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	2^1320057+211517	397377	Enzo Doria	08/2023
752	2^1319770+1884949	397291	Enzo Doria	06/2017
753	2^1319616+30091	397244	Enzo Doria	04/2024
754	2^1317657+31367	396655	Enzo Doria	04/2024
755	2^1316848+43021	396411	Enzo Doria	02/2025
756	2^1315753+226187	396082	Enzo Doria	09/2024
757	2^1314741+219257	395777	Enzo Doria	03/2024
758	2^1313062+1888849	395272	Enzo Doria	08/2017
759	(1073516^81920+1)/(1073516^16384+1)	395236	Serge Batalov	01/2017
760	2^1312349+221177	395057	Enzo Doria	04/2024
761	(1059995^81920+1)/(1059995^16384+1)	394875	Serge Batalov	01/2017
762	2^1311618+783529	394837	Enzo Doria	01/2017
763	2^1310192+232531	394408	Enzo Doria	03/2025
764	2^1308992+28111	394046	Enzo Doria	02/2024
765	2^1308000+1883521	393748	Enzo Doria	02/2017
766	2^1307563+232133	393616	Enzo Doria	03/2025
767	2^1307324+224611	393544	Enzo Doria	07/2024
768	2^1307262+28759	393526	Enzo Doria	02/2024
769	(1009565^81920+1)/(1009565^16384+1)	393487	Serge Batalov	01/2017
770	2^1305860+35461	393104	Enzo Doria	08/2024
771	(995042^81920+1)/(995042^16384+1)	393075	Serge Batalov	01/2017
772	(988945^81920+1)/(988945^16384+1)	392900	Serge Batalov	01/2017
773	(988823^81920+1)/(988823^16384+1)	392897	Serge Batalov	01/2017
774	(2^1304983-1)/52199321	392832	Tony Prest / Never Odd Or Even	03/2014
775	(978970^81920+1)/(978970^16384+1)	392612	Serge Batalov	01/2017
776	2^1303816+38251	392488	Enzo Doria	11/2024
777	2^1303102+1866409	392273	Enzo Doria	09/2017
778	2^1302818+283429	392188	Enzo Doria	01/2017
779	2^1301430+22669	391770	Enzo Doria	10/2023
780	2^1301229+222467	391709	Enzo Doria	04/2024
781	2^1300835+232523	391591	Enzo Doria	03/2025
782	(934422^81920+1)/(934422^16384+1)	391286	Serge Batalov	01/2017
783	2^1299181+1886867	391093	Enzo Doria	04/2017
784	(37^249341-1)/36	391016	Paul Bourdelais	08/2020
785	2^1298304+1882891	390829	Enzo Doria	01/2017
786	2^1297732+228721	390657	Enzo Doria	11/2024
787	95196^12497+12497^95196	390000	Hans Havermann	12/2021
788	2^1295539+35633	389997	Enzo Doria	08/2024
789	86206^33381+33381^86206	389953	Hans Havermann	05/2023
790	2^1294324+25171	389631	Enzo Doria	12/2023
791	(874207^81920+1)/(874207^16384+1)	389390	Serge Batalov	01/2017
792	2^1292338+229249	389033	Enzo Doria	11/2024
793	2^1289624+32551	388216	Enzo Doria	05/2024
794	2^1286857+37967	387383	Enzo Doria	10/2024
795	2^1285456+230611	386961	Enzo Doria	01/2025
796	(7^457871-5^457871)/2	386946	Jon Grantham	08/2023
797	79455^73828+73828^79455	386805	Hans Havermann	03/2023
798	81650^54369+54369^81650	386642	Yusuf AttarBashi	06/2021
799	80565^62824+62824^80565	386561	Hans Havermann	08/2021
800	83747^41272+41272^83747	386548	Hans Havermann	08/2021
801	15^328574+328574^15	386434	Serge Batalov	05/2014
802	2^1282676+30493	386124	Enzo Doria	12/2024
803	2^1280078+1885099	385342	Enzo Doria	08/2017
804	2^1279921+17	385295	Stefano Morozzi	10/2022
805	2^1279245+224087	385092	Enzo Doria	07/2024
806	2^1277980+231391	384711	Enzo Doria	01/2025
807	2^1277688+231241	384623	Enzo Doria	01/2025
808	2^1277142+234979	384459	Enzo Doria	04/2025
809	2^1276977+71657	384409	Enzo Doria	08/2023
810	(76803^78961-1)/(76803^281-1)	384382	Ryan Propper	11/2023
811	2^1276571+26213	384287	Enzo Doria	12/2023
812	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
813	2^1274941+1880717	383796	Enzo Doria	10/2016
814	2^1272632+383431	383101	Enzo Doria	01/2017
815	2^1271346+1889839	382714	Enzo Doria	08/2017
816	2^1271173+219587	382662	Enzo Doria	03/2024
817	5*3^798534-2^798534	380999	Jon Grantham	08/2023
818	(10^380976-7)/3	380976	Leonid Durman	01/2012
819	2^1264748+23221	380728	Enzo Doria	11/2023
820	(4*10^380056+11)/3	380057	Tyler Busby	03/2023
821	2^1262431+228353	380030	Enzo Doria	11/2024
822	2^1260859+222683	379557	Enzo Doria	06/2024
823	2^1258313+43727	378790	Enzo Doria	03/2025
824	2^1257787+1447761	378632	Makoto Morimoto	10/2013
825	(2^1257787+32270)/(223328122073011)	378620	Makoto Morimoto	12/2016
826	2^1257728+20851	378614	Enzo Doria	08/2023
827	(77^200657-1)/76	378536	Paul Bourdelais	08/2020
828	2^1254797+229487	377732	Enzo Doria	11/2024
829	(98^189619+1)/99	377573	Paul Bourdelais	02/2021
830	F(1803059)	376817	Henri Lifchitz	06/2009
831	2^1250590+29389	376466	Enzo Doria	03/2024
832	(10^376417-3^376417)/7	376417	Jon Grantham	08/2023
833	2^1250116+34951	376323	Enzo Doria	08/2024
834	2^1246724+213961	375302	Enzo Doria	10/2023
835	2^1245230+19	374852	Stefano Morozzi	10/2022
836	2^1244263+230033	374561	Enzo Doria	01/2025
837	7^442674+4	374103	Paul Bourdelais	02/2021
838	2^1239151+35633	373022	Enzo Doria	08/2024
839	2^1238732+39181	372896	Enzo Doria	11/2024
840	2^1237699+34703	372585	Enzo Doria	07/2024
841	(97^187393-1)/96	372306	Paul Bourdelais	09/2020
842	10^371696+7	371697	Alfred Reich	05/2021
843	2^1234709+883127	371685	Enzo Doria	12/2016
844	2^1234119+21803	371507	Enzo Doria	09/2023
845	(67^203431+1)/68	371479	Paul Bourdelais	09/2021
846	2^1233971+216593	371463	Enzo Doria	12/2023
847	2^1233212+27301	371234	Enzo Doria	12/2023
848	2^1231466+283819	370709	Enzo Doria	07/2017
849	2^1229766+26659	370197	Enzo Doria	12/2023
850	2^1228899+30713	369936	Enzo Doria	03/2024
851	2^1228892+223831	369934	Enzo Doria	06/2024
852	(49627^78961-1)/(49627^281-1)	369460	Ryan Propper	11/2023
853	2^1227060+226663	369382	Enzo Doria	09/2024
854	2^1226987+28163	369360	Enzo Doria	02/2024
855	2^1226725+234887	369282	Enzo Doria	04/2025
856	2^1226569+30857	369235	Enzo Doria	03/2024
857	73^197880+197880	368715	Kellen Shenton	06/2023
858	5*3^771723-2^771723	368207	Jon Grantham	08/2023
859	2^1222741+231707	368082	Enzo Doria	02/2025
860	2^1222473+221597	368002	Enzo Doria	04/2024
861	2^1222211+22703	367923	Enzo Doria	11/2023
862	(2^1222097+19)/3	367888	Stefano Morozzi	09/2022
863	2^1220335+1881263	367358	Enzo Doria	11/2016
864	2^1218344+215641	366759	Enzo Doria	12/2023
865	2^1217510+220039	366508	Enzo Doria	03/2024
866	2^1217500+226321	366505	Enzo Doria	09/2024
867	(233^154787-1)/232	366434	Anonymous	05/2024
868	2^1216694+1884769	366262	Enzo Doria	02/2017
869	2^1215889-3	366020	Paul Bourdelais	06/2019
870	2^1215296+1885441	365841	Enzo Doria	03/2017
871	(80^192133+1)/81	365645	Paul Bourdelais	01/2021
872	2^1214307+1888115	365543	Enzo Doria	05/2017
873	2^1213815+3	365395	Paul Bourdelais	06/2019
874	(80^191953+1)/81	365302	Paul Bourdelais	01/2021
875	2^1213313+215837	365244	Enzo Doria	11/2023
876	2^1208276+22201	363728	Enzo Doria	09/2023
877	2^1207345+1882577	363448	Enzo Doria	12/2016
878	2^1207336+217801	363445	Enzo Doria	03/2024
879	2^1207073+883727	363366	Enzo Doria	03/2017
880	3^761457-2	363308	Ryan Propper	07/2015
881	(10^363030+7)/337/443	363025	Alfred Reich	12/2021
882	2^1204869+224885	362702	Enzo Doria	07/2024
883	2^1203721+44117	362357	Enzo Doria	04/2025
884	2^1200972+141811	361529	Stefano Morozzi	10/2022
885	(2^1200924+324730)/2	361514	Stefano Morozzi	06/2021
886	(2^1200912+274110)/2	361511	Stefano Morozzi	01/2021
887	2^1200906+165249	361509	Stefano Morozzi	07/2022
888	2^1200890+166339	361504	Stefano Morozzi	01/2023
889	(2^1200887+344126)/2	361503	Stefano Morozzi	10/2020
890	2^1200877+186755	361500	Stefano Morozzi	09/2022
891	2^1200861+198521	361496	Stefano Morozzi	11/2021
892	(2^1200856+305790)/2	361494	Stefano Morozzi	10/2020
893	(2^1200853+372822)/2	361493	Stefano Morozzi	06/2021
894	2^1200812+324178)/2	361481	Stefano Morozzi	06/2021
895	(2^1200768+380458)/2	361467	Stefano Morozzi	01/2021
896	2^1200756+140917	361464	Stefano Morozzi	05/2022
897	2^1200741+184781	361460	Stefano Morozzi	09/2022
898	(2^1200741+293402)/2	361459	Stefano Morozzi	07/2021
899	2^1200734+142653	361457	Stefano Morozzi	02/2023
901	2^1200672+1880881	361439	Enzo Doria	10/2016
900	2^1200672+141535	361439	Stefano Morozzi	09/2022
902	2^1200669+178805	361438	Stefano Morozzi	11/2022
903	2^1200660+198555	361435	Stefano Morozzi	12/2021
904	2^1200657+164837	361434	Stefano Morozzi	05/2022
905	2^1200631+166431	361426	Stefano Morozzi	02/2023
906	2^1200627+150669	361425	Stefano Morozzi	02/2023
907	(2^1200603+356030)/2	361418	Stefano Morozzi	10/2020
908	(2^1200590+275854)/2	361414	Stefano Morozzi	03/2021
909	2^1200550+139297	361402	Stefano Morozzi	10/2021
910	2^1200486+172855	361383	Stefano Morozzi	01/2023
911	(2^1200456+320526)/2	361373	Stefano Morozzi	10/2020
912	2^1200443+142121	361370	Stefano Morozzi	01/2023
913	2^1200416+164065	361362	Stefano Morozzi	01/2022
914	2^1200331+155429	361336	Stefano Morozzi	10/2021
916	(2^1200289+348366)/2	361323	Stefano Morozzi	10/2020
915	2^1200289+141885	361323	Stefano Morozzi	11/2022
917	(2^1200284+273162)/2	361322	Stefano Morozzi	10/2020
918	2^1200252+194535	361312	Stefano Morozzi	11/2021
919	(2^1200250+364230)/2	361311	Stefano Morozzi	10/2020
920	2^1200227+156881	361305	Stefano Morozzi	05/2022
921	(2^1200209+305990)/2	361299	Stefano Morozzi	10/2020
922	(2^1200210+376278)/2	361299	Stefano Morozzi	10/2020
923	2^1200202+216499	361297	Enzo Doria	12/2023
924	(2^1200182+274462)/2	361291	Stefano Morozzi	01/2021
925	2^1200178+149193	361290	Stefano Morozzi	07/2022
926	2^1200168+140403	361287	Stefano Morozzi	03/2022
927	(2^1200162+275910)/2	361285	Stefano Morozzi	03/2021
928	2^1200157+168927	361284	Stefano Morozzi	02/2023
929	2^1200134+141385	361277	Stefano Morozzi	08/2022
930	(2^1200131+360150)/2	361276	Stefano Morozzi	10/2020
931	(2^1200118+290718)/2	361272	Stefano Morozzi	01/2021
932	2^1200022+192777	361243	Stefano Morozzi	09/2022
933	2^1200021+149777	361243	Stefano Morozzi	10/2022
934	(64*10^360173-1)/243	360173	Serge Batalov	09/2014
935	(59^203309+1)/60	360029	Paul Bourdelais	09/2021
936	(2*10^359860-11)/9	359860	Rytis Slatkevicius	01/2023
937	2^1195093+1882577	359759	Enzo Doria	12/2016
938	3^753451+5*2^753451	359488	Jon Grantham	08/2023
939	2^1192258+36739	358906	Enzo Doria	09/2024
940	(6^461108-11)/5	358812	Paul Bourdelais	04/2019
941	2^1191375+8543	358640	Phil Moore	06/2008
942	2^1190972+1880191	358519	Enzo Doria	11/2016
943	2^1189930+28549	358205	Enzo Doria	03/2024
944	(45^216551-1)/44	358004	Paul Bourdelais	08/2020
945	2^1187005+230807	357325	Enzo Doria	01/2025
946	(50^210319-1)/49	357324	Paul Bourdelais	08/2020
947	(531^131072+25^131072)/2	357184	Kellen Shenton	03/2021
948	2^1186366+226747	357132	Enzo Doria	09/2024
949	2^1184565+21227	356590	Enzo Doria	08/2023
950	2^1180312+44173	355310	Enzo Doria	04/2025
951	2^1180159+22823	355264	Enzo Doria	11/2023
952	2^1179836+1885021	355167	Enzo Doria	02/2017
953	2^1178942+32269	354897	Enzo Doria	04/2024
954	2^1178474+43369	354757	Enzo Doria	03/2025
955	2^1177053+28607	354329	Enzo Doria	02/2024
956	2^1177027+234863	354321	Enzo Doria	04/2025
957	(19*10^353884-91)/9	353885	Alfred Reich	02/2023
958	(10^353884*19-91)/9	353885	Alfred Reich	10/2023
959	20^271951+3	353817	Paul Bourdelais	01/2021
960	72722^72722+7^7	353551	Serge Batalov	04/2024
961	2^1173095+21	353137	Stefano Morozzi	10/2022
962	2^1170959+218945	352494	Enzo Doria	03/2024
963	2^1170915+382623	352481	Boyan Hu	08/2024
964	(63^195893-1)/62	352477	Paul Bourdelais	08/2020
965	2^1170331+27293	352305	Enzo Doria	01/2024
966	2^1170326+7	352304	Stefano Morozzi	10/2022
967	numbpart(100000135540)	352269	Serge Batalov	04/2017
968	(10^352237-1)/9/10567111/950335427	352221	Maksym Voznyy	01/2015
969	5*3^737931-2^737931	352084	Jon Grantham	08/2023
970	2^1168851+223613	351860	Enzo Doria	06/2024
971	2^1168554+783529	351770	Enzo Doria	01/2017
972	(2^1168183-1)/54763676838381762583	351639	Matthias Wurtinger	01/2011
973	2^1166950+30409	351287	Enzo Doria	03/2024
974	2^1166563+223103	351171	Enzo Doria	05/2024
975	2^1166248+38251	351076	Enzo Doria	11/2024
976	2^1166152+1882411	351047	Enzo Doria	12/2016
977	2^1163972+20971	350391	Enzo Doria	08/2023
978	2^1163272+22411	350180	Enzo Doria	10/2023
979	10^350071+7	350072	Alfred Reich	05/2021
980	2^1162154+1890207	349844	Enzo Doria	08/2017
981	2^1161076+25	349519	Henri Lifchitz	01/2025
982	(7*10^348724-61)/9	348724	Erik Branger	09/2016
983	(4*10^348453+41)/9	348453	Serge Batalov	11/2022
984	(127^165601-1)/126	348390	Alexander Zhirkov	09/2015
985	2^1155134+43909	347730	Enzo Doria	04/2025
986	2^1155085+213377	347716	Enzo Doria	09/2023
987	2^1153083+1883693	347113	Enzo Doria	04/2017
988	2^1152186+225529	346843	Enzo Doria	07/2024
989	2^1151782+42979	346721	Enzo Doria	02/2025
990	2^1151754+41599	346713	Enzo Doria	02/2025
991	(2^1148729+2^574365+1)/5	345802	Borys Jaworski	03/2007
992	(19*10^345503+53)/9	345504	Rytis Slatkevicius	12/2024
993	2^1145882+80779	344945	Enzo Doria	09/2016
994	2^1143425+221177	344206	Enzo Doria	03/2024
995	2^1141813+27047	343720	Enzo Doria	12/2023
996	2^1141114+221869	343510	Enzo Doria	04/2024
997	2^1139423+231083	343001	Enzo Doria	01/2025
998	2^1138296+27541	342662	Enzo Doria	01/2024
999	2^1136462+1887289	342110	Enzo Doria	05/2017
1000	F(1636007)	341905	Henri Lifchitz	03/2009

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Probable Primes Top 10000

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