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	2^1453419+26783	437523	Enzo Doria	01/2024
502	(67^239053+1)/68	436527	Paul Bourdelais	09/2021
503	2^1448122+74209	435929	Enzo Doria	08/2023
504	2^1446449+221087	435425	Enzo Doria	05/2024
505	2^1446263+74333	435369	Enzo Doria	08/2023
506	2^1444386+221029	434804	Enzo Doria	03/2024
507	(80^228419+1)/81	434701	Paul Bourdelais	02/2021
508	2^1443089+60227	434414	Enzo Doria	10/2017
509	(21^328129-1)/20	433858	Paul Bourdelais	06/2014
510	(35^280979+1)/36	433850	Paul Bourdelais	09/2021
511	2^1438663+214175	433081	Enzo Doria	11/2023
512	2^1434519+215813	431834	Enzo Doria	01/2024
513	2^1434400+3	431798	Paul Bourdelais	06/2019
514	2^1434298+31669	431767	Enzo Doria	08/2024
515	2^1434097+215207	431707	Enzo Doria	11/2023
516	2^1433033+212987	431386	Enzo Doria	10/2023
517	2^1432308+1888801	431168	Enzo Doria	10/2017
518	(2^1430131+1)/(335646873253736519993971459)	430487	Gord Palameta	12/2018
519	(7^508867-2^508867)/5	430042	Jon Grantham	08/2023
520	2^1428489+25097	430019	Enzo Doria	11/2023
521	2^1425483+1886813	429114	Enzo Doria	04/2017
522	(63^238481+1)/64	429107	Paul Bourdelais	12/2020
523	(17^348259+1)/18	428514	Paul Bourdelais	05/2014
524	2^1422688+24391	428272	Enzo Doria	12/2023
525	(10^427912+89)/9	427912	Serge Batalov	12/2014
526	2^1421089+1890167	427791	Enzo Doria	09/2017
527	2^1420902+221149	427735	Enzo Doria	05/2024
528	2^1418388+25771	426978	Enzo Doria	12/2023
529	2^1416724+214981	426477	Enzo Doria	11/2023
530	(96228^85849-1)/(96228^293-1)	426352	Ryan Propper	11/2023
531	20^326600+3	424917	Paul Bourdelais	01/2021
532	(10^424861-7)/3	424861	Leonid Durman	01/2012
533	10^424821-11	424821	Mischa Rodermond	04/2023
534	(2^1411200+13)/7	424813	Stefano Morozzi	09/2022
535	2^1411117+35927	424789	Enzo Doria	09/2024
536	2^1410894+219859	424722	Enzo Doria	03/2024
537	2^1410310+30409	424546	Enzo Doria	05/2024
538	2^1410233+218447	424523	Enzo Doria	03/2024
539	1+3^605376+5^605376	423140	Jon Grantham	08/2023
540	2^1405367+213413	423058	Enzo Doria	10/2023
541	2^1404213+184217	422711	Enzo Doria	09/2017
542	2^1401872+1884385	422006	Enzo Doria	04/2017
543	2^1401257+6077	421821	Enzo Doria	09/2017
544	138^196873-137^196873	421285	Jean-Louis Charton	12/2009
545	2^1398726+7	421059	Stefano Morozzi	10/2022
546	2^1398269+131595	420921	Makoto Morimoto	10/2013
547	2^1397071+684443	420561	Enzo Doria	07/2017
548	953^141023-952^141023	420121	Jean-Louis Charton	10/2016
549	2^1393111+1867211	419369	Enzo Doria	09/2023
550	(3^877843-1)/2	418838	Paul Bourdelais	07/2010
551	2^1389628+28651	418320	Enzo Doria	03/2024
552	2^1386321+60299	417325	Enzo Doria	02/2018
553	2^1386320+184531	417324	Enzo Doria	09/2017
554	2^1382074+1883587	416046	Enzo Doria	01/2017
555	2^1380651+215843	415618	Enzo Doria	12/2023
556	2^1379907+1885223	415394	Enzo Doria	03/2017
557	2^1379111+29693	415154	Enzo Doria	05/2024
558	2^1376707+25763	414431	Enzo Doria	12/2023
559	2^1375751+24443	414143	Enzo Doria	12/2023
560	2^1375574+1886719	414090	Enzo Doria	04/2017
561	2^1373111+1884833	413348	Enzo Doria	02/2017
562	2^1372996+15	413313	Stefano Morozzi	10/2022
563	2^1372515+32393	413169	Enzo Doria	05/2024
564	2^1369171+216593	412162	Enzo Doria	01/2024
565	2^1368632+1889731	412000	Enzo Doria	10/2017
566	(65245^85849-1)/(65245^293-1)	411914	Ryan Propper	11/2023
567	(89*10^411590+1)/9	411591	Serge Batalov	09/2014
568	F(1968721)	411439	Henri Lifchitz	11/2009
569	2^1366066+683749	411227	Enzo Doria	02/2017
570	2^1364401+217727	410726	Enzo Doria	02/2024
571	2^1364303+219533	410697	Enzo Doria	03/2024
572	2^1363434+27589	410435	Enzo Doria	02/2024
573	2^1363068+222631	410325	Enzo Doria	06/2024
574	2^1359550+25819	409266	Enzo Doria	12/2023
575	2^1357392+224401	408616	Enzo Doria	06/2024
576	2^1355826+15	408145	Stefano Morozzi	10/2022
577	2^1355790+1888939	408134	Enzo Doria	07/2017
578	2^1355635+1884203	408087	Enzo Doria	01/2017
579	(22071^94249-1)/(22071^307-1)	408068	Ryan Propper	11/2023
580	2^1355083+221603	407921	Enzo Doria	05/2024
581	2^1349535+218783	406251	Enzo Doria	03/2024
582	(55766^85849-1)/(55766^293-1)	406081	Ryan Propper	11/2023
583	2^1348956+24241	406077	Enzo Doria	11/2023
584	(88^208739+1)/89	405888	Paul Bourdelais	12/2020
585	(2^1347781-2^673891+1)/5	405722	Borys Jaworski	10/2008
586	2^1347744-3	405712	Paul Bourdelais	07/2019
587	2^1346431+691203	405317	Boyan Hu	09/2024
588	9*10^404644-11	404645	Mischa Rodermond	04/2023
589	1215^131072+242^131072	404302	Kellen Shenton	08/2022
590	2^1341908+212911	403955	Enzo Doria	09/2023
591	1196^131072+595^131072	403405	Kellen Shenton	08/2022
592	2^1339302+29389	403171	Enzo Doria	04/2024
593	2^1335130+31669	401915	Enzo Doria	07/2024
594	2^1330371+28313	400482	Enzo Doria	03/2024
595	10^400000+1415223	400001	Patrick De Geest	10/2020
596	10^400000-339233	400000	Patrick De Geest	10/2020
597	2^1323373+27317	398375	Enzo Doria	01/2024
598	Tau(863^24630)	397727	Nik Lygeros / Olivier Rozier	01/2016
599	2^1320423+24293	397487	Enzo Doria	11/2023
600	2^1320057+211517	397377	Enzo Doria	08/2023
601	2^1319770+1884949	397291	Enzo Doria	06/2017
602	2^1319616+30091	397244	Enzo Doria	04/2024
603	2^1317657+31367	396655	Enzo Doria	04/2024
604	2^1314741+219257	395777	Enzo Doria	03/2024
605	2^1313062+1888849	395272	Enzo Doria	08/2017
606	(1073516^81920+1)/(1073516^16384+1)	395236	Serge Batalov	01/2017
607	2^1312349+221177	395057	Enzo Doria	04/2024
608	(1059995^81920+1)/(1059995^16384+1)	394875	Serge Batalov	01/2017
609	2^1311618+783529	394837	Enzo Doria	01/2017
610	2^1308992+28111	394046	Enzo Doria	02/2024
611	2^1308000+1883521	393748	Enzo Doria	02/2017
612	2^1307324+224611	393544	Enzo Doria	07/2024
613	2^1307262+28759	393526	Enzo Doria	02/2024
614	(1009565^81920+1)/(1009565^16384+1)	393487	Serge Batalov	01/2017
615	2^1305860+35461	393104	Enzo Doria	08/2024
616	(995042^81920+1)/(995042^16384+1)	393075	Serge Batalov	01/2017
617	(988945^81920+1)/(988945^16384+1)	392900	Serge Batalov	01/2017
618	(988823^81920+1)/(988823^16384+1)	392897	Serge Batalov	01/2017
619	(2^1304983-1)/52199321	392832	Tony Prest / Never Odd Or Even	03/2014
620	(978970^81920+1)/(978970^16384+1)	392612	Serge Batalov	01/2017
621	2^1303102+1866409	392273	Enzo Doria	09/2017
622	2^1302818+283429	392188	Enzo Doria	01/2017
623	2^1301430+22669	391770	Enzo Doria	10/2023
624	2^1301229+222467	391709	Enzo Doria	04/2024
625	(934422^81920+1)/(934422^16384+1)	391286	Serge Batalov	01/2017
626	2^1299181+1886867	391093	Enzo Doria	04/2017
627	(37^249341-1)/36	391016	Paul Bourdelais	08/2020
628	2^1298304+1882891	390829	Enzo Doria	01/2017
629	95196^12497+12497^95196	390000	Hans Havermann	12/2021
630	2^1295539+35633	389997	Enzo Doria	08/2024
631	86206^33381+33381^86206	389953	Hans Havermann	05/2023
632	2^1294324+25171	389631	Enzo Doria	12/2023
633	(874207^81920+1)/(874207^16384+1)	389390	Serge Batalov	01/2017
634	2^1289624+32551	388216	Enzo Doria	05/2024
635	(7^457871-5^457871)/2	386946	Jon Grantham	08/2023
636	79455^73828+73828^79455	386805	Hans Havermann	03/2023
637	81650^54369+54369^81650	386642	Yusuf AttarBashi	06/2021
638	80565^62824+62824^80565	386561	Hans Havermann	08/2021
639	83747^41272+41272^83747	386548	Hans Havermann	08/2021
640	15^328574+328574^15	386434	Serge Batalov	05/2014
641	2^1280078+1885099	385342	Enzo Doria	08/2017
642	2^1279921+17	385295	Stefano Morozzi	10/2022
643	2^1279245+224087	385092	Enzo Doria	07/2024
644	2^1276977+71657	384409	Enzo Doria	08/2023
645	(76803^78961-1)/(76803^281-1)	384382	Ryan Propper	11/2023
646	2^1276571+26213	384287	Enzo Doria	12/2023
647	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
648	2^1274941+1880717	383796	Enzo Doria	10/2016
649	2^1272632+383431	383101	Enzo Doria	01/2017
650	2^1271346+1889839	382714	Enzo Doria	08/2017
651	2^1271173+219587	382662	Enzo Doria	03/2024
652	5*3^798534-2^798534	380999	Jon Grantham	08/2023
653	(10^380976-7)/3	380976	Leonid Durman	01/2012
654	2^1264748+23221	380728	Enzo Doria	11/2023
655	(4*10^380056+11)/3	380057	Tyler Busby	03/2023
656	2^1260859+222683	379557	Enzo Doria	06/2024
657	2^1257787+1447761	378632	Makoto Morimoto	10/2013
658	(2^1257787+32270)/(223328122073011)	378620	Makoto Morimoto	12/2016
659	2^1257728+20851	378614	Enzo Doria	08/2023
660	(77^200657-1)/76	378536	Paul Bourdelais	08/2020
661	(98^189619+1)/99	377573	Paul Bourdelais	02/2021
662	F(1803059)	376817	Henri Lifchitz	06/2009
663	2^1250590+29389	376466	Enzo Doria	03/2024
664	(10^376417-3^376417)/7	376417	Jon Grantham	08/2023
665	2^1250116+34951	376323	Enzo Doria	08/2024
666	2^1246724+213961	375302	Enzo Doria	10/2023
667	2^1245230+19	374852	Stefano Morozzi	10/2022
668	7^442674+4	374103	Paul Bourdelais	02/2021
669	2^1239151+35633	373022	Enzo Doria	08/2024
670	2^1237699+34703	372585	Enzo Doria	07/2024
671	(97^187393-1)/96	372306	Paul Bourdelais	09/2020
672	10^371696+7	371697	Alfred Reich	05/2021
673	2^1234709+883127	371685	Enzo Doria	12/2016
674	2^1234119+21803	371507	Enzo Doria	09/2023
675	(67^203431+1)/68	371479	Paul Bourdelais	09/2021
676	2^1233971+216593	371463	Enzo Doria	12/2023
677	2^1233212+27301	371234	Enzo Doria	12/2023
678	2^1231466+283819	370709	Enzo Doria	07/2017
679	2^1229766+26659	370197	Enzo Doria	12/2023
680	2^1228899+30713	369936	Enzo Doria	03/2024
681	2^1228892+223831	369934	Enzo Doria	06/2024
682	(49627^78961-1)/(49627^281-1)	369460	Ryan Propper	11/2023
683	2^1227060+226663	369382	Enzo Doria	09/2024
684	2^1226987+28163	369360	Enzo Doria	02/2024
685	2^1226569+30857	369235	Enzo Doria	03/2024
686	73^197880+197880	368715	Kellen Shenton	06/2023
687	5*3^771723-2^771723	368207	Jon Grantham	08/2023
688	2^1222473+221597	368002	Enzo Doria	04/2024
689	2^1222211+22703	367923	Enzo Doria	11/2023
690	(2^1222097+19)/3	367888	Stefano Morozzi	09/2022
691	2^1220335+1881263	367358	Enzo Doria	11/2016
692	2^1218344+215641	366759	Enzo Doria	12/2023
693	2^1217510+220039	366508	Enzo Doria	03/2024
694	(233^154787-1)/232	366434	Anonymous	05/2024
695	2^1216694+1884769	366262	Enzo Doria	02/2017
696	2^1215889-3	366020	Paul Bourdelais	06/2019
697	2^1215296+1885441	365841	Enzo Doria	03/2017
698	(80^192133+1)/81	365645	Paul Bourdelais	01/2021
699	2^1214307+1888115	365543	Enzo Doria	05/2017
700	2^1213815+3	365395	Paul Bourdelais	06/2019
701	(80^191953+1)/81	365302	Paul Bourdelais	01/2021
702	2^1213313+215837	365244	Enzo Doria	11/2023
703	2^1208276+22201	363728	Enzo Doria	09/2023
704	2^1207345+1882577	363448	Enzo Doria	12/2016
705	2^1207336+217801	363445	Enzo Doria	03/2024
706	2^1207073+883727	363366	Enzo Doria	03/2017
707	3^761457-2	363308	Ryan Propper	07/2015
708	(10^363030+7)/337/443	363025	Alfred Reich	12/2021
709	2^1204869+224885	362702	Enzo Doria	07/2024
710	2^1200972+141811	361529	Stefano Morozzi	10/2022
711	(2^1200924+324730)/2	361514	Stefano Morozzi	06/2021
712	(2^1200912+274110)/2	361511	Stefano Morozzi	01/2021
713	2^1200906+165249	361509	Stefano Morozzi	07/2022
714	2^1200890+166339	361504	Stefano Morozzi	01/2023
715	(2^1200887+344126)/2	361503	Stefano Morozzi	10/2020
716	2^1200877+186755	361500	Stefano Morozzi	09/2022
717	2^1200861+198521	361496	Stefano Morozzi	11/2021
718	(2^1200856+305790)/2	361494	Stefano Morozzi	10/2020
719	(2^1200853+372822)/2	361493	Stefano Morozzi	06/2021
720	2^1200812+324178)/2	361481	Stefano Morozzi	06/2021
721	(2^1200768+380458)/2	361467	Stefano Morozzi	01/2021
722	2^1200756+140917	361464	Stefano Morozzi	05/2022
723	2^1200741+184781	361460	Stefano Morozzi	09/2022
724	(2^1200741+293402)/2	361459	Stefano Morozzi	07/2021
725	2^1200734+142653	361457	Stefano Morozzi	02/2023
727	2^1200672+1880881	361439	Enzo Doria	10/2016
726	2^1200672+141535	361439	Stefano Morozzi	09/2022
728	2^1200669+178805	361438	Stefano Morozzi	11/2022
729	2^1200660+198555	361435	Stefano Morozzi	12/2021
730	2^1200657+164837	361434	Stefano Morozzi	05/2022
731	2^1200631+166431	361426	Stefano Morozzi	02/2023
732	2^1200627+150669	361425	Stefano Morozzi	02/2023
733	(2^1200603+356030)/2	361418	Stefano Morozzi	10/2020
734	(2^1200590+275854)/2	361414	Stefano Morozzi	03/2021
735	2^1200550+139297	361402	Stefano Morozzi	10/2021
736	2^1200486+172855	361383	Stefano Morozzi	01/2023
737	(2^1200456+320526)/2	361373	Stefano Morozzi	10/2020
738	2^1200443+142121	361370	Stefano Morozzi	01/2023
739	2^1200416+164065	361362	Stefano Morozzi	01/2022
740	2^1200331+155429	361336	Stefano Morozzi	10/2021
742	(2^1200289+348366)/2	361323	Stefano Morozzi	10/2020
741	2^1200289+141885	361323	Stefano Morozzi	11/2022
743	(2^1200284+273162)/2	361322	Stefano Morozzi	10/2020
744	2^1200252+194535	361312	Stefano Morozzi	11/2021
745	(2^1200250+364230)/2	361311	Stefano Morozzi	10/2020
746	2^1200227+156881	361305	Stefano Morozzi	05/2022
747	(2^1200209+305990)/2	361299	Stefano Morozzi	10/2020
748	(2^1200210+376278)/2	361299	Stefano Morozzi	10/2020
749	2^1200202+216499	361297	Enzo Doria	12/2023
750	(2^1200182+274462)/2	361291	Stefano Morozzi	01/2021

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