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 ?
501	6^584279-5	454658	Paul Bourdelais	02/2021
502	2^1509037-13	454266	Stefano Morozzi	12/2022
503	(52^264697-1)/51	454220	Paul Bourdelais	10/2021
504	2^1507169+29027	453704	Enzo Doria	05/2024
505	2^1506029+1890167	453360	Enzo Doria	02/2018
506	2^1504232+26101	452819	Enzo Doria	01/2024
507	2^1498015+219113	450948	Enzo Doria	03/2024
508	2^1497532+220471	450803	Enzo Doria	04/2024
509	2^1497369+216977	450753	Enzo Doria	01/2024
510	(34^294277+1)/35	450678	Paul Bourdelais	06/2018
511	2^1495434+1890439	450171	Enzo Doria	12/2017
512	2^1495078+227779	450064	Enzo Doria	10/2024
513	2^1494634+7	449930	Stefano Morozzi	10/2022
514	2^1493170+784129	449489	Enzo Doria	08/2017
515	2^1489873+1888277	448497	Enzo Doria	06/2017
516	2^1487389+32417	447749	Enzo Doria	06/2024
517	2^1486846+36019	447586	Enzo Doria	11/2024
518	2^1485471+224789	447172	Enzo Doria	09/2024
519	2^1485203+71663	447091	Enzo Doria	09/2023
520	2^1484671+1888463	446931	Enzo Doria	06/2017
521	2^1483112+23961	446462	Enzo Doria	12/2023
522	2^1482867+1886783	446388	Enzo Doria	04/2017
523	2^1482148+284011	446172	Enzo Doria	04/2017
524	2^1481363+215843	445935	Enzo Doria	12/2023
525	2^1480415+217643	445650	Enzo Doria	02/2024
526	2^1480400+225013	445645	Enzo Doria	10/2024
527	2^1479356+1888291	445331	Enzo Doria	06/2017
528	(157742^85849-1)/(157742^293-1)	444716	Ryan Propper	11/2023
529	2^1476810+23299	444565	Enzo Doria	12/2023
530	2^1474222+38569	443786	Enzo Doria	11/2024
531	2^1474189+36557	443776	Enzo Doria	11/2024
532	2^1473184+212671	443473	Enzo Doria	09/2023
533	2^1472225+37997	443184	Enzo Doria	10/2024
534	2^1466432+20371	441441	Enzo Doria	08/2023
535	14^384558+3	440753	Paul Bourdelais	01/2021
536	2^1463913+219047	440682	Enzo Doria	04/2024
537	2^1461244+784531	439879	Enzo Doria	10/2017
538	2^1461058+34429	439823	Enzo Doria	08/2024
539	2^1459599+215813	439384	Enzo Doria	01/2024
540	2^1457449+25757	438736	Enzo Doria	12/2023
541	3^919094+5*2^919094	438520	Jon Grantham	08/2023
542	2^1456277+28229	438384	Enzo Doria	03/2024
543	2^1455129+218027	438038	Enzo Doria	01/2024
544	2^1454061+216977	437716	Enzo Doria	01/2024
545	2^1453419+26783	437523	Enzo Doria	01/2024
546	(67^239053+1)/68	436527	Paul Bourdelais	09/2021
547	2^1448122+74209	435929	Enzo Doria	08/2023
548	2^1446449+221087	435425	Enzo Doria	05/2024
549	2^1446263+74333	435369	Enzo Doria	08/2023
550	2^1444386+221029	434804	Enzo Doria	03/2024
551	(80^228419+1)/81	434701	Paul Bourdelais	02/2021
552	2^1443089+60227	434414	Enzo Doria	10/2017
553	(21^328129-1)/20	433858	Paul Bourdelais	06/2014
554	(35^280979+1)/36	433850	Paul Bourdelais	09/2021
555	2^1438663+214175	433081	Enzo Doria	11/2023
556	2^1434519+215813	431834	Enzo Doria	01/2024
557	2^1434400+3	431798	Paul Bourdelais	06/2019
558	2^1434298+31669	431767	Enzo Doria	08/2024
559	2^1434097+215207	431707	Enzo Doria	11/2023
560	2^1433033+212987	431386	Enzo Doria	10/2023
561	2^1432308+1888801	431168	Enzo Doria	10/2017
562	(2^1430131+1)/(335646873253736519993971459)	430487	Gord Palameta	12/2018
563	(7^508867-2^508867)/5	430042	Jon Grantham	08/2023
564	2^1428489+25097	430019	Enzo Doria	11/2023
565	2^1425483+1886813	429114	Enzo Doria	04/2017
566	(63^238481+1)/64	429107	Paul Bourdelais	12/2020
567	(17^348259+1)/18	428514	Paul Bourdelais	05/2014
568	2^1422688+24391	428272	Enzo Doria	12/2023
569	2^1422654+226249	428262	Enzo Doria	09/2024
570	(10^427912+89)/9	427912	Serge Batalov	12/2014
571	2^1421089+1890167	427791	Enzo Doria	09/2017
572	2^1420902+221149	427735	Enzo Doria	05/2024
573	2^1418388+25771	426978	Enzo Doria	12/2023
574	2^1416724+214981	426477	Enzo Doria	11/2023
575	(96228^85849-1)/(96228^293-1)	426352	Ryan Propper	11/2023
576	2^1414012+36991	425661	Enzo Doria	09/2024
577	2^1413721+225269	425573	Enzo Doria	10/2024
578	20^326600+3	424917	Paul Bourdelais	01/2021
579	2^1411443+228023	424887	Enzo Doria	11/2024
580	(10^424861-7)/3	424861	Leonid Durman	01/2012
581	10^424821-11	424821	Mischa Rodermond	04/2023
582	(2^1411200+13)/7	424813	Stefano Morozzi	09/2022
583	2^1411117+35927	424789	Enzo Doria	09/2024
584	2^1410894+219859	424722	Enzo Doria	03/2024
585	2^1410310+30409	424546	Enzo Doria	05/2024
586	2^1410233+218447	424523	Enzo Doria	03/2024
587	1+3^605376+5^605376	423140	Jon Grantham	08/2023
588	2^1405367+213413	423058	Enzo Doria	10/2023
589	2^1404213+184217	422711	Enzo Doria	09/2017
590	2^1401872+1884385	422006	Enzo Doria	04/2017
591	2^1401257+6077	421821	Enzo Doria	09/2017
592	138^196873-137^196873	421285	Jean-Louis Charton	12/2009
593	2^1398726+7	421059	Stefano Morozzi	10/2022
594	2^1398269+131595	420921	Makoto Morimoto	10/2013
595	2^1398238+227119	420912	Enzo Doria	10/2024
596	2^1397089-1397089	420566	Henri Lifchitz	10/2024
597	2^1397071+684443	420561	Enzo Doria	07/2017
598	953^141023-952^141023	420121	Jean-Louis Charton	10/2016
599	2^1393111+1867211	419369	Enzo Doria	09/2023
600	2^1391771+36623	418965	Enzo Doria	09/2024
601	(3^877843-1)/2	418838	Paul Bourdelais	07/2010
602	2^1389628+28651	418320	Enzo Doria	03/2024
603	2^1386321+60299	417325	Enzo Doria	02/2018
604	2^1386320+184531	417324	Enzo Doria	09/2017
605	2^1382074+1883587	416046	Enzo Doria	01/2017
606	2^1380651+215843	415618	Enzo Doria	12/2023
607	2^1379907+1885223	415394	Enzo Doria	03/2017
608	2^1379111+29693	415154	Enzo Doria	05/2024
609	2^1376707+25763	414431	Enzo Doria	12/2023
610	2^1375751+24443	414143	Enzo Doria	12/2023
611	2^1375574+1886719	414090	Enzo Doria	04/2017
612	2^1373111+1884833	413348	Enzo Doria	02/2017
613	2^1372996+15	413313	Stefano Morozzi	10/2022
614	2^1372515+32393	413169	Enzo Doria	05/2024
615	2^1372092+228751	413041	Enzo Doria	11/2024
616	2^1370877+38747	412676	Enzo Doria	11/2024
617	2^1369207+36833	412173	Enzo Doria	10/2024
618	2^1369171+216593	412162	Enzo Doria	01/2024
619	2^1368632+1889731	412000	Enzo Doria	10/2017
620	(65245^85849-1)/(65245^293-1)	411914	Ryan Propper	11/2023
621	(89*10^411590+1)/9	411591	Serge Batalov	09/2014
622	F(1968721)	411439	Henri Lifchitz	11/2009
623	2^1366066+683749	411227	Enzo Doria	02/2017
624	2^1365077+228257	410930	Enzo Doria	11/2024
625	2^1364401+217727	410726	Enzo Doria	02/2024
626	2^1364303+219533	410697	Enzo Doria	03/2024
627	2^1363434+27589	410435	Enzo Doria	02/2024
628	2^1363068+222631	410325	Enzo Doria	06/2024
629	2^1359550+25819	409266	Enzo Doria	12/2023
630	2^1357392+224401	408616	Enzo Doria	06/2024
631	2^1355826+15	408145	Stefano Morozzi	10/2022
632	2^1355790+1888939	408134	Enzo Doria	07/2017
633	2^1355635+1884203	408087	Enzo Doria	01/2017
634	(22071^94249-1)/(22071^307-1)	408068	Ryan Propper	11/2023
635	2^1355083+221603	407921	Enzo Doria	05/2024
636	2^1351989+36587	406990	Enzo Doria	09/2024
637	2^1349535+218783	406251	Enzo Doria	03/2024
638	(55766^85849-1)/(55766^293-1)	406081	Ryan Propper	11/2023
639	2^1348956+24241	406077	Enzo Doria	11/2023
640	(88^208739+1)/89	405888	Paul Bourdelais	12/2020
641	(2^1347781-2^673891+1)/5	405722	Borys Jaworski	10/2008
642	2^1347744-3	405712	Paul Bourdelais	07/2019
643	2^1346431+691203	405317	Boyan Hu	09/2024
644	9*10^404644-11	404645	Mischa Rodermond	04/2023
645	1215^131072+242^131072	404302	Kellen Shenton	08/2022
646	2^1341908+212911	403955	Enzo Doria	09/2023
647	2^1341625+226187	403870	Enzo Doria	09/2024
648	1196^131072+595^131072	403405	Kellen Shenton	08/2022
649	2^1339302+29389	403171	Enzo Doria	04/2024
650	2^1335130+31669	401915	Enzo Doria	07/2024
651	2^1330388+38527	400487	Enzo Doria	11/2024
652	2^1330371+28313	400482	Enzo Doria	03/2024
653	10^400000+1415223	400001	Patrick De Geest	10/2020
654	10^400000-339233	400000	Patrick De Geest	10/2020
655	2^1323373+27317	398375	Enzo Doria	01/2024
656	Tau(863^24630)	397727	Nik Lygeros / Olivier Rozier	01/2016
657	2^1320423+24293	397487	Enzo Doria	11/2023
658	2^1320057+211517	397377	Enzo Doria	08/2023
659	2^1319770+1884949	397291	Enzo Doria	06/2017
660	2^1319616+30091	397244	Enzo Doria	04/2024
661	2^1317657+31367	396655	Enzo Doria	04/2024
662	2^1315753+226187	396082	Enzo Doria	09/2024
663	2^1314741+219257	395777	Enzo Doria	03/2024
664	2^1313062+1888849	395272	Enzo Doria	08/2017
665	(1073516^81920+1)/(1073516^16384+1)	395236	Serge Batalov	01/2017
666	2^1312349+221177	395057	Enzo Doria	04/2024
667	(1059995^81920+1)/(1059995^16384+1)	394875	Serge Batalov	01/2017
668	2^1311618+783529	394837	Enzo Doria	01/2017
669	2^1308992+28111	394046	Enzo Doria	02/2024
670	2^1308000+1883521	393748	Enzo Doria	02/2017
671	2^1307324+224611	393544	Enzo Doria	07/2024
672	2^1307262+28759	393526	Enzo Doria	02/2024
673	(1009565^81920+1)/(1009565^16384+1)	393487	Serge Batalov	01/2017
674	2^1305860+35461	393104	Enzo Doria	08/2024
675	(995042^81920+1)/(995042^16384+1)	393075	Serge Batalov	01/2017
676	(988945^81920+1)/(988945^16384+1)	392900	Serge Batalov	01/2017
677	(988823^81920+1)/(988823^16384+1)	392897	Serge Batalov	01/2017
678	(2^1304983-1)/52199321	392832	Tony Prest / Never Odd Or Even	03/2014
679	(978970^81920+1)/(978970^16384+1)	392612	Serge Batalov	01/2017
680	2^1303816+38251	392488	Enzo Doria	11/2024
681	2^1303102+1866409	392273	Enzo Doria	09/2017
682	2^1302818+283429	392188	Enzo Doria	01/2017
683	2^1301430+22669	391770	Enzo Doria	10/2023
684	2^1301229+222467	391709	Enzo Doria	04/2024
685	(934422^81920+1)/(934422^16384+1)	391286	Serge Batalov	01/2017
686	2^1299181+1886867	391093	Enzo Doria	04/2017
687	(37^249341-1)/36	391016	Paul Bourdelais	08/2020
688	2^1298304+1882891	390829	Enzo Doria	01/2017
689	2^1297732+228721	390657	Enzo Doria	11/2024
690	95196^12497+12497^95196	390000	Hans Havermann	12/2021
691	2^1295539+35633	389997	Enzo Doria	08/2024
692	86206^33381+33381^86206	389953	Hans Havermann	05/2023
693	2^1294324+25171	389631	Enzo Doria	12/2023
694	(874207^81920+1)/(874207^16384+1)	389390	Serge Batalov	01/2017
695	2^1292338+229249	389033	Enzo Doria	11/2024
696	2^1289624+32551	388216	Enzo Doria	05/2024
697	2^1286857+37967	387383	Enzo Doria	10/2024
698	(7^457871-5^457871)/2	386946	Jon Grantham	08/2023
699	79455^73828+73828^79455	386805	Hans Havermann	03/2023
700	81650^54369+54369^81650	386642	Yusuf AttarBashi	06/2021
701	80565^62824+62824^80565	386561	Hans Havermann	08/2021
702	83747^41272+41272^83747	386548	Hans Havermann	08/2021
703	15^328574+328574^15	386434	Serge Batalov	05/2014
704	2^1280078+1885099	385342	Enzo Doria	08/2017
705	2^1279921+17	385295	Stefano Morozzi	10/2022
706	2^1279245+224087	385092	Enzo Doria	07/2024
707	2^1276977+71657	384409	Enzo Doria	08/2023
708	(76803^78961-1)/(76803^281-1)	384382	Ryan Propper	11/2023
709	2^1276571+26213	384287	Enzo Doria	12/2023
710	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
711	2^1274941+1880717	383796	Enzo Doria	10/2016
712	2^1272632+383431	383101	Enzo Doria	01/2017
713	2^1271346+1889839	382714	Enzo Doria	08/2017
714	2^1271173+219587	382662	Enzo Doria	03/2024
715	5*3^798534-2^798534	380999	Jon Grantham	08/2023
716	(10^380976-7)/3	380976	Leonid Durman	01/2012
717	2^1264748+23221	380728	Enzo Doria	11/2023
718	(4*10^380056+11)/3	380057	Tyler Busby	03/2023
719	2^1262431+228353	380030	Enzo Doria	11/2024
720	2^1260859+222683	379557	Enzo Doria	06/2024
721	2^1257787+1447761	378632	Makoto Morimoto	10/2013
722	(2^1257787+32270)/(223328122073011)	378620	Makoto Morimoto	12/2016
723	2^1257728+20851	378614	Enzo Doria	08/2023
724	(77^200657-1)/76	378536	Paul Bourdelais	08/2020
725	2^1254797+229487	377732	Enzo Doria	11/2024
726	(98^189619+1)/99	377573	Paul Bourdelais	02/2021
727	F(1803059)	376817	Henri Lifchitz	06/2009
728	2^1250590+29389	376466	Enzo Doria	03/2024
729	(10^376417-3^376417)/7	376417	Jon Grantham	08/2023
730	2^1250116+34951	376323	Enzo Doria	08/2024
731	2^1246724+213961	375302	Enzo Doria	10/2023
732	2^1245230+19	374852	Stefano Morozzi	10/2022
733	7^442674+4	374103	Paul Bourdelais	02/2021
734	2^1239151+35633	373022	Enzo Doria	08/2024
735	2^1238732+39181	372896	Enzo Doria	11/2024
736	2^1237699+34703	372585	Enzo Doria	07/2024
737	(97^187393-1)/96	372306	Paul Bourdelais	09/2020
738	10^371696+7	371697	Alfred Reich	05/2021
739	2^1234709+883127	371685	Enzo Doria	12/2016
740	2^1234119+21803	371507	Enzo Doria	09/2023
741	(67^203431+1)/68	371479	Paul Bourdelais	09/2021
742	2^1233971+216593	371463	Enzo Doria	12/2023
743	2^1233212+27301	371234	Enzo Doria	12/2023
744	2^1231466+283819	370709	Enzo Doria	07/2017
745	2^1229766+26659	370197	Enzo Doria	12/2023
746	2^1228899+30713	369936	Enzo Doria	03/2024
747	2^1228892+223831	369934	Enzo Doria	06/2024
748	(49627^78961-1)/(49627^281-1)	369460	Ryan Propper	11/2023
749	2^1227060+226663	369382	Enzo Doria	09/2024
750	2^1226987+28163	369360	Enzo Doria	02/2024

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