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	2^874073+2792957	263123	Enzo Doria	02/2016
502	2^873628+1878751	262989	Enzo Doria	08/2016
503	2^873288-269	262886	Yves Minet	01/2015
504	2^871146-3173	262242	Yves Minet	07/2016
505	2^869601-163	261776	Yves Minet	01/2015
506	2^869326+282859	261694	Enzo Doria	11/2016
507	2^869035-114181	261606	Enzo Doria	12/2014
508	2^865715+80303	260607	Enzo Doria	07/2016
509	2^865048+1882411	260406	Enzo Doria	12/2016
510	2^864899-113871	260361	Enzo Doria	10/2014
511	(7*10^260198-61)/9	260198	Erik Branger	11/2011
512	2^864298-2788421	260180	Enzo Doria	12/2015
513	2^864039-2791357	260102	Enzo Doria	01/2016
514	2^863621-113833	259976	Enzo Doria	10/2014
515	2^862837+75767	259740	Enzo Doria	05/2016
516	2^862637-31	259680	Jorge Menendez	05/2019
517	2^862088+1874941	259515	Enzo Doria	06/2016
518	2^861987-134557	259484	Hans Havermann	10/2018
519	2^861516-1854029	259343	Enzo Doria	09/2015
520	2^860975-1853977	259180	Enzo Doria	09/2015
521	3^543128+16	259138	Robert Price	04/2020
522	2^860625-1858843	259074	Enzo Doria	10/2015
523	2^860110+77689	258919	Enzo Doria	05/2016
524	2^859600+1880371	258766	Enzo Doria	10/2016
525	2^859433+494711	258716	Makoto Morimoto	10/2013
526	(2^859433-44)/(2^2*3)	258715	Makoto Morimoto	08/2019
527	(2^859433+39899)/(73390746301)	258705	Makoto Morimoto	10/2016
528	2^859240+1875271	258658	Enzo Doria	06/2016
529	Tau(971^15738)	258571	Nik Lygeros / Olivier Rozier	05/2015
530	(144^119671+1)/145	258292	Paul Bourdelais	08/2019
531	(11*2^857159-13)/15	258031	Renaud Lifchitz	08/2011
532	2^857016-633113	257988	Enzo Doria	12/2013
533	2^855732-113969	257602	Enzo Doria	10/2014
534	2^853682-3911	256984	Enzo Doria	05/2014
535	11^246668-90	256879	Enzo Doria	12/2012
536	2^851904-113939	256449	Enzo Doria	10/2014
537	2^851725-851725^2	256395	Henri Lifchitz	03/2019
538	11^246167-90	256357	Enzo Doria	12/2012
539	2^850700-569049	256087	Enzo Doria	11/2013
540	21^193601-20^193601	255983	Jean-Louis Charton	02/2015
541	(37^163193+1)/38	255918	Paul Bourdelais	07/2019
542	2^849177-114025	255628	Enzo Doria	12/2014
543	2^848502-3173	255425	Yves Minet	07/2016
544	2^848178-140291	255328	Enzo Doria	01/2014
545	2^847622-2441	255160	Yves Minet	02/2016
546	2^847291+182843	255061	Enzo Doria	11/2016
547	2^847174+1879429	255025	Enzo Doria	09/2016
548	24*29^174239+13361	254809	Curtis Bright	04/2015
549	2^845610-1868591	254554	Enzo Doria	04/2016
550	2^845484+81931	254517	Enzo Doria	08/2016
551	2^845402-114761	254492	Enzo Doria	05/2015
552	2^844334-2792441	254170	Enzo Doria	02/2016
553	11^243796-90	253888	Enzo Doria	12/2012
554	30^171733-29^171733	253671	Jean-Louis Charton	10/2018
555	2^842209+1876037	253531	Enzo Doria	07/2016
556	2^842123-59197	253505	Enzo Doria	10/2015
557	2^840797-3	253106	Paul Bourdelais	06/2019
558	2^840716-2969	253081	Yves Minet	05/2016
559	2^840358-462491	252973	Enzo Doria	08/2015
560	2^840310+1878379	252959	Enzo Doria	08/2016
561	11^242579-60	252620	Enzo Doria	10/2012
562	45^152659+2	252378	Robert Price	09/2015
563	(95^127583+1)/96	252322	Paul Bourdelais	07/2019
564	2^837725+1869377	252181	Enzo Doria	05/2016
565	2^837536-311039	252124	Enzo Doria	06/2015
566	21^190632-2	252058	Robert Price	07/2015
567	2^837242+1873297	252035	Enzo Doria	06/2016
568	2^836656-2787929	251859	Enzo Doria	11/2015
569	2^836380+1875541	251776	Enzo Doria	07/2016
570	(359^98327-1)/358	251233	Alexander Zhirkov	11/2017
571	tau(41^28288)	250924	Nik Lygeros / Olivier Rozier	10/2013
572	2^832511-461197	250611	Enzo Doria	07/2015
573	2^832505+1881137	250609	Enzo Doria	11/2016
574	2^832363+583295	250567	Enzo Doria	12/2016
575	2^832244-403635	250531	Enzo Doria	01/2014
576	2^831157+1880657	250204	Enzo Doria	11/2016
577	2^831088-7200899	250183	Enzo Doria	01/2015
578	2^830956-1349	250143	Yves Minet	07/2015
579	2^830037+282317	249867	Enzo Doria	09/2016
580	2^829589-113653	249732	Enzo Doria	09/2014
581	2^828281-3193	249338	Yves Minet	08/2016
582	2^828064-2785619	249273	Enzo Doria	10/2015
583	2^827602+60409	249134	Enzo Doria	03/2016
584	10^249010+348861	249011	Patrick De Geest	04/2016
585	10^249010-21	249010	Serge Batalov	12/2014
586	2^826733+1882907	248872	Enzo Doria	12/2016
587	2^825682+1876549	248556	Enzo Doria	07/2016
588	2^824991-114121	248348	Enzo Doria	12/2014
589	2^824642-362727	248242	Enzo Doria	12/2013
590	2^824565-114265	248219	Enzo Doria	01/2015
591	(73*10^248145-1)/9	248146	Robert Price	01/2015
592	(2^823337+1)/(3*362268281)	247841	Gord Palameta	08/2018
593	(2^822971-1)/6583769/28211445881/21255852651726486149207	247700	Robert Kinser	09/2016
594	2^822296+76501	247536	Enzo Doria	05/2016
595	2^821590-114167	247324	Enzo Doria	12/2014
596	2^821512-2790659	247300	Enzo Doria	12/2015
597	2^820077+382847	246868	Enzo Doria	11/2016
598	2^820001+81269	246845	Enzo Doria	07/2016
599	2^819463-59197	246683	Enzo Doria	10/2015
600	2^819296+80581	246633	Enzo Doria	07/2016
601	2^817160-350369	245990	Enzo Doria	06/2015
602	88093#+(653879#)/(88093#)	245374	Makoto Morimoto	11/2017
603	2^815111-113857	245373	Enzo Doria	10/2014
604	2^814914-4001	245314	Yves Minet	05/2017
605	846^83761-845^83761	245200	Jean-Louis Charton	12/2012
606	2^814356-2790449	245146	Enzo Doria	12/2015
607	2^814276-459029	245122	Enzo Doria	04/2015
608	2^814023+180923	245046	Enzo Doria	07/2016
609	(3^513059-2^513059)/(1026119*5430216457)	244776	Mike Oakes	03/2017
610	3^513007+16	244767	Robert Price	04/2020
611	2^811842-113675	244389	Enzo Doria	09/2014
612	2^811132-2787929	244176	Enzo Doria	11/2015
613	2^809746-2790971	243758	Enzo Doria	01/2016
614	2^808767-3295	243464	Yves Minet	12/2016
615	2^808621-113809	243420	Enzo Doria	09/2014
616	2^807724+1879621	243150	Enzo Doria	09/2016
617	2^805843-113611	242583	Enzo Doria	08/2014
618	2^805745-459763	242554	Enzo Doria	05/2015
619	2^805353+782687	242436	Enzo Doria	11/2016
620	2^804277-417933	242112	Enzo Doria	01/2014
621	2^803468-269039	241868	Enzo Doria	10/2013
622	2^803172+80851	241779	Enzo Doria	07/2016
623	3^506233-2	241535	Robert Price	11/2013
624	2^802025-25999	241434	Enzo Doria	10/2013
625	(3^505823+3^252912+1)/7	241339	Serge Batalov	03/2014
626	2^801303+1872923	241217	Enzo Doria	05/2016
627	2^800579-1862947	240999	Enzo Doria	12/2015
628	3^504206+2	240568	Luke W. Richards	03/2018
629	2^798973-26283	240515	Enzo Doria	10/2013
630	2^798671-69487	240424	Enzo Doria	12/2015
631	2^797220+79831	239988	Enzo Doria	06/2016
632	2^796910-26001	239894	Enzo Doria	10/2013
633	2^796598+653119	239800	Enzo Doria	12/2016
634	2^796432-1859729	239750	Enzo Doria	11/2015
635	2^796002-1852211	239621	Enzo Doria	08/2015
636	2^795709+75767	239533	Enzo Doria	04/2016
637	2^795708+81721	239532	Enzo Doria	08/2016
638	2^795468-2786249	239460	Enzo Doria	10/2015
639	2^795442+80779	239452	Enzo Doria	07/2016
640	2^795075-1852057	239342	Enzo Doria	08/2015
641	(86^123677+1)/87	239252	Paul Bourdelais	01/2019
642	2^794043+1875023	239031	Enzo Doria	06/2016
643	2^793347-69577	238822	Enzo Doria	01/2016
644	2^792988-344429	238714	Enzo Doria	08/2015
645	2^792700-2786369	238627	Enzo Doria	11/2015
646	2^792663-1844797	238616	Enzo Doria	06/2015
647	2^792605-291943	238598	Enzo Doria	07/2015
648	(2^792061-2^396031+1)/5	238434	Thomas Ritschel	03/2014
649	2^789373+1869377	237625	Enzo Doria	05/2016
650	((10^59387+1)^3(10^59387+1+10^29694)-(10^118774+10^59387)(10^29694-1)+10^178161)/27961	237544	Serge Batalov	04/2015
651	2^788942+1866409	237496	Enzo Doria	02/2016
652	2^788844-114329	237466	Enzo Doria	01/2015
653	2^788705-1859713	237424	Enzo Doria	11/2015
654	2^786180+1871971	236664	Enzo Doria	05/2016
655	11^227092-90	236492	Enzo Doria	11/2012
656	2^785260+1866361	236387	Enzo Doria	02/2016
657	2^785220+1880611	236375	Enzo Doria	10/2016
658	19^184650-2	236122	Robert Price	10/2014
659	10^236059+216513	236060	Patrick De Geest	04/2016
660	10^236059-20909	236059	Robert Price	09/2015
661	(87^121487-1)/86	235625	Paul Bourdelais	12/2018
662	2^782634-113981	235597	Enzo Doria	11/2014
663	2^782423+1879733	235533	Enzo Doria	09/2016
664	2^781682-2789543	235310	Enzo Doria	12/2015
665	2^780408-113453	234927	Enzo Doria	08/2014
666	2^780368-1864829	234915	Enzo Doria	01/2016
667	2^779593-1836559	234681	Enzo Doria	05/2015
668	(8713#+(549391#)/(8713#))/360295171	234487	Makoto Morimoto	11/2017
669	(5^335429+1)/6	234455	Paul Bourdelais	08/2010
670	2^778395-113617	234321	Enzo Doria	08/2014
671	2^776245-2792353	233674	Enzo Doria	02/2016
672	2^776060-114029	233618	Enzo Doria	11/2014
673	2^775987-2789557	233596	Enzo Doria	12/2015
674	2^775672+1866721	233501	Enzo Doria	03/2016
675	(11^223999+1)/12	233270	Paul Bourdelais	02/2010
676	2^774118+1885789	233033	Enzo Doria	04/2017
677	21^176191-20^176191	232964	Jean-Louis Charton	01/2015
678	2^773679-113425	232901	Enzo Doria	08/2014
679	10^232599+192489	232600	Patrick De Geest	12/2013
680	10^232599-3	232599	Markus Tervooren	10/2010
681	2^772552-458879	232562	Enzo Doria	04/2015
682	2^772214+1874899	232460	Enzo Doria	06/2016
683	2^771994-1862771	232394	Enzo Doria	12/2015
684	2^771889+1876037	232362	Enzo Doria	07/2016
685	2^771660+1866511	232293	Enzo Doria	02/2016
686	5^332150-18188	232163	Enzo Doria	06/2014
687	3^485977-2^485977	231870	Mike Oakes	09/2009
688	2^770082-114161	231818	Enzo Doria	01/2015
689	(20^177967+1)/21	231540	Paul Bourdelais	05/2013
690	2^767622-9221	231078	Lelio R Paula	01/2016
691	2^767344+1880311	230994	Enzo Doria	09/2016
692	(3^483611-1)/2	230741	Paul Bourdelais	02/2010
693	(10^230706+179)/9	230706	Serge Batalov	12/2014
694	2^766309+1875257	230682	Enzo Doria	06/2016
695	2^765635+1879883	230480	Enzo Doria	09/2016
696	2^764348-113697	230092	Enzo Doria	09/2014
697	2^764131+78863	230027	Enzo Doria	05/2016
698	2^763701+60197	229897	Enzo Doria	03/2016
699	2^762841-25905	229639	Enzo Doria	10/2013
700	2^761117-113569	229120	Enzo Doria	08/2014
701	(98^114859+1)/99	228709	Paul Bourdelais	12/2018
702	(2^758231+1)/(32714694297653973236839266867)	228223	Gord Palameta	12/2018
703	2^757985-2790013	228177	Enzo Doria	12/2015
704	2^757038-1862081	227892	Enzo Doria	12/2015
705	2^756839+95849	227832	Makoto Morimoto	10/2013
706	(2^756839+6989)/756091	227826	Makoto Morimoto	09/2016
707	(2^756839-50211)/(137*3203)	227826	Makoto Morimoto	08/2019
708	2^756773-112723	227812	Enzo Doria	07/2014
709	524309#+616367	227431	Makoto Morimoto	02/2016
710	2^755097-114193	227307	Enzo Doria	12/2014
711	2^754473-2791513	227120	Enzo Doria	01/2016
712	2^751426-764321	226202	Enzo Doria	12/2013
713	(18^180181-1)/17	226176	Andy Steward	04/2007
714	2^750740-3	225996	Paul Bourdelais	03/2012
715	2^750725+60227	225991	Enzo Doria	02/2016
716	2^750525-113743	225931	Enzo Doria	09/2014
717	(2^750151-1)/(4299340426317590093831289397764574647511836143783478715117383638888678527263)	225744	Dario Alpern	10/2014
718	2^749444-1861889	225606	Enzo Doria	12/2015
719	tau(311^16452)	225560	Nik Lygeros / Olivier Rozier / LR team	10/2013
720	2^749096+1876861	225501	Enzo Doria	07/2016
721	(519643#+43033)/(2318712706283)	225379	Makoto Morimoto	08/2019
722	2^748657+79607	225369	Enzo Doria	06/2016
723	2^746653-291583	224765	Enzo Doria	07/2015
724	2^746461-114043	224708	Enzo Doria	11/2014
725	2^745098-350471	224297	Enzo Doria	06/2015
726	(154*10^224061-1)/9	224063	Serge Batalov	12/2014
727	2^744211-1845787	224030	Enzo Doria	07/2015
728	2^743592-134579	223844	Hans Havermann	10/2018
729	2^742452+3	223501	Paul Bourdelais	06/2019
730	234178^9+9^234178	223463	Anatoly F. Selevich	07/2011
731	2^741651-461197	223260	Enzo Doria	07/2015
732	2^741362-1845251	223173	Enzo Doria	07/2015
733	2^740455-1863877	222900	Enzo Doria	12/2015
734	2^739636-2792219	222653	Enzo Doria	02/2016
735	11^213654-180	222498	Enzo Doria	01/2013
736	2^738957-1859743	222449	Enzo Doria	11/2015
737	(54^128189+1)/55	222073	Paul Bourdelais	11/2018
738	(10^221654+179)/9	221654	Serge Batalov	12/2014
739	2^736281+79817	221643	Enzo Doria	06/2016
740	10^221631+247617	221632	Patrick De Geest	10/2013
741	10^221631-9	221631	Alexander Gramolin	02/2011
742	2^735970-1839821	221550	Enzo Doria	06/2015
743	2^735367+60293	221368	Enzo Doria	03/2016
744	(29^151153+1)/30	221045	Paul Bourdelais	09/2017
745	2^733264-2784089	220735	Enzo Doria	10/2015
746	2^733114-24555	220690	Enzo Doria	09/2013
747	2^731891-636259	220322	Enzo Doria	12/2013
748	2^731124-25539	220091	Enzo Doria	09/2013
749	2^730972-462029	220045	Enzo Doria	07/2015
750	2^730833+1868627	220003	Enzo Doria	04/2016

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Probable Primes Top 10000

(271019 PRPs in the top)