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	2^1443089+60227	434414	Enzo Doria	10/2017
752	(21^328129-1)/20	433858	Paul Bourdelais	06/2014
753	(35^280979+1)/36	433850	Paul Bourdelais	09/2021
754	2^1439822+51799	433430	Enzo Doria	11/2025
755	2^1438663+214175	433081	Enzo Doria	11/2023
756	2^1436073+241547	432302	Enzo Doria	10/2025
757	2^1434519+215813	431834	Enzo Doria	01/2024
758	2^1434400+3	431798	Paul Bourdelais	06/2019
759	2^1434298+31669	431767	Enzo Doria	08/2024
760	2^1434097+215207	431707	Enzo Doria	11/2023
761	2^1433033+212987	431386	Enzo Doria	10/2023
762	2^1432308+1888801	431168	Enzo Doria	10/2017
763	(2^1430131+1)/(335646873253736519993971459)	430487	Gord Palameta	12/2018
764	2^1429978+233839	430467	Enzo Doria	04/2025
765	(7^508867-2^508867)/5	430042	Jon Grantham	08/2023
766	2^1428489+25097	430019	Enzo Doria	11/2023
767	2^1425595+237413	429147	Enzo Doria	07/2025
768	2^1425483+1886813	429114	Enzo Doria	04/2017
769	(63^238481+1)/64	429107	Paul Bourdelais	12/2020
770	(((91969+1)/2)^91969+((91969-1)/2)^91969)/(91969^2)	428807	Henri Lifchitz	11/2025
771	(17^348259+1)/18	428514	Paul Bourdelais	05/2014
772	2^1422688+24391	428272	Enzo Doria	12/2023
773	2^1422654+226249	428262	Enzo Doria	09/2024
774	2^1421514+2351163	427919	Enzo Doria	05/2025
775	(10^427912+89)/9	427912	Serge Batalov	12/2014
776	2^1421311+40613	427858	Enzo Doria	01/2025
777	2^1421089+1890167	427791	Enzo Doria	09/2017
778	2^1420902+221149	427735	Enzo Doria	05/2024
779	2^1418388+25771	426978	Enzo Doria	12/2023
780	2^1416724+214981	426477	Enzo Doria	11/2023
781	(96228^85849-1)/(96228^293-1)	426352	Ryan Propper	11/2023
782	2^1414012+36991	425661	Enzo Doria	09/2024
783	2^1413774+49789	425589	Enzo Doria	10/2025
784	2^1413721+225269	425573	Enzo Doria	10/2024
785	2^1412006+233899	425057	Enzo Doria	04/2025
786	20^326600+3	424917	Paul Bourdelais	01/2021
787	2^1411443+228023	424887	Enzo Doria	11/2024
788	(10^424861-7)/3	424861	Leonid Durman	01/2012
789	10^424821-11	424821	Mischa Rodermond	04/2023
790	(2^1411200+13)/7	424813	Stefano Morozzi	09/2022
791	2^1411117+35927	424789	Enzo Doria	09/2024
792	2^1410894+219859	424722	Enzo Doria	03/2024
793	2^1410310+30409	424546	Enzo Doria	05/2024
794	2^1410233+218447	424523	Enzo Doria	03/2024
795	2^1408670+238579	424052	Enzo Doria	09/2025
796	2^1408457+232007	423988	Enzo Doria	02/2025
797	2^1407515+241883	423705	Enzo Doria	11/2025
798	2^1407208+45751	423612	Enzo Doria	06/2025
799	2^1406408+50371	423371	Enzo Doria	09/2025
800	2^1405715-1405715^2	423163	Henri Lifchitz	03/2025
801	1+3^605376+5^605376	423140	Jon Grantham	08/2023
802	2^1405367+213413	423058	Enzo Doria	10/2023
803	2^1404213+184217	422711	Enzo Doria	09/2017
804	2^1403156+40921	422393	Enzo Doria	02/2025
805	2^1402886+50629	422311	Enzo Doria	12/2025
806	2^1401872+1884385	422006	Enzo Doria	04/2017
807	2^1401257+6077	421821	Enzo Doria	09/2017
808	2^1400648+44881	421638	Enzo Doria	05/2025
809	138^196873-137^196873	421285	Jean-Louis Charton	12/2009
810	2^1398726+7	421059	Stefano Morozzi	10/2022
811	2^1398269+131595	420921	Makoto Morimoto	10/2013
812	2^1398238+227119	420912	Enzo Doria	10/2024
813	2^1398062+40639	420859	Enzo Doria	01/2025
814	2^1398016+229357	420845	Enzo Doria	02/2025
815	2^1397089-1397089	420566	Henri Lifchitz	10/2024
816	2^1397071+684443	420561	Enzo Doria	07/2017
817	953^141023-952^141023	420121	Jean-Louis Charton	10/2016
818	2^1393449+45197	419470	Enzo Doria	05/2025
819	2^1393409+52037	419458	Enzo Doria	11/2025
820	2^1393111+1867211	419369	Enzo Doria	09/2023
821	2^1392384+44371	419150	Enzo Doria	03/2025
822	2^1391771+36623	418965	Enzo Doria	09/2024
823	(3^877843-1)/2	418838	Paul Bourdelais	07/2010
824	2^1389843+53273	418385	Enzo Doria	01/2026
825	2^1389628+28651	418320	Enzo Doria	03/2024
826	2^1389064+45751	418150	Enzo Doria	06/2025
827	2^1388780+50311	418065	Enzo Doria	09/2025
828	2^1386321+60299	417325	Enzo Doria	02/2018
829	2^1386320+184531	417324	Enzo Doria	09/2017
830	2^1382074+1883587	416046	Enzo Doria	01/2017
831	2^1380651+215843	415618	Enzo Doria	12/2023
832	2^1380634+40639	415613	Enzo Doria	01/2025
833	2^1379907+1885223	415394	Enzo Doria	03/2017
834	2^1379815+47333	415366	Enzo Doria	07/2025
835	2^1379792+45421	415359	Enzo Doria	06/2025
836	2^1379111+29693	415154	Enzo Doria	05/2024
837	2^1377927+45083	414798	Enzo Doria	06/2025
838	2^1377501+46427	414670	Enzo Doria	07/2025
839	2^1376707+25763	414431	Enzo Doria	12/2023
840	2^1376534+54913	414379	Enzo Doria	01/2026
841	2^1375751+24443	414143	Enzo Doria	12/2023
842	2^1375574+1886719	414090	Enzo Doria	04/2017
843	2^1373958+42649	413603	Enzo Doria	02/2025
844	2^1373551+49343	413481	Enzo Doria	08/2025
845	2^1373111+1884833	413348	Enzo Doria	02/2017
846	2^1372996+15	413313	Stefano Morozzi	10/2022
847	2^1372515+32393	413169	Enzo Doria	05/2024
848	2^1372092+228751	413041	Enzo Doria	11/2024
849	2^1372033+238427	413024	Enzo Doria	07/2025
850	2^1370877+38747	412676	Enzo Doria	11/2024
851	2^1369291+40943	412198	Enzo Doria	02/2025
852	2^1369207+36833	412173	Enzo Doria	10/2024
853	2^1369171+216593	412162	Enzo Doria	01/2024
854	2^1368632+1889731	412000	Enzo Doria	10/2017
855	(65245^85849-1)/(65245^293-1)	411914	Ryan Propper	11/2023
856	(89*10^411590+1)/9	411591	Serge Batalov	09/2014
857	F(1968721)	411439	Henri Lifchitz	11/2009
858	2^1366066+683749	411227	Enzo Doria	02/2017
859	2^1365324+233341	411004	Enzo Doria	03/2025
860	2^1365077+228257	410930	Enzo Doria	11/2024
861	2^1364401+217727	410726	Enzo Doria	02/2024
862	2^1364303+219533	410697	Enzo Doria	03/2024
863	2^1363802+51169	410546	Enzo Doria	10/2025
864	2^1363434+27589	410435	Enzo Doria	02/2024
865	2^1363068+222631	410325	Enzo Doria	06/2024
866	2^1360101+51287	409432	Enzo Doria	10/2025
867	2^1359550+25819	409266	Enzo Doria	12/2023
868	2^1359515+236423	409255	Enzo Doria	05/2025
869	2^1357392+224401	408616	Enzo Doria	06/2024
870	2^1355826+15	408145	Stefano Morozzi	10/2022
871	2^1355790+1888939	408134	Enzo Doria	07/2017
872	2^1355635+1884203	408087	Enzo Doria	01/2017
873	(22071^94249-1)/(22071^307-1)	408068	Ryan Propper	11/2023
874	2^1355083+221603	407921	Enzo Doria	05/2024
875	2^1355041+239777	407908	Enzo Doria	08/2025
876	2^1351989+36587	406990	Enzo Doria	09/2024
877	2^1351675+231083	406895	Enzo Doria	02/2025
878	2^1349535+218783	406251	Enzo Doria	03/2024
879	(55766^85849-1)/(55766^293-1)	406081	Ryan Propper	11/2023
880	2^1348956+24241	406077	Enzo Doria	11/2023
881	(88^208739+1)/89	405888	Paul Bourdelais	12/2020
882	(2^1347781-2^673891+1)/5	405722	Borys Jaworski	10/2008
883	2^1347744-3	405712	Paul Bourdelais	07/2019
884	2^1347546+39133	405652	Enzo Doria	12/2024
885	2^1346431+691203	405317	Boyan Hu	09/2024
886	82358^82358+2025^2025	404848	Henri Lifchitz	01/2025
887	9*10^404644-11	404645	Mischa Rodermond	04/2023
888	2^1343509+237947	404437	Enzo Doria	07/2025
889	1215^131072+242^131072	404302	Kellen Shenton	08/2022
890	2^1341908+212911	403955	Enzo Doria	09/2023
891	2^1341625+226187	403870	Enzo Doria	09/2024
892	2^1340881+53255	403646	Enzo Doria	01/2026
893	2^1340284+43801	403466	Enzo Doria	04/2025
894	2^1340172+240991	403432	Enzo Doria	10/2025
895	1196^131072+595^131072	403405	Kellen Shenton	08/2022
896	2^1339302+29389	403171	Enzo Doria	04/2024
897	2^1335130+31669	401915	Enzo Doria	07/2024
898	2^1333062+236449	401292	Enzo Doria	07/2025
899	2^1330791+46763	400609	Enzo Doria	06/2025
900	2^1330712+45631	400585	Enzo Doria	05/2025
901	2^1330388+38527	400487	Enzo Doria	11/2024
902	2^1330371+28313	400482	Enzo Doria	03/2024
903	10^400310+9	400311	Boyan Hu	06/2025
904	10^400000+1415223	400001	Patrick De Geest	10/2020
905	10^400000-339233	400000	Patrick De Geest	10/2020
906	2^1327766+48019	399698	Enzo Doria	06/2025
907	2^1323373+27317	398375	Enzo Doria	01/2024
908	Tau(863^24630)	397727	Nik Lygeros / Olivier Rozier	01/2016
909	2^1320423+24293	397487	Enzo Doria	11/2023
910	2^1320057+211517	397377	Enzo Doria	08/2023
911	2^1319770+1884949	397291	Enzo Doria	06/2017
912	2^1319616+30091	397244	Enzo Doria	04/2024
913	2^1317657+31367	396655	Enzo Doria	04/2024
914	2^1316848+43021	396411	Enzo Doria	02/2025
915	2^1316687+45983	396363	Enzo Doria	05/2025
916	2^1315753+226187	396082	Enzo Doria	09/2024
917	2^1314741+219257	395777	Enzo Doria	03/2024
918	2^1313062+1888849	395272	Enzo Doria	08/2017
919	(1073516^81920+1)/(1073516^16384+1)	395236	Serge Batalov	01/2017
920	2^1312349+221177	395057	Enzo Doria	04/2024
921	(1059995^81920+1)/(1059995^16384+1)	394875	Serge Batalov	01/2017
922	2^1311618+783529	394837	Enzo Doria	01/2017
923	2^1310192+232531	394408	Enzo Doria	03/2025
924	2^1308992+28111	394046	Enzo Doria	02/2024
925	2^1308000+1883521	393748	Enzo Doria	02/2017
926	2^1307563+232133	393616	Enzo Doria	03/2025
927	2^1307324+224611	393544	Enzo Doria	07/2024
928	2^1307262+28759	393526	Enzo Doria	02/2024
929	(1009565^81920+1)/(1009565^16384+1)	393487	Serge Batalov	01/2017
930	2^1306643+47333	393339	Enzo Doria	07/2025
931	2^1305860+35461	393104	Enzo Doria	08/2024
932	(995042^81920+1)/(995042^16384+1)	393075	Serge Batalov	01/2017
933	2^1305333+47717	392945	Enzo Doria	06/2025
934	2^1305200+54571	392905	Enzo Doria	01/2026
935	(988945^81920+1)/(988945^16384+1)	392900	Serge Batalov	01/2017
936	(988823^81920+1)/(988823^16384+1)	392897	Serge Batalov	01/2017
937	(2^1304983-1)/52199321	392832	Tony Prest / Never Odd Or Even	03/2014
938	2^1304675+243713	392747	Enzo Doria	01/2026
939	(978970^81920+1)/(978970^16384+1)	392612	Serge Batalov	01/2017
940	2^1303816+38251	392488	Enzo Doria	11/2024
941	2^1303257+48527	392320	Enzo Doria	07/2025
942	2^1303102+1866409	392273	Enzo Doria	09/2017
943	2^1302818+283429	392188	Enzo Doria	01/2017
944	2^1301430+22669	391770	Enzo Doria	10/2023
945	2^1301229+222467	391709	Enzo Doria	04/2024
946	2^1300835+232523	391591	Enzo Doria	03/2025
947	(934422^81920+1)/(934422^16384+1)	391286	Serge Batalov	01/2017
948	2^1299181+1886867	391093	Enzo Doria	04/2017
949	(37^249341-1)/36	391016	Paul Bourdelais	08/2020
950	2^1298304+1882891	390829	Enzo Doria	01/2017
951	2^1297732+228721	390657	Enzo Doria	11/2024
952	2^1295728+240751	390053	Enzo Doria	09/2025
953	95196^12497+12497^95196	390000	Hans Havermann	12/2021
954	2^1295539+35633	389997	Enzo Doria	08/2024
955	86206^33381+33381^86206	389953	Hans Havermann	05/2023
956	2^1294976+236731	389827	Enzo Doria	06/2025
957	2^1294324+25171	389631	Enzo Doria	12/2023
958	2^1294298+243649	389623	Enzo Doria	01/2026
959	(874207^81920+1)/(874207^16384+1)	389390	Serge Batalov	01/2017
960	2^1292338+229249	389033	Enzo Doria	11/2024
961	2^1289624+32551	388216	Enzo Doria	05/2024
962	2^1286857+37967	387383	Enzo Doria	10/2024
963	2^1285458+46159	386962	Enzo Doria	06/2025
964	2^1285456+230611	386961	Enzo Doria	01/2025
965	(7^457871-5^457871)/2	386946	Jon Grantham	08/2023
966	79455^73828+73828^79455	386805	Hans Havermann	03/2023
967	81650^54369+54369^81650	386642	Yusuf AttarBashi	06/2021
968	80565^62824+62824^80565	386561	Hans Havermann	08/2021
969	83747^41272+41272^83747	386548	Hans Havermann	08/2021
970	15^328574+328574^15	386434	Serge Batalov	05/2014
971	2^1283304+53551	386313	Enzo Doria	01/2026
972	2^1282676+30493	386124	Enzo Doria	12/2024
973	2^1280078+1885099	385342	Enzo Doria	08/2017
974	2^1279921+17	385295	Stefano Morozzi	10/2022
975	2^1279245+224087	385092	Enzo Doria	07/2024
976	2^1278091+47963	384744	Enzo Doria	07/2025
977	2^1277980+231391	384711	Enzo Doria	01/2025
978	2^1277688+231241	384623	Enzo Doria	01/2025
979	2^1277142+234979	384459	Enzo Doria	04/2025
980	2^1276977+71657	384409	Enzo Doria	08/2023
981	(76803^78961-1)/(76803^281-1)	384382	Ryan Propper	11/2023
982	2^1276571+26213	384287	Enzo Doria	12/2023
983	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
984	2^1274941+1880717	383796	Enzo Doria	10/2016
985	2^1272632+383431	383101	Enzo Doria	01/2017
986	2^1271346+1889839	382714	Enzo Doria	08/2017
987	2^1271173+219587	382662	Enzo Doria	03/2024
988	2^1266263+239783	381184	Enzo Doria	09/2025
989	5*3^798534-2^798534	380999	Jon Grantham	08/2023
990	(10^380976-7)/3	380976	Leonid Durman	01/2012
991	2^1264748+23221	380728	Enzo Doria	11/2023
992	(4*10^380056+11)/3	380057	Tyler Busby	03/2023
993	2^1262504+242821	380052	Enzo Doria	12/2025
994	2^1262431+228353	380030	Enzo Doria	11/2024
995	2^1260859+222683	379557	Enzo Doria	06/2024
996	2^1258313+43727	378790	Enzo Doria	03/2025
997	2^1257787+1447761	378632	Makoto Morimoto	10/2013
998	(2^1257787+32270)/(223328122073011)	378620	Makoto Morimoto	12/2016
999	2^1257728+20851	378614	Enzo Doria	08/2023
1000	(77^200657-1)/76	378536	Paul Bourdelais	08/2020

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