo Doria	10/2016
818	2^1101895+29963	331704	Enzo Doria	03/2024
819	2^1101167-1101167^2	331485	Henri Lifchitz	07/2024
820	2^1101091+224153	331462	Enzo Doria	06/2024
821	2^1100655+683513	331331	Enzo Doria	01/2017
822	(10^330906+71)/9	330906	Serge Batalov	07/2015
823	2^1098346+482899	330636	Enzo Doria	11/2016
824	(2^1096212+19)/5	329992	Stefano Morozzi	09/2022
825	2^1095679+1878713	329833	Enzo Doria	09/2016
826	2^1094874+27499	329590	Enzo Doria	01/2024
827	2^1094740-1851539	329550	Enzo Doria	08/2015
828	2^1092242+19	328798	Stefano Morozzi	10/2022
829	2^1091469-379369	328565	Enzo Doria	03/2014
830	2^1090801+24227	328364	Enzo Doria	10/2023
831	(69^178093-1)/68	327485	Paul Bourdelais	08/2020
832	(10^326884+7)/421	326882	Alfred Reich	12/2021
833	2^1085750+582349	326844	Enzo Doria	11/2016
834	(54308^69169-1)/(54308^263-1)	326261	Ryan Propper	11/2023
835	2^1083596+483061	326195	Enzo Doria	12/2016
836	(2^541456-1)*10^162995+2^541455-1	325990	paolo galliani	01/2019
837	2^1082908+583561	325988	Enzo Doria	05/2017
838	30^220411-29^220411	325574	Jean-Louis Charton	10/2018
839	2^1081308+7	325507	Stefano Morozzi	10/2022
840	2^1080032+25171	325123	Enzo Doria	11/2023
841	2^1078242+1881649	324584	Enzo Doria	11/2016
842	2^1077737+1880117	324432	Enzo Doria	10/2016
843	3^679017-5*2^679017	323974	Jon Grantham	08/2023
844	2^1076006+29539	323911	Enzo Doria	03/2024
845	2^1075573+32417	323780	Enzo Doria	05/2024
846	2^1075425+1880117	323736	Enzo Doria	10/2016
847	(28^223381+1)/29	323267	Paul Bourdelais	12/2020
848	10^322999+187071	323000	Stefano Morozzi	03/2019
849	10^322999-143151	322999	Patrick De Geest	05/2020
850	2^1072744+32641	322929	Enzo Doria	05/2024
851	2^1072146+1886869	322749	Enzo Doria	04/2017
852	2^1072118-7321953	322740	Enzo Doria	02/2015
853	2^1071026+1886869	322411	Enzo Doria	04/2017
854	2^1070539+1880633	322265	Enzo Doria	10/2016
855	2^1069788+26587	322039	Enzo Doria	12/2023
856	2^1069293-1147195	321890	Enzo Doria	05/2015
857	2^1065968+1880941	320889	Enzo Doria	10/2016
858	2^1065897-1147195	320867	Enzo Doria	05/2015
859	2^1063427+1882103	320124	Enzo Doria	12/2016
860	2^1061095-1061095	319422	Henri Lifchitz	10/2013
861	2^1060950+653119	319378	Enzo Doria	12/2016
862	2^1060363+782753	319202	Enzo Doria	11/2016
863	2^1060028+31771	319101	Enzo Doria	04/2024
864	(71^172259-1)/70	318895	Paul Bourdelais	08/2020
865	-30*Bern(85996)/236037521	318354	Sergey Batalov	10/2023
866	2^1055665+30407	317787	Enzo Doria	03/2024
867	2^1054736+483061	317508	Enzo Doria	12/2016
868	2^1053965+1879667	317276	Enzo Doria	10/2016
869	(43^194119-1)/42	317086	Paul Bourdelais	08/2020
870	2^1052186-458165	316740	Enzo Doria	03/2015
871	11^303909+2	316489	Paul Bourdelais	08/2023
872	2^1049026+214609	315789	Enzo Doria	11/2023
873	2^1046613-114685	315062	Enzo Doria	04/2015
874	2^1045625-459373	314765	Enzo Doria	06/2015
875	10^(2157363+1)-810^157363-1	314727	Robert Price	07/2023
876	(7*10^314564-61)/9	314564	Erik Branger	09/2016
877	2^1044206+7	314338	Stefano Morozzi	10/2022
878	(7^371669-1)/6	314096	Paul Bourdelais	02/2010
879	(53^181981-1)/52	313784	Paul Bourdelais	08/2020
880	(8^347437-5^347437)/3	313767	Jon Grantham	08/2023
881	(10^313741+1)/11/11294677	313733	Alfred Reich	04/2024
882	2^1041944+283051	313657	Enzo Doria	12/2016
883	(1624^97969-1)/(1624^313-1)	313533	Sergey Batalov	11/2023
884	2^1041153-114391	313419	Enzo Doria	02/2015
885	(2^1039700+9)/5	312981	Stefano Morozzi	09/2022
886	(74^167311+1)/75	312742	Paul Bourdelais	12/2020
887	2^1038871+1866983	312732	Enzo Doria	04/2016
888	2^1038545+71657	312634	Enzo Doria	08/2023
889	(55^179573-1)/54	312521	Paul Bourdelais	08/2020
890	2^1037647+1881263	312363	Enzo Doria	11/2016
891	2^1037226+1879699	312237	Enzo Doria	10/2016
892	2^1036867+1865843	312129	Enzo Doria	02/2016
893	(76^165947+1)/77	312114	Paul Bourdelais	01/2021
894	2^1036020-114539	311874	Enzo Doria	02/2015
895	(90^159463-1)/89	311628	Paul Bourdelais	08/2020
896	2^1034546+28819	311430	Enzo Doria	02/2024
897	2^1032240+1883431	310736	Enzo Doria	01/2017
898	64211^64588+64588^64211	310514	Norbert Schneider	11/2023
899	2^1031450+29629	310498	Enzo Doria	03/2024
900	2^1030352+1870021	310167	Enzo Doria	06/2016
901	2^1030046+1882843	310075	Enzo Doria	11/2016
902	3^648872+16	309591	Robert Price	04/2020
903	(16976^73441-1)/(16976^271-1)	309498	Ryan Propper	11/2023
904	64221^64366+64366^64221	309451	Norbert Schneider	06/2023
905	(11121^76729-1)/(11121^277-1)	309336	Ryan Propper	11/2023
906	2^1027478+219259	309302	Enzo Doria	02/2024
907	2^1026999+20513	309158	Enzo Doria	07/2023
908	5^442281+2	309142	Paul Bourdelais	01/2021
909	2^1026204+22741	308919	Enzo Doria	09/2023
910	2^1026190+15	308914	Stefano Morozzi	10/2022
911	2^1025108+20851	308589	Enzo Doria	08/2023
912	A352736(16)	306985	Kellen Shenton	05/2022
913	2^1019777+213947	306984	Enzo Doria	10/2023
914	(11^293831-1)/10	305993	Paul Bourdelais	03/2010
915	(67^167449-1)/66	305773	Paul Bourdelais	08/2020
916	(62^170539+1)/63	305671	Paul Bourdelais	12/2020
917	2^1015321-1015321	305643	Henri Lifchitz	08/2013
918	2^1014775+27113	305478	Enzo Doria	12/2023
919	2^1014450+7	305380	Stefano Morozzi	10/2022
920	2^1014336+215731	305346	Enzo Doria	12/2023
921	2^1014224-2791229	305312	Enzo Doria	01/2016
922	(10^304986+7)/673	304984	Alfred Reich	11/2021
923	65473^45250+45250^65473	304818	Hans Havermann	02/2022
924	66012^41423+41423^66012	304794	Hans Havermann	03/2022
925	65073^48202+48202^65073	304742	Hans Havermann	04/2022
926	2^1012054+31669	304659	Enzo Doria	06/2024
927	238176^19+19^238176	304569	Hans Havermann	03/2022
928	73122^14615+14615^73122	304539	Hans Havermann	05/2022
929	64492^52639+52639^64492	304487	Hans Havermann	03/2022
930	65955^41288+41288^65955	304437	Hans Havermann	04/2022
931	71729^17530+17530^71729	304403	Hans Havermann	03/2022
932	70170^21733+21733^70170	304336	Hans Havermann	03/2022
933	2^1010751-107709	304267	Enzo Doria	03/2014
934	84473^3994+3994^84473	304222	Hans Havermann	03/2022
935	(2^1010623-1)/12602017578957977	304212	Tony Prest / Never Odd Or Even	02/2014
936	74442^12125+12125^74442	303998	Hans Havermann	02/2022
937	77842^8039+8039^77842	303989	Hans Havermann	01/2022
938	64209^54140+54140^64209	303935	Hans Havermann	02/2022
939	2^1009577+1869587	303913	Enzo Doria	06/2016
940	67389^32338+32338^67389	303906	Hans Havermann	02/2022
941	8^336419-7^336419	303817	Jean-Louis Charton	01/2008
942	2^1009168+15	303790	Stefano Morozzi	10/2022
943	80766^5771+5771^80766	303782	Hans Havermann	01/2022
944	66094^39385+39385^66094	303724	Hans Havermann	01/2022
945	69147^24574+24574^69147	303589	Hans Havermann	02/2022
946	78390^7459+7459^78390	303580	Hans Havermann	01/2022
947	2^1008301+1869377	303529	Enzo Doria	06/2016
948	65008^46615+46615^65008	303492	Hans Havermann	02/2022
949	(2^1007838+5)/3	303389	Serge Batalov	08/2015
950	65018^46293+46293^65018	303343	Hans Havermann	01/2022
951	6^389756+5	303290	Paul Bourdelais	02/2021
952	71016^18649+18649^71016	303285	Hans Havermann	01/2022
953	2^1007065+29231	303157	Enzo Doria	03/2024
954	80160^6047+6047^80160	303129	Hans Havermann	01/2022
955	67434^31237+31237^67434	303094	Hans Havermann	03/2022
956	65537^42102+42102^65537	303063	Hans Havermann	02/2022
957	71790^16553+16553^71790	302874	Hans Havermann	11/2021
958	65208^44129+44129^65208	302874	Hans Havermann	11/2021
959	84181^3960+3960^84181	302858	Hans Havermann	11/2021
960	(13703^73441-1)/(13703^271-1)	302691	Ryan Propper	11/2023
961	71956^16087+16087^71956	302682	Hans Havermann	11/2021
962	2^1005326+383059	302634	Enzo Doria	12/2016
963	2^1004929+1877567	302514	Enzo Doria	08/2016
964	69341^22978+22978^69341	302418	Hans Havermann	12/2021
965	111443^516+516^111443	302306	Hans Havermann	12/2021
966	67638^29387+29387^67638	302218	Hans Havermann	11/2021
967	2^1003494+1874899	302082	Enzo Doria	06/2016
968	75189^10400+10400^75189	302037	Hans Havermann	12/2021
969	67237^31042+31042^67237	302026	Hans Havermann	12/2021
970	64540^47791+47791^64540	302005	Hans Havermann	11/2021
971	2^1003046+60529	301947	Enzo Doria	04/2016
972	83278^4209+4209^83278	301815	Hans Havermann	09/2021
973	64431^48250+48250^64431	301763	Hans Havermann	09/2021
974	67237^30714+30714^67237	301716	Hans Havermann	09/2021
975	64641^46288+46288^64641	301581	Hans Havermann	09/2021
976	71513^16482+16482^71513	301572	Hans Havermann	10/2021
977	72017^15396+15396^72017	301565	Hans Havermann	09/2021
978	65534^39927+39927^65534	301540	Hans Havermann	10/2021
979	(23^221411-1)/22	301501	Paul Bourdelais	08/2020
980	63169^59152+59152^63169	301441	Hans Havermann	09/2021
981	75055^10348+10348^75055	301336	Hans Havermann	09/2021
982	2^1000647+1881353	301225	Enzo Doria	11/2016
983	83686^3961+3961^83686	301086	Hans Havermann	10/2021
984	68529^24742+24742^68529	301078	Hans Havermann	09/2021
985	65207^41416+41416^65207	301072	Hans Havermann	10/2021
987	2^1000000+821751	301030	Tony Prest / Never Odd Or Even	10/2015
986	2^999999+77151	301030	Norman Luhn	09/2023
988	90762^2071+2071^90762	300984	Hans Havermann	06/2021
989	63909^51142+51142^63909	300934	Hans Havermann	08/2021
990	2^999646+1874029	300924	Enzo Doria	06/2016
991	66280^34607+34607^66280	300856	Hans Havermann	06/2021
992	65534^38925+38925^65534	300817	Hans Havermann	07/2021
993	63296^56517+56517^63296	300794	Hans Havermann	06/2021
994	110610^523+523^110610	300694	Hans Havermann	06/2021
995	66428^33609+33609^66428	300684	Hans Havermann	06/2021
996	74247^11210+11210^74247	300672	Hans Havermann	06/2021
997	(59^169777-1)/58	300649	Paul Bourdelais	08/2020
998	10^300476+3	300477	Ed Trice	10/2012
999	10^300476-530913	300476	Patrick De Geest	03/2016
1000	66703^31960+31960^66703	300471	Hans Havermann	06/2021

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