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	2^1307563+232133	393616	Enzo Doria	03/2025
752	2^1307324+224611	393544	Enzo Doria	07/2024
753	2^1307262+28759	393526	Enzo Doria	02/2024
754	(1009565^81920+1)/(1009565^16384+1)	393487	Serge Batalov	01/2017
755	2^1305860+35461	393104	Enzo Doria	08/2024
756	(995042^81920+1)/(995042^16384+1)	393075	Serge Batalov	01/2017
757	(988945^81920+1)/(988945^16384+1)	392900	Serge Batalov	01/2017
758	(988823^81920+1)/(988823^16384+1)	392897	Serge Batalov	01/2017
759	(2^1304983-1)/52199321	392832	Tony Prest / Never Odd Or Even	03/2014
760	(978970^81920+1)/(978970^16384+1)	392612	Serge Batalov	01/2017
761	2^1303816+38251	392488	Enzo Doria	11/2024
762	2^1303102+1866409	392273	Enzo Doria	09/2017
763	2^1302818+283429	392188	Enzo Doria	01/2017
764	2^1301430+22669	391770	Enzo Doria	10/2023
765	2^1301229+222467	391709	Enzo Doria	04/2024
766	2^1300835+232523	391591	Enzo Doria	03/2025
767	(934422^81920+1)/(934422^16384+1)	391286	Serge Batalov	01/2017
768	2^1299181+1886867	391093	Enzo Doria	04/2017
769	(37^249341-1)/36	391016	Paul Bourdelais	08/2020
770	2^1298304+1882891	390829	Enzo Doria	01/2017
771	2^1297732+228721	390657	Enzo Doria	11/2024
772	95196^12497+12497^95196	390000	Hans Havermann	12/2021
773	2^1295539+35633	389997	Enzo Doria	08/2024
774	86206^33381+33381^86206	389953	Hans Havermann	05/2023
775	2^1294324+25171	389631	Enzo Doria	12/2023
776	(874207^81920+1)/(874207^16384+1)	389390	Serge Batalov	01/2017
777	2^1292338+229249	389033	Enzo Doria	11/2024
778	2^1289624+32551	388216	Enzo Doria	05/2024
779	2^1286857+37967	387383	Enzo Doria	10/2024
780	2^1285456+230611	386961	Enzo Doria	01/2025
781	(7^457871-5^457871)/2	386946	Jon Grantham	08/2023
782	79455^73828+73828^79455	386805	Hans Havermann	03/2023
783	81650^54369+54369^81650	386642	Yusuf AttarBashi	06/2021
784	80565^62824+62824^80565	386561	Hans Havermann	08/2021
785	83747^41272+41272^83747	386548	Hans Havermann	08/2021
786	15^328574+328574^15	386434	Serge Batalov	05/2014
787	2^1282676+30493	386124	Enzo Doria	12/2024
788	2^1280078+1885099	385342	Enzo Doria	08/2017
789	2^1279921+17	385295	Stefano Morozzi	10/2022
790	2^1279245+224087	385092	Enzo Doria	07/2024
791	2^1277980+231391	384711	Enzo Doria	01/2025
792	2^1277688+231241	384623	Enzo Doria	01/2025
793	2^1276977+71657	384409	Enzo Doria	08/2023
794	(76803^78961-1)/(76803^281-1)	384382	Ryan Propper	11/2023
795	2^1276571+26213	384287	Enzo Doria	12/2023
796	MillsLike(2,1,4,12,4,22,12,114,4,138,142,2956,6388,5248,17532,96930,83782,1464,897448,300832,26908)	384166	Sergey Batalov	05/2024
797	2^1274941+1880717	383796	Enzo Doria	10/2016
798	2^1272632+383431	383101	Enzo Doria	01/2017
799	2^1271346+1889839	382714	Enzo Doria	08/2017
800	2^1271173+219587	382662	Enzo Doria	03/2024
801	5*3^798534-2^798534	380999	Jon Grantham	08/2023
802	(10^380976-7)/3	380976	Leonid Durman	01/2012
803	2^1264748+23221	380728	Enzo Doria	11/2023
804	(4*10^380056+11)/3	380057	Tyler Busby	03/2023
805	2^1262431+228353	380030	Enzo Doria	11/2024
806	2^1260859+222683	379557	Enzo Doria	06/2024
807	2^1258313+43727	378790	Enzo Doria	03/2025
808	2^1257787+1447761	378632	Makoto Morimoto	10/2013
809	(2^1257787+32270)/(223328122073011)	378620	Makoto Morimoto	12/2016
810	2^1257728+20851	378614	Enzo Doria	08/2023
811	(77^200657-1)/76	378536	Paul Bourdelais	08/2020
812	2^1254797+229487	377732	Enzo Doria	11/2024
813	(98^189619+1)/99	377573	Paul Bourdelais	02/2021
814	F(1803059)	376817	Henri Lifchitz	06/2009
815	2^1250590+29389	376466	Enzo Doria	03/2024
816	(10^376417-3^376417)/7	376417	Jon Grantham	08/2023
817	2^1250116+34951	376323	Enzo Doria	08/2024
818	2^1246724+213961	375302	Enzo Doria	10/2023
819	2^1245230+19	374852	Stefano Morozzi	10/2022
820	2^1244263+230033	374561	Enzo Doria	01/2025
821	7^442674+4	374103	Paul Bourdelais	02/2021
822	2^1239151+35633	373022	Enzo Doria	08/2024
823	2^1238732+39181	372896	Enzo Doria	11/2024
824	2^1237699+34703	372585	Enzo Doria	07/2024
825	(97^187393-1)/96	372306	Paul Bourdelais	09/2020
826	10^371696+7	371697	Alfred Reich	05/2021
827	2^1234709+883127	371685	Enzo Doria	12/2016
828	2^1234119+21803	371507	Enzo Doria	09/2023
829	(67^203431+1)/68	371479	Paul Bourdelais	09/2021
830	2^1233971+216593	371463	Enzo Doria	12/2023
831	2^1233212+27301	371234	Enzo Doria	12/2023
832	2^1231466+283819	370709	Enzo Doria	07/2017
833	2^1229766+26659	370197	Enzo Doria	12/2023
834	2^1228899+30713	369936	Enzo Doria	03/2024
835	2^1228892+223831	369934	Enzo Doria	06/2024
836	(49627^78961-1)/(49627^281-1)	369460	Ryan Propper	11/2023
837	2^1227060+226663	369382	Enzo Doria	09/2024
838	2^1226987+28163	369360	Enzo Doria	02/2024
839	2^1226569+30857	369235	Enzo Doria	03/2024
840	73^197880+197880	368715	Kellen Shenton	06/2023
841	5*3^771723-2^771723	368207	Jon Grantham	08/2023
842	2^1222741+231707	368082	Enzo Doria	02/2025
843	2^1222473+221597	368002	Enzo Doria	04/2024
844	2^1222211+22703	367923	Enzo Doria	11/2023
845	(2^1222097+19)/3	367888	Stefano Morozzi	09/2022
846	2^1220335+1881263	367358	Enzo Doria	11/2016
847	2^1218344+215641	366759	Enzo Doria	12/2023
848	2^1217510+220039	366508	Enzo Doria	03/2024
849	2^1217500+226321	366505	Enzo Doria	09/2024
850	(233^154787-1)/232	366434	Anonymous	05/2024
851	2^1216694+1884769	366262	Enzo Doria	02/2017
852	2^1215889-3	366020	Paul Bourdelais	06/2019
853	2^1215296+1885441	365841	Enzo Doria	03/2017
854	(80^192133+1)/81	365645	Paul Bourdelais	01/2021
855	2^1214307+1888115	365543	Enzo Doria	05/2017
856	2^1213815+3	365395	Paul Bourdelais	06/2019
857	(80^191953+1)/81	365302	Paul Bourdelais	01/2021
858	2^1213313+215837	365244	Enzo Doria	11/2023
859	2^1208276+22201	363728	Enzo Doria	09/2023
860	2^1207345+1882577	363448	Enzo Doria	12/2016
861	2^1207336+217801	363445	Enzo Doria	03/2024
862	2^1207073+883727	363366	Enzo Doria	03/2017
863	3^761457-2	363308	Ryan Propper	07/2015
864	(10^363030+7)/337/443	363025	Alfred Reich	12/2021
865	2^1204869+224885	362702	Enzo Doria	07/2024
866	2^1200972+141811	361529	Stefano Morozzi	10/2022
867	(2^1200924+324730)/2	361514	Stefano Morozzi	06/2021
868	(2^1200912+274110)/2	361511	Stefano Morozzi	01/2021
869	2^1200906+165249	361509	Stefano Morozzi	07/2022
870	2^1200890+166339	361504	Stefano Morozzi	01/2023
871	(2^1200887+344126)/2	361503	Stefano Morozzi	10/2020
872	2^1200877+186755	361500	Stefano Morozzi	09/2022
873	2^1200861+198521	361496	Stefano Morozzi	11/2021
874	(2^1200856+305790)/2	361494	Stefano Morozzi	10/2020
875	(2^1200853+372822)/2	361493	Stefano Morozzi	06/2021
876	2^1200812+324178)/2	361481	Stefano Morozzi	06/2021
877	(2^1200768+380458)/2	361467	Stefano Morozzi	01/2021
878	2^1200756+140917	361464	Stefano Morozzi	05/2022
879	2^1200741+184781	361460	Stefano Morozzi	09/2022
880	(2^1200741+293402)/2	361459	Stefano Morozzi	07/2021
881	2^1200734+142653	361457	Stefano Morozzi	02/2023
883	2^1200672+1880881	361439	Enzo Doria	10/2016
882	2^1200672+141535	361439	Stefano Morozzi	09/2022
884	2^1200669+178805	361438	Stefano Morozzi	11/2022
885	2^1200660+198555	361435	Stefano Morozzi	12/2021
886	2^1200657+164837	361434	Stefano Morozzi	05/2022
887	2^1200631+166431	361426	Stefano Morozzi	02/2023
888	2^1200627+150669	361425	Stefano Morozzi	02/2023
889	(2^1200603+356030)/2	361418	Stefano Morozzi	10/2020
890	(2^1200590+275854)/2	361414	Stefano Morozzi	03/2021
891	2^1200550+139297	361402	Stefano Morozzi	10/2021
892	2^1200486+172855	361383	Stefano Morozzi	01/2023
893	(2^1200456+320526)/2	361373	Stefano Morozzi	10/2020
894	2^1200443+142121	361370	Stefano Morozzi	01/2023
895	2^1200416+164065	361362	Stefano Morozzi	01/2022
896	2^1200331+155429	361336	Stefano Morozzi	10/2021
898	(2^1200289+348366)/2	361323	Stefano Morozzi	10/2020
897	2^1200289+141885	361323	Stefano Morozzi	11/2022
899	(2^1200284+273162)/2	361322	Stefano Morozzi	10/2020
900	2^1200252+194535	361312	Stefano Morozzi	11/2021
901	(2^1200250+364230)/2	361311	Stefano Morozzi	10/2020
902	2^1200227+156881	361305	Stefano Morozzi	05/2022
903	(2^1200209+305990)/2	361299	Stefano Morozzi	10/2020
904	(2^1200210+376278)/2	361299	Stefano Morozzi	10/2020
905	2^1200202+216499	361297	Enzo Doria	12/2023
906	(2^1200182+274462)/2	361291	Stefano Morozzi	01/2021
907	2^1200178+149193	361290	Stefano Morozzi	07/2022
908	2^1200168+140403	361287	Stefano Morozzi	03/2022
909	(2^1200162+275910)/2	361285	Stefano Morozzi	03/2021
910	2^1200157+168927	361284	Stefano Morozzi	02/2023
911	2^1200134+141385	361277	Stefano Morozzi	08/2022
912	(2^1200131+360150)/2	361276	Stefano Morozzi	10/2020
913	(2^1200118+290718)/2	361272	Stefano Morozzi	01/2021
914	2^1200022+192777	361243	Stefano Morozzi	09/2022
915	2^1200021+149777	361243	Stefano Morozzi	10/2022
916	(64*10^360173-1)/243	360173	Serge Batalov	09/2014
917	(59^203309+1)/60	360029	Paul Bourdelais	09/2021
918	(2*10^359860-11)/9	359860	Rytis Slatkevicius	01/2023
919	2^1195093+1882577	359759	Enzo Doria	12/2016
920	3^753451+5*2^753451	359488	Jon Grantham	08/2023
921	2^1192258+36739	358906	Enzo Doria	09/2024
922	(6^461108-11)/5	358812	Paul Bourdelais	04/2019
923	2^1191375+8543	358640	Phil Moore	06/2008
924	2^1190972+1880191	358519	Enzo Doria	11/2016
925	2^1189930+28549	358205	Enzo Doria	03/2024
926	(45^216551-1)/44	358004	Paul Bourdelais	08/2020
927	2^1187005+230807	357325	Enzo Doria	01/2025
928	(50^210319-1)/49	357324	Paul Bourdelais	08/2020
929	(531^131072+25^131072)/2	357184	Kellen Shenton	03/2021
930	2^1186366+226747	357132	Enzo Doria	09/2024
931	2^1184565+21227	356590	Enzo Doria	08/2023
932	2^1180159+22823	355264	Enzo Doria	11/2023
933	2^1179836+1885021	355167	Enzo Doria	02/2017
934	2^1178942+32269	354897	Enzo Doria	04/2024
935	2^1178474+43369	354757	Enzo Doria	03/2025
936	2^1177053+28607	354329	Enzo Doria	02/2024
937	(19*10^353884-91)/9	353885	Alfred Reich	02/2023
938	(10^353884*19-91)/9	353885	Alfred Reich	10/2023
939	20^271951+3	353817	Paul Bourdelais	01/2021
940	72722^72722+7^7	353551	Serge Batalov	04/2024
941	2^1173095+21	353137	Stefano Morozzi	10/2022
942	2^1170959+218945	352494	Enzo Doria	03/2024
943	2^1170915+382623	352481	Boyan Hu	08/2024
944	(63^195893-1)/62	352477	Paul Bourdelais	08/2020
945	2^1170331+27293	352305	Enzo Doria	01/2024
946	2^1170326+7	352304	Stefano Morozzi	10/2022
947	numbpart(100000135540)	352269	Serge Batalov	04/2017
948	(10^352237-1)/9/10567111/950335427	352221	Maksym Voznyy	01/2015
949	5*3^737931-2^737931	352084	Jon Grantham	08/2023
950	2^1168851+223613	351860	Enzo Doria	06/2024
951	2^1168554+783529	351770	Enzo Doria	01/2017
952	(2^1168183-1)/54763676838381762583	351639	Matthias Wurtinger	01/2011
953	2^1166950+30409	351287	Enzo Doria	03/2024
954	2^1166563+223103	351171	Enzo Doria	05/2024
955	2^1166248+38251	351076	Enzo Doria	11/2024
956	2^1166152+1882411	351047	Enzo Doria	12/2016
957	2^1163972+20971	350391	Enzo Doria	08/2023
958	2^1163272+22411	350180	Enzo Doria	10/2023
959	10^350071+7	350072	Alfred Reich	05/2021
960	2^1162154+1890207	349844	Enzo Doria	08/2017
961	2^1161076+25	349519	Henri Lifchitz	01/2025
962	(7*10^348724-61)/9	348724	Erik Branger	09/2016
963	(4*10^348453+41)/9	348453	Serge Batalov	11/2022
964	(127^165601-1)/126	348390	Alexander Zhirkov	09/2015
965	2^1155085+213377	347716	Enzo Doria	09/2023
966	2^1153083+1883693	347113	Enzo Doria	04/2017
967	2^1152186+225529	346843	Enzo Doria	07/2024
968	2^1151782+42979	346721	Enzo Doria	02/2025
969	2^1151754+41599	346713	Enzo Doria	02/2025
970	(2^1148729+2^574365+1)/5	345802	Borys Jaworski	03/2007
971	(19*10^345503+53)/9	345504	Rytis Slatkevicius	12/2024
972	2^1145882+80779	344945	Enzo Doria	09/2016
973	2^1143425+221177	344206	Enzo Doria	03/2024
974	2^1141813+27047	343720	Enzo Doria	12/2023
975	2^1141114+221869	343510	Enzo Doria	04/2024
976	2^1139423+231083	343001	Enzo Doria	01/2025
977	2^1138296+27541	342662	Enzo Doria	01/2024
978	2^1136462+1887289	342110	Enzo Doria	05/2017
979	F(1636007)	341905	Henri Lifchitz	03/2009
980	(2^1135567+13)/3	341840	Stefano Morozzi	09/2022
981	2^1134873+223637	341631	Enzo Doria	06/2024
982	2^1133678+782569	341272	Enzo Doria	11/2016
983	(11^327001+1)/12	340536	Paul Bourdelais	09/2013
984	2^1129965+223667	340154	Enzo Doria	06/2024
985	2^1129361+221597	339972	Enzo Doria	04/2024
986	2^1128706+225529	339775	Enzo Doria	07/2024
987	2^1128621+25919	339749	Enzo Doria	12/2023
988	2^1127479+234083	339405	Enzo Doria	03/2025
989	(2^1127239+2^563620+1)/5	339333	Borys Jaworski	11/2006
990	Tau(907^20848)	339132	Nik Lygeros / Olivier Rozier	01/2016
991	2^1126380-3	339075	Paul Bourdelais	06/2019
992	2^1125784+24331	338895	Enzo Doria	10/2023
993	2^1125446+1885099	338794	Enzo Doria	08/2017
994	(63^188147+1)/64	338539	Paul Bourdelais	12/2020
995	2^1124549+143807	338523	Enzo Doria	10/2016
996	(4*10^338476+23)/9	338476	Serge Batalov	11/2022
997	2^1121187+1886783	337511	Enzo Doria	04/2017
998	(48^200443-1)/47	336992	Paul Bourdelais	08/2020
999	(2*10^336405+43)/9	336405	Rytis Slatkevicius	01/2023
1000	(94^170371-1)/93	336162	Paul Bourdelais	09/2020

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Probable Primes Top 10000

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