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	2^1428489+25097	430019	Enzo Doria	11/2023
502	2^1425483+1886813	429114	Enzo Doria	04/2017
503	(63^238481+1)/64	429107	Paul Bourdelais	12/2020
504	(17^348259+1)/18	428514	Paul Bourdelais	05/2014
505	2^1422688+24391	428272	Enzo Doria	12/2023
506	(10^427912+89)/9	427912	Serge Batalov	12/2014
507	2^1421089+1890167	427791	Enzo Doria	09/2017
508	2^1420902+221149	427735	Enzo Doria	05/2024
509	2^1418388+25771	426978	Enzo Doria	12/2023
510	2^1416724+214981	426477	Enzo Doria	11/2023
511	(96228^85849-1)/(96228^293-1)	426352	Ryan Propper	11/2023
512	20^326600+3	424917	Paul Bourdelais	01/2021
513	(10^424861-7)/3	424861	Leonid Durman	01/2012
514	10^424821-11	424821	Mischa Rodermond	04/2023
515	(2^1411200+13)/7	424813	Stefano Morozzi	09/2022
516	2^1410894+219859	424722	Enzo Doria	03/2024
517	2^1410310+30409	424546	Enzo Doria	05/2024
518	2^1410233+218447	424523	Enzo Doria	03/2024
519	1+3^605376+5^605376	423140	Jon Grantham	08/2023
520	2^1405367+213413	423058	Enzo Doria	10/2023
521	2^1404213+184217	422711	Enzo Doria	09/2017
522	2^1401872+1884385	422006	Enzo Doria	04/2017
523	2^1401257+6077	421821	Enzo Doria	09/2017
524	138^196873-137^196873	421285	Jean-Louis Charton	12/2009
525	2^1398726+7	421059	Stefano Morozzi	10/2022
526	2^1398269+131595	420921	Makoto Morimoto	10/2013
527	2^1397071+684443	420561	Enzo Doria	07/2017
528	953^141023-952^141023	420121	Jean-Louis Charton	10/2016
529	2^1393111+1867211	419369	Enzo Doria	09/2023
530	(3^877843-1)/2	418838	Paul Bourdelais	07/2010
531	2^1389628+28651	418320	Enzo Doria	03/2024
532	2^1386321+60299	417325	Enzo Doria	02/2018
533	2^1386320+184531	417324	Enzo Doria	09/2017
534	2^1382074+1883587	416046	Enzo Doria	01/2017
535	2^1380651+215843	415618	Enzo Doria	12/2023
536	2^1379907+1885223	415394	Enzo Doria	03/2017
537	2^1379111+29693	415154	Enzo Doria	05/2024
538	2^1376707+25763	414431	Enzo Doria	12/2023
539	2^1375751+24443	414143	Enzo Doria	12/2023
540	2^1375574+1886719	414090	Enzo Doria	04/2017
541	2^1373111+1884833	413348	Enzo Doria	02/2017
542	2^1372996+15	413313	Stefano Morozzi	10/2022
543	2^1372515+32393	413169	Enzo Doria	05/2024
544	2^1369171+216593	412162	Enzo Doria	01/2024
545	2^1368632+1889731	412000	Enzo Doria	10/2017
546	(65245^85849-1)/(65245^293-1)	411914	Ryan Propper	11/2023
547	(89*10^411590+1)/9	411591	Serge Batalov	09/2014
548	F(1968721)	411439	Henri Lifchitz	11/2009
549	2^1366066+683749	411227	Enzo Doria	02/2017
550	2^1364401+217727	410726	Enzo Doria	02/2024
551	2^1364303+219533	410697	Enzo Doria	03/2024
552	2^1363434+27589	410435	Enzo Doria	02/2024
553	2^1363068+222631	410325	Enzo Doria	06/2024
554	2^1359550+25819	409266	Enzo Doria	12/2023
555	2^1357392+224401	408616	Enzo Doria	06/2024
556	2^1355826+15	408145	Stefano Morozzi	10/2022
557	2^1355790+1888939	408134	Enzo Doria	07/2017
558	2^1355635+1884203	408087	Enzo Doria	01/2017
559	(22071^94249-1)/(22071^307-1)	408068	Ryan Propper	11/2023
560	2^1355083+221603	407921	Enzo Doria	05/2024
561	2^1349535+218783	406251	Enzo Doria	03/2024
562	(55766^85849-1)/(55766^293-1)	406081	Ryan Propper	11/2023
563	2^1348956+24241	406077	Enzo Doria	11/2023
564	(88^208739+1)/89	405888	Paul Bourdelais	12/2020
565	(2^1347781-2^673891+1)/5	405722	Borys Jaworski	10/2008
566	2^1347744-3	405712	Paul Bourdelais	07/2019
567	9*10^404644-11	404645	Mischa Rodermond	04/2023
568	1215^131072+242^131072	404302	Kellen Shenton	08/2022
569	2^1341908+212911	403955	Enzo Doria	09/2023
570	1196^131072+595^131072	403405	Kellen Shenton	08/2022
571	2^1339302+29389	403171	Enzo Doria	04/2024
572	2^1335130+31669	401915	Enzo Doria	07/2024
573	2^1330371+28313	400482	Enzo Doria	03/2024
574	10^400000+1415223	400001	Patrick De Geest	10/2020
575	10^400000-339233	400000	Patrick De Geest	10/2020
576	2^1323373+27317	398375	Enzo Doria	01/2024
577	Tau(863^24630)	397727	Nik Lygeros / Olivier Rozier	01/2016
578	2^1320423+24293	397487	Enzo Doria	11/2023
579	2^1320057+211517	397377	Enzo Doria	08/2023
580	2^1319770+1884949	397291	Enzo Doria	06/2017
581	2^1319616+30091	397244	Enzo Doria	04/2024
582	2^1317657+31367	396655	Enzo Doria	04/2024
583	2^1314741+219257	395777	Enzo Doria	03/2024
584	2^1313062+1888849	395272	Enzo Doria	08/2017
585	(1073516^81920+1)/(1073516^16384+1)	395236	Serge Batalov	01/2017
586	2^1312349+221177	395057	Enzo Doria	04/2024
587	(1059995^81920+1)/(1059995^16384+1)	394875	Serge Batalov	01/2017
588	2^1311618+783529	394837	Enzo Doria	01/2017
589	2^1308992+28111	394046	Enzo Doria	02/2024
590	2^1308000+1883521	393748	Enzo Doria	02/2017
591	2^1307324+224611	393544	Enzo Doria	07/2024
592	2^1307262+28759	393526	Enzo Doria	02/2024
593	(1009565^81920+1)/(1009565^16384+1)	393487	Serge Batalov	01/2017
594	(995042^81920+1)/(995042^16384+1)	393075	Serge Batalov	01/2017
595	(988945^81920+1)/(988945^16384+1)	392900	Serge Batalov	01/2017
596	(988823^81920+1)/(988823^16384+1)	392897	Serge Batalov	01/2017
597	(2^1304983-1)/52199321	392832	Tony Prest / Never Odd Or Even	03/2014
598	(978970^81920+1)/(978970^16384+1)	392612	Serge Batalov	01/2017
599	2^1303102+1866409	392273	Enzo Doria	09/2017
600	2^1302818+283429	392188	Enzo Doria	01/2017
601	2^1301430+22669	391770	Enzo Doria	10/2023
602	2^1301229+222467	391709	Enzo Doria	04/2024
603	(934422^81920+1)/(934422^16384+1)	391286	Serge Batalov	01/2017
604	2^1299181+1886867	391093	Enzo Doria	04/2017
605	(37^249341-1)/36	391016	Paul Bourdelais	08/2020
606	2^1298304+1882891	390829	Enzo Doria	01/2017
607	95196^12497+12497^95196	390000	Hans Havermann	12/2021
608	86206^33381+33381^86206	389953	Hans Havermann	05/2023
609	2^1294324+25171	389631	Enzo Doria	12/2023
610	(874207^81920+1)/(874207^16384+1)	389390	Serge Batalov	01/2017
611	2^1289624+32551	388216	Enzo Doria	05/2024
612	(7^457871-5^457871)/2	386946	Jon Grantham	08/2023
613	79455^73828+73828^79455	386805	Hans Havermann	03/2023
614	81650^54369+54369^81650	386642	Yusuf AttarBashi	06/2021
615	80565^62824+62824^80565	386561	Hans Havermann	08/2021
616	83747^41272+41272^83747	386548	Hans Havermann	08/2021
617	15^328574+328574^15	386434	Serge Batalov	05/2014
618	2^1280078+1885099	385342	Enzo Doria	08/2017
619	2^1279921+17	385295	Stefano Morozzi	10/2022
620	2^1279245+224087	385092	Enzo Doria	07/2024
621	2^1276977+71657	384409	Enzo Doria	08/2023
622	(76803^78961-1)/(76803^281-1)	384382	Ryan Propper	11/2023
623	2^1276571+26213	384287	Enzo Doria	12/2023
624	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
625	2^1274941+1880717	383796	Enzo Doria	10/2016
626	2^1272632+383431	383101	Enzo Doria	01/2017
627	2^1271346+1889839	382714	Enzo Doria	08/2017
628	2^1271173+219587	382662	Enzo Doria	03/2024
629	5*3^798534-2^798534	380999	Jon Grantham	08/2023
630	(10^380976-7)/3	380976	Leonid Durman	01/2012
631	2^1264748+23221	380728	Enzo Doria	11/2023
632	(4*10^380056+11)/3	380057	Tyler Busby	03/2023
633	2^1260859+222683	379557	Enzo Doria	06/2024
634	2^1257787+1447761	378632	Makoto Morimoto	10/2013
635	(2^1257787+32270)/(223328122073011)	378620	Makoto Morimoto	12/2016
636	2^1257728+20851	378614	Enzo Doria	08/2023
637	(77^200657-1)/76	378536	Paul Bourdelais	08/2020
638	(98^189619+1)/99	377573	Paul Bourdelais	02/2021
639	F(1803059)	376817	Henri Lifchitz	06/2009
640	2^1250590+29389	376466	Enzo Doria	03/2024
641	(10^376417-3^376417)/7	376417	Jon Grantham	08/2023
642	2^1246724+213961	375302	Enzo Doria	10/2023
643	2^1245230+19	374852	Stefano Morozzi	10/2022
644	7^442674+4	374103	Paul Bourdelais	02/2021
645	2^1237699+34703	372585	Enzo Doria	07/2024
646	(97^187393-1)/96	372306	Paul Bourdelais	09/2020
647	10^371696+7	371697	Alfred Reich	05/2021
648	2^1234709+883127	371685	Enzo Doria	12/2016
649	2^1234119+21803	371507	Enzo Doria	09/2023
650	(67^203431+1)/68	371479	Paul Bourdelais	09/2021
651	2^1233971+216593	371463	Enzo Doria	12/2023
652	2^1233212+27301	371234	Enzo Doria	12/2023
653	2^1231466+283819	370709	Enzo Doria	07/2017
654	2^1229766+26659	370197	Enzo Doria	12/2023
655	2^1228899+30713	369936	Enzo Doria	03/2024
656	2^1228892+223831	369934	Enzo Doria	06/2024
657	(49627^78961-1)/(49627^281-1)	369460	Ryan Propper	11/2023
658	2^1226987+28163	369360	Enzo Doria	02/2024
659	2^1226569+30857	369235	Enzo Doria	03/2024
660	73^197880+197880	368715	Kellen Shenton	06/2023
661	5*3^771723-2^771723	368207	Jon Grantham	08/2023
662	2^1222473+221597	368002	Enzo Doria	04/2024
663	2^1222211+22703	367923	Enzo Doria	11/2023
664	(2^1222097+19)/3	367888	Stefano Morozzi	09/2022
665	2^1220335+1881263	367358	Enzo Doria	11/2016
666	2^1218344+215641	366759	Enzo Doria	12/2023
667	2^1217510+220039	366508	Enzo Doria	03/2024
668	(233^154787-1)/232	366434	Anonymous	05/2024
669	2^1216694+1884769	366262	Enzo Doria	02/2017
670	2^1215889-3	366020	Paul Bourdelais	06/2019
671	2^1215296+1885441	365841	Enzo Doria	03/2017
672	(80^192133+1)/81	365645	Paul Bourdelais	01/2021
673	2^1214307+1888115	365543	Enzo Doria	05/2017
674	2^1213815+3	365395	Paul Bourdelais	06/2019
675	(80^191953+1)/81	365302	Paul Bourdelais	01/2021
676	2^1213313+215837	365244	Enzo Doria	11/2023
677	2^1208276+22201	363728	Enzo Doria	09/2023
678	2^1207345+1882577	363448	Enzo Doria	12/2016
679	2^1207336+217801	363445	Enzo Doria	03/2024
680	2^1207073+883727	363366	Enzo Doria	03/2017
681	3^761457-2	363308	Ryan Propper	07/2015
682	(10^363030+7)/337/443	363025	Alfred Reich	12/2021
683	2^1204869+224885	362702	Enzo Doria	07/2024
684	2^1200972+141811	361529	Stefano Morozzi	10/2022
685	(2^1200924+324730)/2	361514	Stefano Morozzi	06/2021
686	(2^1200912+274110)/2	361511	Stefano Morozzi	01/2021
687	2^1200906+165249	361509	Stefano Morozzi	07/2022
688	2^1200890+166339	361504	Stefano Morozzi	01/2023
689	(2^1200887+344126)/2	361503	Stefano Morozzi	10/2020
690	2^1200877+186755	361500	Stefano Morozzi	09/2022
691	2^1200861+198521	361496	Stefano Morozzi	11/2021
692	(2^1200856+305790)/2	361494	Stefano Morozzi	10/2020
693	(2^1200853+372822)/2	361493	Stefano Morozzi	06/2021
694	2^1200812+324178)/2	361481	Stefano Morozzi	06/2021
695	(2^1200768+380458)/2	361467	Stefano Morozzi	01/2021
696	2^1200756+140917	361464	Stefano Morozzi	05/2022
697	2^1200741+184781	361460	Stefano Morozzi	09/2022
698	(2^1200741+293402)/2	361459	Stefano Morozzi	07/2021
699	2^1200734+142653	361457	Stefano Morozzi	02/2023
701	2^1200672+1880881	361439	Enzo Doria	10/2016
700	2^1200672+141535	361439	Stefano Morozzi	09/2022
702	2^1200669+178805	361438	Stefano Morozzi	11/2022
703	2^1200660+198555	361435	Stefano Morozzi	12/2021
704	2^1200657+164837	361434	Stefano Morozzi	05/2022
705	2^1200631+166431	361426	Stefano Morozzi	02/2023
706	2^1200627+150669	361425	Stefano Morozzi	02/2023
707	(2^1200603+356030)/2	361418	Stefano Morozzi	10/2020
708	(2^1200590+275854)/2	361414	Stefano Morozzi	03/2021
709	2^1200550+139297	361402	Stefano Morozzi	10/2021
710	2^1200486+172855	361383	Stefano Morozzi	01/2023
711	(2^1200456+320526)/2	361373	Stefano Morozzi	10/2020
712	2^1200443+142121	361370	Stefano Morozzi	01/2023
713	2^1200416+164065	361362	Stefano Morozzi	01/2022
714	2^1200331+155429	361336	Stefano Morozzi	10/2021
716	(2^1200289+348366)/2	361323	Stefano Morozzi	10/2020
715	2^1200289+141885	361323	Stefano Morozzi	11/2022
717	(2^1200284+273162)/2	361322	Stefano Morozzi	10/2020
718	2^1200252+194535	361312	Stefano Morozzi	11/2021
719	(2^1200250+364230)/2	361311	Stefano Morozzi	10/2020
720	2^1200227+156881	361305	Stefano Morozzi	05/2022
721	(2^1200209+305990)/2	361299	Stefano Morozzi	10/2020
722	(2^1200210+376278)/2	361299	Stefano Morozzi	10/2020
723	2^1200202+216499	361297	Enzo Doria	12/2023
724	(2^1200182+274462)/2	361291	Stefano Morozzi	01/2021
725	2^1200178+149193	361290	Stefano Morozzi	07/2022
726	2^1200168+140403	361287	Stefano Morozzi	03/2022
727	(2^1200162+275910)/2	361285	Stefano Morozzi	03/2021
728	2^1200157+168927	361284	Stefano Morozzi	02/2023
729	2^1200134+141385	361277	Stefano Morozzi	08/2022
730	(2^1200131+360150)/2	361276	Stefano Morozzi	10/2020
731	(2^1200118+290718)/2	361272	Stefano Morozzi	01/2021
732	2^1200022+192777	361243	Stefano Morozzi	09/2022
733	2^1200021+149777	361243	Stefano Morozzi	10/2022
734	(64*10^360173-1)/243	360173	Serge Batalov	09/2014
735	(59^203309+1)/60	360029	Paul Bourdelais	09/2021
736	(2*10^359860-11)/9	359860	Rytis Slatkevicius	01/2023
737	2^1195093+1882577	359759	Enzo Doria	12/2016
738	3^753451+5*2^753451	359488	Jon Grantham	08/2023
739	(6^461108-11)/5	358812	Paul Bourdelais	04/2019
740	2^1191375+8543	358640	Phil Moore	06/2008
741	2^1190972+1880191	358519	Enzo Doria	11/2016
742	2^1189930+28549	358205	Enzo Doria	03/2024
743	(45^216551-1)/44	358004	Paul Bourdelais	08/2020
744	(50^210319-1)/49	357324	Paul Bourdelais	08/2020
745	(531^131072+25^131072)/2	357184	Kellen Shenton	03/2021
746	2^1184565+21227	356590	Enzo Doria	08/2023
747	2^1180159+22823	355264	Enzo Doria	11/2023
748	2^1179836+1885021	355167	Enzo Doria	02/2017
749	2^1178942+32269	354897	Enzo Doria	04/2024
750	2^1177053+28607	354329	Enzo Doria	02/2024

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