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	2^1504232+26101	452819	Enzo Doria	01/2024
502	2^1498015+219113	450948	Enzo Doria	03/2024
503	2^1497532+220471	450803	Enzo Doria	04/2024
504	2^1497369+216977	450753	Enzo Doria	01/2024
505	(34^294277+1)/35	450678	Paul Bourdelais	06/2018
506	2^1495434+1890439	450171	Enzo Doria	12/2017
507	2^1495078+227779	450064	Enzo Doria	10/2024
508	2^1494634+7	449930	Stefano Morozzi	10/2022
509	2^1493170+784129	449489	Enzo Doria	08/2017
510	2^1489873+1888277	448497	Enzo Doria	06/2017
511	2^1487389+32417	447749	Enzo Doria	06/2024
512	2^1486846+36019	447586	Enzo Doria	11/2024
513	2^1485471+224789	447172	Enzo Doria	09/2024
514	2^1485203+71663	447091	Enzo Doria	09/2023
515	2^1484671+1888463	446931	Enzo Doria	06/2017
516	2^1483112+23961	446462	Enzo Doria	12/2023
517	2^1482867+1886783	446388	Enzo Doria	04/2017
518	2^1482148+284011	446172	Enzo Doria	04/2017
519	2^1481363+215843	445935	Enzo Doria	12/2023
520	2^1480415+217643	445650	Enzo Doria	02/2024
521	2^1480400+225013	445645	Enzo Doria	10/2024
522	2^1479356+1888291	445331	Enzo Doria	06/2017
523	(157742^85849-1)/(157742^293-1)	444716	Ryan Propper	11/2023
524	2^1476810+23299	444565	Enzo Doria	12/2023
525	2^1474222+38569	443786	Enzo Doria	11/2024
526	2^1474189+36557	443776	Enzo Doria	11/2024
527	2^1473184+212671	443473	Enzo Doria	09/2023
528	2^1472225+37997	443184	Enzo Doria	10/2024
529	2^1466432+20371	441441	Enzo Doria	08/2023
530	14^384558+3	440753	Paul Bourdelais	01/2021
531	2^1463913+219047	440682	Enzo Doria	04/2024
532	2^1461244+784531	439879	Enzo Doria	10/2017
533	2^1461058+34429	439823	Enzo Doria	08/2024
534	2^1459599+215813	439384	Enzo Doria	01/2024
535	2^1457449+25757	438736	Enzo Doria	12/2023
536	3^919094+5*2^919094	438520	Jon Grantham	08/2023
537	2^1456277+28229	438384	Enzo Doria	03/2024
538	2^1455129+218027	438038	Enzo Doria	01/2024
539	2^1454061+216977	437716	Enzo Doria	01/2024
540	2^1453419+26783	437523	Enzo Doria	01/2024
541	(67^239053+1)/68	436527	Paul Bourdelais	09/2021
542	2^1448122+74209	435929	Enzo Doria	08/2023
543	2^1446449+221087	435425	Enzo Doria	05/2024
544	2^1446263+74333	435369	Enzo Doria	08/2023
545	2^1444386+221029	434804	Enzo Doria	03/2024
546	(80^228419+1)/81	434701	Paul Bourdelais	02/2021
547	2^1443089+60227	434414	Enzo Doria	10/2017
548	(21^328129-1)/20	433858	Paul Bourdelais	06/2014
549	(35^280979+1)/36	433850	Paul Bourdelais	09/2021
550	2^1438663+214175	433081	Enzo Doria	11/2023
551	2^1434519+215813	431834	Enzo Doria	01/2024
552	2^1434400+3	431798	Paul Bourdelais	06/2019
553	2^1434298+31669	431767	Enzo Doria	08/2024
554	2^1434097+215207	431707	Enzo Doria	11/2023
555	2^1433033+212987	431386	Enzo Doria	10/2023
556	2^1432308+1888801	431168	Enzo Doria	10/2017
557	(2^1430131+1)/(335646873253736519993971459)	430487	Gord Palameta	12/2018
558	(7^508867-2^508867)/5	430042	Jon Grantham	08/2023
559	2^1428489+25097	430019	Enzo Doria	11/2023
560	2^1425483+1886813	429114	Enzo Doria	04/2017
561	(63^238481+1)/64	429107	Paul Bourdelais	12/2020
562	(17^348259+1)/18	428514	Paul Bourdelais	05/2014
563	2^1422688+24391	428272	Enzo Doria	12/2023
564	2^1422654+226249	428262	Enzo Doria	09/2024
565	(10^427912+89)/9	427912	Serge Batalov	12/2014
566	2^1421089+1890167	427791	Enzo Doria	09/2017
567	2^1420902+221149	427735	Enzo Doria	05/2024
568	2^1418388+25771	426978	Enzo Doria	12/2023
569	2^1416724+214981	426477	Enzo Doria	11/2023
570	(96228^85849-1)/(96228^293-1)	426352	Ryan Propper	11/2023
571	2^1414012+36991	425661	Enzo Doria	09/2024
572	2^1413721+225269	425573	Enzo Doria	10/2024
573	20^326600+3	424917	Paul Bourdelais	01/2021
574	2^1411443+228023	424887	Enzo Doria	11/2024
575	(10^424861-7)/3	424861	Leonid Durman	01/2012
576	10^424821-11	424821	Mischa Rodermond	04/2023
577	(2^1411200+13)/7	424813	Stefano Morozzi	09/2022
578	2^1411117+35927	424789	Enzo Doria	09/2024
579	2^1410894+219859	424722	Enzo Doria	03/2024
580	2^1410310+30409	424546	Enzo Doria	05/2024
581	2^1410233+218447	424523	Enzo Doria	03/2024
582	1+3^605376+5^605376	423140	Jon Grantham	08/2023
583	2^1405367+213413	423058	Enzo Doria	10/2023
584	2^1404213+184217	422711	Enzo Doria	09/2017
585	2^1401872+1884385	422006	Enzo Doria	04/2017
586	2^1401257+6077	421821	Enzo Doria	09/2017
587	138^196873-137^196873	421285	Jean-Louis Charton	12/2009
588	2^1398726+7	421059	Stefano Morozzi	10/2022
589	2^1398269+131595	420921	Makoto Morimoto	10/2013
590	2^1398238+227119	420912	Enzo Doria	10/2024
591	2^1397089-1397089	420566	Henri Lifchitz	10/2024
592	2^1397071+684443	420561	Enzo Doria	07/2017
593	953^141023-952^141023	420121	Jean-Louis Charton	10/2016
594	2^1393111+1867211	419369	Enzo Doria	09/2023
595	2^1391771+36623	418965	Enzo Doria	09/2024
596	(3^877843-1)/2	418838	Paul Bourdelais	07/2010
597	2^1389628+28651	418320	Enzo Doria	03/2024
598	2^1386321+60299	417325	Enzo Doria	02/2018
599	2^1386320+184531	417324	Enzo Doria	09/2017
600	2^1382074+1883587	416046	Enzo Doria	01/2017
601	2^1380651+215843	415618	Enzo Doria	12/2023
602	2^1379907+1885223	415394	Enzo Doria	03/2017
603	2^1379111+29693	415154	Enzo Doria	05/2024
604	2^1376707+25763	414431	Enzo Doria	12/2023
605	2^1375751+24443	414143	Enzo Doria	12/2023
606	2^1375574+1886719	414090	Enzo Doria	04/2017
607	2^1373111+1884833	413348	Enzo Doria	02/2017
608	2^1372996+15	413313	Stefano Morozzi	10/2022
609	2^1372515+32393	413169	Enzo Doria	05/2024
610	2^1370877+38747	412676	Enzo Doria	11/2024
611	2^1369207+36833	412173	Enzo Doria	10/2024
612	2^1369171+216593	412162	Enzo Doria	01/2024
613	2^1368632+1889731	412000	Enzo Doria	10/2017
614	(65245^85849-1)/(65245^293-1)	411914	Ryan Propper	11/2023
615	(89*10^411590+1)/9	411591	Serge Batalov	09/2014
616	F(1968721)	411439	Henri Lifchitz	11/2009
617	2^1366066+683749	411227	Enzo Doria	02/2017
618	2^1365077+228257	410930	Enzo Doria	11/2024
619	2^1364401+217727	410726	Enzo Doria	02/2024
620	2^1364303+219533	410697	Enzo Doria	03/2024
621	2^1363434+27589	410435	Enzo Doria	02/2024
622	2^1363068+222631	410325	Enzo Doria	06/2024
623	2^1359550+25819	409266	Enzo Doria	12/2023
624	2^1357392+224401	408616	Enzo Doria	06/2024
625	2^1355826+15	408145	Stefano Morozzi	10/2022
626	2^1355790+1888939	408134	Enzo Doria	07/2017
627	2^1355635+1884203	408087	Enzo Doria	01/2017
628	(22071^94249-1)/(22071^307-1)	408068	Ryan Propper	11/2023
629	2^1355083+221603	407921	Enzo Doria	05/2024
630	2^1351989+36587	406990	Enzo Doria	09/2024
631	2^1349535+218783	406251	Enzo Doria	03/2024
632	(55766^85849-1)/(55766^293-1)	406081	Ryan Propper	11/2023
633	2^1348956+24241	406077	Enzo Doria	11/2023
634	(88^208739+1)/89	405888	Paul Bourdelais	12/2020
635	(2^1347781-2^673891+1)/5	405722	Borys Jaworski	10/2008
636	2^1347744-3	405712	Paul Bourdelais	07/2019
637	2^1346431+691203	405317	Boyan Hu	09/2024
638	9*10^404644-11	404645	Mischa Rodermond	04/2023
639	1215^131072+242^131072	404302	Kellen Shenton	08/2022
640	2^1341908+212911	403955	Enzo Doria	09/2023
641	2^1341625+226187	403870	Enzo Doria	09/2024
642	1196^131072+595^131072	403405	Kellen Shenton	08/2022
643	2^1339302+29389	403171	Enzo Doria	04/2024
644	2^1335130+31669	401915	Enzo Doria	07/2024
645	2^1330371+28313	400482	Enzo Doria	03/2024
646	10^400000+1415223	400001	Patrick De Geest	10/2020
647	10^400000-339233	400000	Patrick De Geest	10/2020
648	2^1323373+27317	398375	Enzo Doria	01/2024
649	Tau(863^24630)	397727	Nik Lygeros / Olivier Rozier	01/2016
650	2^1320423+24293	397487	Enzo Doria	11/2023
651	2^1320057+211517	397377	Enzo Doria	08/2023
652	2^1319770+1884949	397291	Enzo Doria	06/2017
653	2^1319616+30091	397244	Enzo Doria	04/2024
654	2^1317657+31367	396655	Enzo Doria	04/2024
655	2^1315753+226187	396082	Enzo Doria	09/2024
656	2^1314741+219257	395777	Enzo Doria	03/2024
657	2^1313062+1888849	395272	Enzo Doria	08/2017
658	(1073516^81920+1)/(1073516^16384+1)	395236	Serge Batalov	01/2017
659	2^1312349+221177	395057	Enzo Doria	04/2024
660	(1059995^81920+1)/(1059995^16384+1)	394875	Serge Batalov	01/2017
661	2^1311618+783529	394837	Enzo Doria	01/2017
662	2^1308992+28111	394046	Enzo Doria	02/2024
663	2^1308000+1883521	393748	Enzo Doria	02/2017
664	2^1307324+224611	393544	Enzo Doria	07/2024
665	2^1307262+28759	393526	Enzo Doria	02/2024
666	(1009565^81920+1)/(1009565^16384+1)	393487	Serge Batalov	01/2017
667	2^1305860+35461	393104	Enzo Doria	08/2024
668	(995042^81920+1)/(995042^16384+1)	393075	Serge Batalov	01/2017
669	(988945^81920+1)/(988945^16384+1)	392900	Serge Batalov	01/2017
670	(988823^81920+1)/(988823^16384+1)	392897	Serge Batalov	01/2017
671	(2^1304983-1)/52199321	392832	Tony Prest / Never Odd Or Even	03/2014
672	(978970^81920+1)/(978970^16384+1)	392612	Serge Batalov	01/2017
673	2^1303816+38251	392488	Enzo Doria	11/2024
674	2^1303102+1866409	392273	Enzo Doria	09/2017
675	2^1302818+283429	392188	Enzo Doria	01/2017
676	2^1301430+22669	391770	Enzo Doria	10/2023
677	2^1301229+222467	391709	Enzo Doria	04/2024
678	(934422^81920+1)/(934422^16384+1)	391286	Serge Batalov	01/2017
679	2^1299181+1886867	391093	Enzo Doria	04/2017
680	(37^249341-1)/36	391016	Paul Bourdelais	08/2020
681	2^1298304+1882891	390829	Enzo Doria	01/2017
682	2^1297732+228721	390657	Enzo Doria	11/2024
683	95196^12497+12497^95196	390000	Hans Havermann	12/2021
684	2^1295539+35633	389997	Enzo Doria	08/2024
685	86206^33381+33381^86206	389953	Hans Havermann	05/2023
686	2^1294324+25171	389631	Enzo Doria	12/2023
687	(874207^81920+1)/(874207^16384+1)	389390	Serge Batalov	01/2017
688	2^1289624+32551	388216	Enzo Doria	05/2024
689	2^1286857+37967	387383	Enzo Doria	10/2024
690	(7^457871-5^457871)/2	386946	Jon Grantham	08/2023
691	79455^73828+73828^79455	386805	Hans Havermann	03/2023
692	81650^54369+54369^81650	386642	Yusuf AttarBashi	06/2021
693	80565^62824+62824^80565	386561	Hans Havermann	08/2021
694	83747^41272+41272^83747	386548	Hans Havermann	08/2021
695	15^328574+328574^15	386434	Serge Batalov	05/2014
696	2^1280078+1885099	385342	Enzo Doria	08/2017
697	2^1279921+17	385295	Stefano Morozzi	10/2022
698	2^1279245+224087	385092	Enzo Doria	07/2024
699	2^1276977+71657	384409	Enzo Doria	08/2023
700	(76803^78961-1)/(76803^281-1)	384382	Ryan Propper	11/2023
701	2^1276571+26213	384287	Enzo Doria	12/2023
702	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
703	2^1274941+1880717	383796	Enzo Doria	10/2016
704	2^1272632+383431	383101	Enzo Doria	01/2017
705	2^1271346+1889839	382714	Enzo Doria	08/2017
706	2^1271173+219587	382662	Enzo Doria	03/2024
707	5*3^798534-2^798534	380999	Jon Grantham	08/2023
708	(10^380976-7)/3	380976	Leonid Durman	01/2012
709	2^1264748+23221	380728	Enzo Doria	11/2023
710	(4*10^380056+11)/3	380057	Tyler Busby	03/2023
711	2^1262431+228353	380030	Enzo Doria	11/2024
712	2^1260859+222683	379557	Enzo Doria	06/2024
713	2^1257787+1447761	378632	Makoto Morimoto	10/2013
714	(2^1257787+32270)/(223328122073011)	378620	Makoto Morimoto	12/2016
715	2^1257728+20851	378614	Enzo Doria	08/2023
716	(77^200657-1)/76	378536	Paul Bourdelais	08/2020
717	(98^189619+1)/99	377573	Paul Bourdelais	02/2021
718	F(1803059)	376817	Henri Lifchitz	06/2009
719	2^1250590+29389	376466	Enzo Doria	03/2024
720	(10^376417-3^376417)/7	376417	Jon Grantham	08/2023
721	2^1250116+34951	376323	Enzo Doria	08/2024
722	2^1246724+213961	375302	Enzo Doria	10/2023
723	2^1245230+19	374852	Stefano Morozzi	10/2022
724	7^442674+4	374103	Paul Bourdelais	02/2021
725	2^1239151+35633	373022	Enzo Doria	08/2024
726	2^1238732+39181	372896	Enzo Doria	11/2024
727	2^1237699+34703	372585	Enzo Doria	07/2024
728	(97^187393-1)/96	372306	Paul Bourdelais	09/2020
729	10^371696+7	371697	Alfred Reich	05/2021
730	2^1234709+883127	371685	Enzo Doria	12/2016
731	2^1234119+21803	371507	Enzo Doria	09/2023
732	(67^203431+1)/68	371479	Paul Bourdelais	09/2021
733	2^1233971+216593	371463	Enzo Doria	12/2023
734	2^1233212+27301	371234	Enzo Doria	12/2023
735	2^1231466+283819	370709	Enzo Doria	07/2017
736	2^1229766+26659	370197	Enzo Doria	12/2023
737	2^1228899+30713	369936	Enzo Doria	03/2024
738	2^1228892+223831	369934	Enzo Doria	06/2024
739	(49627^78961-1)/(49627^281-1)	369460	Ryan Propper	11/2023
740	2^1227060+226663	369382	Enzo Doria	09/2024
741	2^1226987+28163	369360	Enzo Doria	02/2024
742	2^1226569+30857	369235	Enzo Doria	03/2024
743	73^197880+197880	368715	Kellen Shenton	06/2023
744	5*3^771723-2^771723	368207	Jon Grantham	08/2023
745	2^1222473+221597	368002	Enzo Doria	04/2024
746	2^1222211+22703	367923	Enzo Doria	11/2023
747	(2^1222097+19)/3	367888	Stefano Morozzi	09/2022
748	2^1220335+1881263	367358	Enzo Doria	11/2016
749	2^1218344+215641	366759	Enzo Doria	12/2023
750	2^1217510+220039	366508	Enzo Doria	03/2024

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Probable Primes Top 10000

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