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	2^1217500+226321	366505	Enzo Doria	09/2024
752	(233^154787-1)/232	366434	Anonymous	05/2024
753	2^1216694+1884769	366262	Enzo Doria	02/2017
754	2^1215889-3	366020	Paul Bourdelais	06/2019
755	2^1215296+1885441	365841	Enzo Doria	03/2017
756	(80^192133+1)/81	365645	Paul Bourdelais	01/2021
757	2^1214307+1888115	365543	Enzo Doria	05/2017
758	2^1213815+3	365395	Paul Bourdelais	06/2019
759	(80^191953+1)/81	365302	Paul Bourdelais	01/2021
760	2^1213313+215837	365244	Enzo Doria	11/2023
761	2^1208276+22201	363728	Enzo Doria	09/2023
762	2^1207345+1882577	363448	Enzo Doria	12/2016
763	2^1207336+217801	363445	Enzo Doria	03/2024
764	2^1207073+883727	363366	Enzo Doria	03/2017
765	3^761457-2	363308	Ryan Propper	07/2015
766	(10^363030+7)/337/443	363025	Alfred Reich	12/2021
767	2^1204869+224885	362702	Enzo Doria	07/2024
768	2^1200972+141811	361529	Stefano Morozzi	10/2022
769	(2^1200924+324730)/2	361514	Stefano Morozzi	06/2021
770	(2^1200912+274110)/2	361511	Stefano Morozzi	01/2021
771	2^1200906+165249	361509	Stefano Morozzi	07/2022
772	2^1200890+166339	361504	Stefano Morozzi	01/2023
773	(2^1200887+344126)/2	361503	Stefano Morozzi	10/2020
774	2^1200877+186755	361500	Stefano Morozzi	09/2022
775	2^1200861+198521	361496	Stefano Morozzi	11/2021
776	(2^1200856+305790)/2	361494	Stefano Morozzi	10/2020
777	(2^1200853+372822)/2	361493	Stefano Morozzi	06/2021
778	2^1200812+324178)/2	361481	Stefano Morozzi	06/2021
779	(2^1200768+380458)/2	361467	Stefano Morozzi	01/2021
780	2^1200756+140917	361464	Stefano Morozzi	05/2022
781	2^1200741+184781	361460	Stefano Morozzi	09/2022
782	(2^1200741+293402)/2	361459	Stefano Morozzi	07/2021
783	2^1200734+142653	361457	Stefano Morozzi	02/2023
785	2^1200672+1880881	361439	Enzo Doria	10/2016
784	2^1200672+141535	361439	Stefano Morozzi	09/2022
786	2^1200669+178805	361438	Stefano Morozzi	11/2022
787	2^1200660+198555	361435	Stefano Morozzi	12/2021
788	2^1200657+164837	361434	Stefano Morozzi	05/2022
789	2^1200631+166431	361426	Stefano Morozzi	02/2023
790	2^1200627+150669	361425	Stefano Morozzi	02/2023
791	(2^1200603+356030)/2	361418	Stefano Morozzi	10/2020
792	(2^1200590+275854)/2	361414	Stefano Morozzi	03/2021
793	2^1200550+139297	361402	Stefano Morozzi	10/2021
794	2^1200486+172855	361383	Stefano Morozzi	01/2023
795	(2^1200456+320526)/2	361373	Stefano Morozzi	10/2020
796	2^1200443+142121	361370	Stefano Morozzi	01/2023
797	2^1200416+164065	361362	Stefano Morozzi	01/2022
798	2^1200331+155429	361336	Stefano Morozzi	10/2021
800	(2^1200289+348366)/2	361323	Stefano Morozzi	10/2020
799	2^1200289+141885	361323	Stefano Morozzi	11/2022
801	(2^1200284+273162)/2	361322	Stefano Morozzi	10/2020
802	2^1200252+194535	361312	Stefano Morozzi	11/2021
803	(2^1200250+364230)/2	361311	Stefano Morozzi	10/2020
804	2^1200227+156881	361305	Stefano Morozzi	05/2022
805	(2^1200209+305990)/2	361299	Stefano Morozzi	10/2020
806	(2^1200210+376278)/2	361299	Stefano Morozzi	10/2020
807	2^1200202+216499	361297	Enzo Doria	12/2023
808	(2^1200182+274462)/2	361291	Stefano Morozzi	01/2021
809	2^1200178+149193	361290	Stefano Morozzi	07/2022
810	2^1200168+140403	361287	Stefano Morozzi	03/2022
811	(2^1200162+275910)/2	361285	Stefano Morozzi	03/2021
812	2^1200157+168927	361284	Stefano Morozzi	02/2023
813	2^1200134+141385	361277	Stefano Morozzi	08/2022
814	(2^1200131+360150)/2	361276	Stefano Morozzi	10/2020
815	(2^1200118+290718)/2	361272	Stefano Morozzi	01/2021
816	2^1200022+192777	361243	Stefano Morozzi	09/2022
817	2^1200021+149777	361243	Stefano Morozzi	10/2022
818	(64*10^360173-1)/243	360173	Serge Batalov	09/2014
819	(59^203309+1)/60	360029	Paul Bourdelais	09/2021
820	(2*10^359860-11)/9	359860	Rytis Slatkevicius	01/2023
821	2^1195093+1882577	359759	Enzo Doria	12/2016
822	3^753451+5*2^753451	359488	Jon Grantham	08/2023
823	2^1192258+36739	358906	Enzo Doria	09/2024
824	(6^461108-11)/5	358812	Paul Bourdelais	04/2019
825	2^1191375+8543	358640	Phil Moore	06/2008
826	2^1190972+1880191	358519	Enzo Doria	11/2016
827	2^1189930+28549	358205	Enzo Doria	03/2024
828	(45^216551-1)/44	358004	Paul Bourdelais	08/2020
829	(50^210319-1)/49	357324	Paul Bourdelais	08/2020
830	(531^131072+25^131072)/2	357184	Kellen Shenton	03/2021
831	2^1186366+226747	357132	Enzo Doria	09/2024
832	2^1184565+21227	356590	Enzo Doria	08/2023
833	2^1180159+22823	355264	Enzo Doria	11/2023
834	2^1179836+1885021	355167	Enzo Doria	02/2017
835	2^1178942+32269	354897	Enzo Doria	04/2024
836	2^1177053+28607	354329	Enzo Doria	02/2024
837	(19*10^353884-91)/9	353885	Alfred Reich	02/2023
838	(10^353884*19-91)/9	353885	Alfred Reich	10/2023
839	20^271951+3	353817	Paul Bourdelais	01/2021
840	72722^72722+7^7	353551	Serge Batalov	04/2024
841	2^1173095+21	353137	Stefano Morozzi	10/2022
842	2^1170959+218945	352494	Enzo Doria	03/2024
843	2^1170915+382623	352481	Boyan Hu	08/2024
844	(63^195893-1)/62	352477	Paul Bourdelais	08/2020
845	2^1170331+27293	352305	Enzo Doria	01/2024
846	2^1170326+7	352304	Stefano Morozzi	10/2022
847	numbpart(100000135540)	352269	Serge Batalov	04/2017
848	(10^352237-1)/9/10567111/950335427	352221	Maksym Voznyy	01/2015
849	5*3^737931-2^737931	352084	Jon Grantham	08/2023
850	2^1168851+223613	351860	Enzo Doria	06/2024
851	2^1168554+783529	351770	Enzo Doria	01/2017
852	(2^1168183-1)/54763676838381762583	351639	Matthias Wurtinger	01/2011
853	2^1166950+30409	351287	Enzo Doria	03/2024
854	2^1166563+223103	351171	Enzo Doria	05/2024
855	2^1166248+38251	351076	Enzo Doria	11/2024
856	2^1166152+1882411	351047	Enzo Doria	12/2016
857	2^1163972+20971	350391	Enzo Doria	08/2023
858	2^1163272+22411	350180	Enzo Doria	10/2023
859	10^350071+7	350072	Alfred Reich	05/2021
860	2^1162154+1890207	349844	Enzo Doria	08/2017
861	(7*10^348724-61)/9	348724	Erik Branger	09/2016
862	(4*10^348453+41)/9	348453	Serge Batalov	11/2022
863	(127^165601-1)/126	348390	Alexander Zhirkov	09/2015
864	2^1155085+213377	347716	Enzo Doria	09/2023
865	2^1153083+1883693	347113	Enzo Doria	04/2017
866	2^1152186+225529	346843	Enzo Doria	07/2024
867	(2^1148729+2^574365+1)/5	345802	Borys Jaworski	03/2007
868	2^1145882+80779	344945	Enzo Doria	09/2016
869	2^1143425+221177	344206	Enzo Doria	03/2024
870	2^1141813+27047	343720	Enzo Doria	12/2023
871	2^1141114+221869	343510	Enzo Doria	04/2024
872	2^1138296+27541	342662	Enzo Doria	01/2024
873	2^1136462+1887289	342110	Enzo Doria	05/2017
874	F(1636007)	341905	Henri Lifchitz	03/2009
875	(2^1135567+13)/3	341840	Stefano Morozzi	09/2022
876	2^1134873+223637	341631	Enzo Doria	06/2024
877	2^1133678+782569	341272	Enzo Doria	11/2016
878	(11^327001+1)/12	340536	Paul Bourdelais	09/2013
879	2^1129965+223667	340154	Enzo Doria	06/2024
880	2^1129361+221597	339972	Enzo Doria	04/2024
881	2^1128706+225529	339775	Enzo Doria	07/2024
882	2^1128621+25919	339749	Enzo Doria	12/2023
883	(2^1127239+2^563620+1)/5	339333	Borys Jaworski	11/2006
884	Tau(907^20848)	339132	Nik Lygeros / Olivier Rozier	01/2016
885	2^1126380-3	339075	Paul Bourdelais	06/2019
886	2^1125784+24331	338895	Enzo Doria	10/2023
887	2^1125446+1885099	338794	Enzo Doria	08/2017
888	(63^188147+1)/64	338539	Paul Bourdelais	12/2020
889	2^1124549+143807	338523	Enzo Doria	10/2016
890	(4*10^338476+23)/9	338476	Serge Batalov	11/2022
891	2^1121187+1886783	337511	Enzo Doria	04/2017
892	(48^200443-1)/47	336992	Paul Bourdelais	08/2020
893	(2*10^336405+43)/9	336405	Rytis Slatkevicius	01/2023
894	(94^170371-1)/93	336162	Paul Bourdelais	09/2020
895	2^1116184+1883521	336005	Enzo Doria	02/2017
896	2^1115727+27683	335868	Enzo Doria	01/2024
897	2^1114974+28759	335641	Enzo Doria	02/2024
898	2^1114517+1880087	335504	Enzo Doria	10/2016
899	(5*10^335480+31)/9	335480	Serge Batalov	11/2022
900	5*3^701688+2^701688	334791	Jon Grantham	08/2023
901	(101^166849+1)/102	334418	Paul Bourdelais	12/2020
902	(3^700897+1)/4	334413	Paul Bourdelais	04/2010
903	2^1109200+223201	333903	Enzo Doria	05/2024
904	2^1108463+32513	333681	Enzo Doria	05/2024
905	2^1104500+22411	332488	Enzo Doria	10/2023
906	2^1104408-114539	332460	Enzo Doria	03/2015
907	2^1101921+82085	331712	Enzo Doria	10/2016
908	2^1101895+29963	331704	Enzo Doria	03/2024
909	2^1101167-1101167^2	331485	Henri Lifchitz	07/2024
910	2^1101091+224153	331462	Enzo Doria	06/2024
911	2^1100655+683513	331331	Enzo Doria	01/2017
912	(10^330906+71)/9	330906	Serge Batalov	07/2015
913	2^1098346+482899	330636	Enzo Doria	11/2016
914	2^1096976+25	330223	Henri Lifchitz	11/2024
915	(2^1096212+19)/5	329992	Stefano Morozzi	09/2022
916	2^1095679+1878713	329833	Enzo Doria	09/2016
917	2^1094874+27499	329590	Enzo Doria	01/2024
918	2^1094740-1851539	329550	Enzo Doria	08/2015
919	2^1092242+19	328798	Stefano Morozzi	10/2022
920	2^1091469-379369	328565	Enzo Doria	03/2014
921	2^1090801+24227	328364	Enzo Doria	10/2023
922	(69^178093-1)/68	327485	Paul Bourdelais	08/2020
923	(10^326884+7)/421	326882	Alfred Reich	12/2021
924	2^1085750+582349	326844	Enzo Doria	11/2016
925	(54308^69169-1)/(54308^263-1)	326261	Ryan Propper	11/2023
926	2^1083596+483061	326195	Enzo Doria	12/2016
927	(2^541456-1)*10^162995+2^541455-1	325990	paolo galliani	01/2019
928	2^1082908+583561	325988	Enzo Doria	05/2017
929	30^220411-29^220411	325574	Jean-Louis Charton	10/2018
930	2^1081308+7	325507	Stefano Morozzi	10/2022
931	2^1080151+225413	325158	Enzo Doria	08/2024
932	2^1080032+25171	325123	Enzo Doria	11/2023
933	2^1078242+1881649	324584	Enzo Doria	11/2016
934	2^1077737+1880117	324432	Enzo Doria	10/2016
935	3^679017-5*2^679017	323974	Jon Grantham	08/2023
936	2^1076006+29539	323911	Enzo Doria	03/2024
937	2^1075573+32417	323780	Enzo Doria	05/2024
938	2^1075425+1880117	323736	Enzo Doria	10/2016
939	(28^223381+1)/29	323267	Paul Bourdelais	12/2020
940	10^322999+187071	323000	Stefano Morozzi	03/2019
941	10^322999-143151	322999	Patrick De Geest	05/2020
942	2^1072744+32641	322929	Enzo Doria	05/2024
943	2^1072146+1886869	322749	Enzo Doria	04/2017
944	2^1072118-7321953	322740	Enzo Doria	02/2015
945	2^1071026+1886869	322411	Enzo Doria	04/2017
946	2^1070539+1880633	322265	Enzo Doria	10/2016
947	2^1069788+26587	322039	Enzo Doria	12/2023
948	2^1069293-1147195	321890	Enzo Doria	05/2015
949	2^1065968+1880941	320889	Enzo Doria	10/2016
950	2^1065897-1147195	320867	Enzo Doria	05/2015
951	2^1063427+1882103	320124	Enzo Doria	12/2016
952	2^1061095-1061095	319422	Henri Lifchitz	10/2013
953	2^1060950+653119	319378	Enzo Doria	12/2016
954	2^1060363+782753	319202	Enzo Doria	11/2016
955	2^1060028+31771	319101	Enzo Doria	04/2024
956	(71^172259-1)/70	318895	Paul Bourdelais	08/2020
957	2^1058425+38507	318618	Enzo Doria	11/2024
958	-30*Bern(85996)/236037521	318354	Sergey Batalov	10/2023
959	2^1055665+30407	317787	Enzo Doria	03/2024
960	2^1054736+483061	317508	Enzo Doria	12/2016
961	2^1053965+1879667	317276	Enzo Doria	10/2016
962	(43^194119-1)/42	317086	Paul Bourdelais	08/2020
963	2^1052899+225413	316955	Enzo Doria	08/2024
964	2^1052186-458165	316740	Enzo Doria	03/2015
965	11^303909+2	316489	Paul Bourdelais	08/2023
966	2^1049026+214609	315789	Enzo Doria	11/2023
967	2^1048576+69661	315653	Boyan Hu	08/2024
968	2^1046613-114685	315062	Enzo Doria	04/2015
969	2^1045625-459373	314765	Enzo Doria	06/2015
970	10^(2157363+1)-810^157363-1	314727	Robert Price	07/2023
971	(7*10^314564-61)/9	314564	Erik Branger	09/2016
972	2^1044771+228023	314508	Enzo Doria	11/2024
973	2^1044206+7	314338	Stefano Morozzi	10/2022
974	(7^371669-1)/6	314096	Paul Bourdelais	02/2010
975	(53^181981-1)/52	313784	Paul Bourdelais	08/2020
976	(8^347437-5^347437)/3	313767	Jon Grantham	08/2023
977	(10^313741+1)/11/11294677	313733	Alfred Reich	04/2024
978	2^1041944+283051	313657	Enzo Doria	12/2016
979	(1624^97969-1)/(1624^313-1)	313533	Sergey Batalov	11/2023
980	2^1041153-114391	313419	Enzo Doria	02/2015
981	(2^1039700+9)/5	312981	Stefano Morozzi	09/2022
982	(74^167311+1)/75	312742	Paul Bourdelais	12/2020
983	2^1038871+1866983	312732	Enzo Doria	04/2016
984	2^1038545+71657	312634	Enzo Doria	08/2023
985	(55^179573-1)/54	312521	Paul Bourdelais	08/2020
986	2^1037647+1881263	312363	Enzo Doria	11/2016
987	2^1037226+1879699	312237	Enzo Doria	10/2016
988	2^1036867+1865843	312129	Enzo Doria	02/2016
989	(76^165947+1)/77	312114	Paul Bourdelais	01/2021
990	2^1036020-114539	311874	Enzo Doria	02/2015
991	(90^159463-1)/89	311628	Paul Bourdelais	08/2020
992	2^1034546+28819	311430	Enzo Doria	02/2024
993	2^1032240+1883431	310736	Enzo Doria	01/2017
994	64211^64588+64588^64211	310514	Norbert Schneider	11/2023
995	2^1031450+29629	310498	Enzo Doria	03/2024
996	2^1030352+1870021	310167	Enzo Doria	06/2016
997	2^1030046+1882843	310075	Enzo Doria	11/2016
998	2^1029120+227971	309796	Enzo Doria	11/2024
999	3^648872+16	309591	Robert Price	04/2020
1000	(16976^73441-1)/(16976^271-1)	309498	Ryan Propper	11/2023

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Probable Primes Top 10000

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