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	2^898762-251511	270555	Enzo Doria	12/2013
502	2^898589+47	270503	Lelio R Paula	03/2016
503	187322*10^270343-187321	270349	Danilo Nitsche	09/2013
504	48358*10^270343-48357	270348	Danilo Nitsche	09/2013
505	(10^270343-1)/9	270343	Maksym Voznyy	07/2007
506	2^897867-3217	270285	Yves Minet	12/2016
507	2^897849-115273	270280	Enzo Doria	07/2015
508	2^896616-114179	269909	Enzo Doria	12/2014
509	2^894928+583561	269401	Enzo Doria	04/2017
510	2^894673-39343	269324	Enzo Doria	08/2015
511	F(1285607)	268676	Henri Lifchitz	11/2008
512	2^892112+187663	268553	Enzo Doria	08/2016
513	(10^268207+1)/11	268206	Paul Bourdelais	02/2010
514	2^890957-69583	268205	Enzo Doria	12/2015
515	32841!^2+32840!^2+...+2!^2+1!^2	268128	Serge Batalov	07/2017
516	2^890122-351401	267954	Enzo Doria	07/2015
517	(19^209359-1)/18	267718	Paul Bourdelais	08/2010
518	(85^138647+1)/86	267507	Paul Bourdelais	07/2019
519	(485^99523-1)/484	267291	Michael Stocker	05/2020
520	2^886324+77791	266811	Enzo Doria	06/2016
521	2^884714+1880527	266326	Enzo Doria	10/2016
522	11^255426+255426^11	265999	Serge Batalov	05/2014
523	2^883462-343421	265949	Enzo Doria	07/2015
524	2^883442+1875019	265943	Enzo Doria	06/2016
525	2^883333-291583	265910	Enzo Doria	07/2015
526	2^880411+1882673	265031	Enzo Doria	12/2016
527	2^879530-2788031	264765	Enzo Doria	12/2015
528	2^878118+2793079	264340	Enzo Doria	02/2016
529	(37^168527-1)/36	264283	Paul Bourdelais	08/2019
530	2^875748-461129	263627	Enzo Doria	07/2015
531	2^875181-2789923	263456	Enzo Doria	12/2015
532	2^875101-350083	263432	Enzo Doria	08/2015
533	2^874684+1883587	263307	Enzo Doria	01/2017
534	2^874616+1872211	263286	Enzo Doria	05/2016
535	3^551491+16	263129	Robert Price	04/2020
536	2^874073+2792957	263123	Enzo Doria	02/2016
537	2^873628+1878751	262989	Enzo Doria	08/2016
538	2^873288-269	262886	Yves Minet	01/2015
539	2^871146-3173	262242	Yves Minet	07/2016
540	2^869601-163	261776	Yves Minet	01/2015
541	2^869326+282859	261694	Enzo Doria	11/2016
542	2^869035-114181	261606	Enzo Doria	12/2014
543	2^865715+80303	260607	Enzo Doria	07/2016
544	2^865048+1882411	260406	Enzo Doria	12/2016
545	2^864899-113871	260361	Enzo Doria	10/2014
546	(7*10^260198-61)/9	260198	Erik Branger	11/2011
547	2^864298-2788421	260180	Enzo Doria	12/2015
548	2^864039-2791357	260102	Enzo Doria	01/2016
549	2^863621-113833	259976	Enzo Doria	10/2014
550	2^862837+75767	259740	Enzo Doria	05/2016
551	2^862637-31	259680	Jorge Menendez	05/2019
552	2^862088+1874941	259515	Enzo Doria	06/2016
553	2^861987-134557	259484	Hans Havermann	10/2018
554	2^861516-1854029	259343	Enzo Doria	09/2015
555	2^860975-1853977	259180	Enzo Doria	09/2015
556	3^543128+16	259138	Robert Price	04/2020
557	2^860625-1858843	259074	Enzo Doria	10/2015
558	2^860110+77689	258919	Enzo Doria	05/2016
559	2^859600+1880371	258766	Enzo Doria	10/2016
560	2^859433+494711	258716	Makoto Morimoto	10/2013
561	(2^859433-44)/(2^2*3)	258715	Makoto Morimoto	08/2019
562	(2^859433+39899)/(73390746301)	258705	Makoto Morimoto	10/2016
563	2^859240+1875271	258658	Enzo Doria	06/2016
564	Tau(971^15738)	258571	Nik Lygeros / Olivier Rozier	05/2015
565	(144^119671+1)/145	258292	Paul Bourdelais	08/2019
566	(11*2^857159-13)/15	258031	Renaud Lifchitz	08/2011
567	2^857016-633113	257988	Enzo Doria	12/2013
568	2^855732-113969	257602	Enzo Doria	10/2014
569	2^853682-3911	256984	Enzo Doria	05/2014
570	11^246668-90	256879	Enzo Doria	12/2012
571	2^851904-113939	256449	Enzo Doria	10/2014
572	2^851725-851725^2	256395	Henri Lifchitz	03/2019
573	11^246167-90	256357	Enzo Doria	12/2012
574	2^850700-569049	256087	Enzo Doria	11/2013
575	21^193601-20^193601	255983	Jean-Louis Charton	02/2015
576	(37^163193+1)/38	255918	Paul Bourdelais	07/2019
577	2^849177-114025	255628	Enzo Doria	12/2014
578	2^848502-3173	255425	Yves Minet	07/2016
579	2^848178-140291	255328	Enzo Doria	01/2014
580	2^847622-2441	255160	Yves Minet	02/2016
581	2^847291+182843	255061	Enzo Doria	11/2016
582	2^847174+1879429	255025	Enzo Doria	09/2016
583	24*29^174239+13361	254809	Curtis Bright	04/2015
584	2^845610-1868591	254554	Enzo Doria	04/2016
585	2^845484+81931	254517	Enzo Doria	08/2016
586	2^845402-114761	254492	Enzo Doria	05/2015
587	2^844334-2792441	254170	Enzo Doria	02/2016
588	11^243796-90	253888	Enzo Doria	12/2012
589	30^171733-29^171733	253671	Jean-Louis Charton	10/2018
590	2^842209+1876037	253531	Enzo Doria	07/2016
591	2^842123-59197	253505	Enzo Doria	10/2015
592	2^840797-3	253106	Paul Bourdelais	06/2019
593	2^840716-2969	253081	Yves Minet	05/2016
594	2^840358-462491	252973	Enzo Doria	08/2015
595	2^840310+1878379	252959	Enzo Doria	08/2016
596	11^242579-60	252620	Enzo Doria	10/2012
597	45^152659+2	252378	Robert Price	09/2015
598	(95^127583+1)/96	252322	Paul Bourdelais	07/2019
599	2^837725+1869377	252181	Enzo Doria	05/2016
600	2^837536-311039	252124	Enzo Doria	06/2015
601	21^190632-2	252058	Robert Price	07/2015
602	2^837242+1873297	252035	Enzo Doria	06/2016
603	2^836656-2787929	251859	Enzo Doria	11/2015
604	2^836380+1875541	251776	Enzo Doria	07/2016
605	(359^98327-1)/358	251233	Alexander Zhirkov	11/2017
606	tau(41^28288)	250924	Nik Lygeros / Olivier Rozier	10/2013
607	2^832511-461197	250611	Enzo Doria	07/2015
608	2^832505+1881137	250609	Enzo Doria	11/2016
609	2^832363+583295	250567	Enzo Doria	12/2016
610	2^832244-403635	250531	Enzo Doria	01/2014
611	2^831157+1880657	250204	Enzo Doria	11/2016
612	2^831088-7200899	250183	Enzo Doria	01/2015
613	2^830956-1349	250143	Yves Minet	07/2015
614	2^830037+282317	249867	Enzo Doria	09/2016
615	2^829589-113653	249732	Enzo Doria	09/2014
616	2^828281-3193	249338	Yves Minet	08/2016
617	2^828064-2785619	249273	Enzo Doria	10/2015
618	2^827602+60409	249134	Enzo Doria	03/2016
619	10^249010+348861	249011	Patrick De Geest	04/2016
620	10^249010-21	249010	Serge Batalov	12/2014
621	2^826733+1882907	248872	Enzo Doria	12/2016
622	2^825682+1876549	248556	Enzo Doria	07/2016
623	2^824991-114121	248348	Enzo Doria	12/2014
624	2^824642-362727	248242	Enzo Doria	12/2013
625	2^824565-114265	248219	Enzo Doria	01/2015
626	(73*10^248145-1)/9	248146	Robert Price	01/2015
627	(2^823337+1)/(3*362268281)	247841	Gord Palameta	08/2018
628	(2^822971-1)/6583769/28211445881/21255852651726486149207	247700	Robert Kinser	09/2016
629	2^822296+76501	247536	Enzo Doria	05/2016
630	2^821590-114167	247324	Enzo Doria	12/2014
631	2^821512-2790659	247300	Enzo Doria	12/2015
632	2^820077+382847	246868	Enzo Doria	11/2016
633	2^820001+81269	246845	Enzo Doria	07/2016
634	2^819463-59197	246683	Enzo Doria	10/2015
635	2^819296+80581	246633	Enzo Doria	07/2016
636	2^817160-350369	245990	Enzo Doria	06/2015
637	88093#+(653879#)/(88093#)	245374	Makoto Morimoto	11/2017
638	2^815111-113857	245373	Enzo Doria	10/2014
639	2^814914-4001	245314	Yves Minet	05/2017
640	846^83761-845^83761	245200	Jean-Louis Charton	12/2012
641	2^814356-2790449	245146	Enzo Doria	12/2015
642	2^814276-459029	245122	Enzo Doria	04/2015
643	2^814023+180923	245046	Enzo Doria	07/2016
644	(3^513059-2^513059)/(1026119*5430216457)	244776	Mike Oakes	03/2017
645	3^513007+16	244767	Robert Price	04/2020
646	2^811842-113675	244389	Enzo Doria	09/2014
647	2^811132-2787929	244176	Enzo Doria	11/2015
648	2^809746-2790971	243758	Enzo Doria	01/2016
649	2^808767-3295	243464	Yves Minet	12/2016
650	2^808621-113809	243420	Enzo Doria	09/2014
651	2^807724+1879621	243150	Enzo Doria	09/2016
652	20^186554-3	242713	Paul Bourdelais	12/2020
653	2^805843-113611	242583	Enzo Doria	08/2014
654	2^805745-459763	242554	Enzo Doria	05/2015
655	2^805353+782687	242436	Enzo Doria	11/2016
656	2^804277-417933	242112	Enzo Doria	01/2014
657	2^803468-269039	241868	Enzo Doria	10/2013
658	2^803172+80851	241779	Enzo Doria	07/2016
659	3^506233-2	241535	Robert Price	11/2013
660	2^802025-25999	241434	Enzo Doria	10/2013
661	(3^505823+3^252912+1)/7	241339	Serge Batalov	03/2014
662	2^801303+1872923	241217	Enzo Doria	05/2016
663	2^800579-1862947	240999	Enzo Doria	12/2015
664	3^504206+2	240568	Luke W. Richards	03/2018
665	2^798973-26283	240515	Enzo Doria	10/2013
666	2^798671-69487	240424	Enzo Doria	12/2015
667	2^797220+79831	239988	Enzo Doria	06/2016
668	2^796910-26001	239894	Enzo Doria	10/2013
669	2^796598+653119	239800	Enzo Doria	12/2016
670	2^796432-1859729	239750	Enzo Doria	11/2015
671	2^796002-1852211	239621	Enzo Doria	08/2015
672	2^795709+75767	239533	Enzo Doria	04/2016
673	2^795708+81721	239532	Enzo Doria	08/2016
674	2^795468-2786249	239460	Enzo Doria	10/2015
675	2^795442+80779	239452	Enzo Doria	07/2016
676	2^795075-1852057	239342	Enzo Doria	08/2015
677	(86^123677+1)/87	239252	Paul Bourdelais	01/2019
678	2^794043+1875023	239031	Enzo Doria	06/2016
679	2^793347-69577	238822	Enzo Doria	01/2016
680	2^792988-344429	238714	Enzo Doria	08/2015
681	2^792700-2786369	238627	Enzo Doria	11/2015
682	2^792663-1844797	238616	Enzo Doria	06/2015
683	2^792605-291943	238598	Enzo Doria	07/2015
684	(2^792061-2^396031+1)/5	238434	Thomas Ritschel	03/2014
685	2^789373+1869377	237625	Enzo Doria	05/2016
686	((10^59387+1)^3(10^59387+1+10^29694)-(10^118774+10^59387)(10^29694-1)+10^178161)/27961	237544	Serge Batalov	04/2015
687	2^788942+1866409	237496	Enzo Doria	02/2016
688	2^788844-114329	237466	Enzo Doria	01/2015
689	2^788705-1859713	237424	Enzo Doria	11/2015
690	2^786180+1871971	236664	Enzo Doria	05/2016
691	11^227092-90	236492	Enzo Doria	11/2012
692	2^785260+1866361	236387	Enzo Doria	02/2016
693	2^785220+1880611	236375	Enzo Doria	10/2016
694	19^184650-2	236122	Robert Price	10/2014
695	10^236059+216513	236060	Patrick De Geest	04/2016
696	10^236059-20909	236059	Robert Price	09/2015
697	(87^121487-1)/86	235625	Paul Bourdelais	12/2018
698	2^782634-113981	235597	Enzo Doria	11/2014
699	2^782423+1879733	235533	Enzo Doria	09/2016
700	2^781682-2789543	235310	Enzo Doria	12/2015
701	2^780408-113453	234927	Enzo Doria	08/2014
702	2^780368-1864829	234915	Enzo Doria	01/2016
703	2^779593-1836559	234681	Enzo Doria	05/2015
704	(8713#+(549391#)/(8713#))/360295171	234487	Makoto Morimoto	11/2017
705	(5^335429+1)/6	234455	Paul Bourdelais	08/2010
706	2^778395-113617	234321	Enzo Doria	08/2014
707	2^776245-2792353	233674	Enzo Doria	02/2016
708	2^776060-114029	233618	Enzo Doria	11/2014
709	2^775987-2789557	233596	Enzo Doria	12/2015
710	2^775672+1866721	233501	Enzo Doria	03/2016
711	(11^223999+1)/12	233270	Paul Bourdelais	02/2010
712	2^774118+1885789	233033	Enzo Doria	04/2017
713	21^176191-20^176191	232964	Jean-Louis Charton	01/2015
714	2^773679-113425	232901	Enzo Doria	08/2014
715	10^232599+192489	232600	Patrick De Geest	12/2013
716	10^232599-3	232599	Markus Tervooren	10/2010
717	2^772552-458879	232562	Enzo Doria	04/2015
718	2^772214+1874899	232460	Enzo Doria	06/2016
719	2^771994-1862771	232394	Enzo Doria	12/2015
720	2^771889+1876037	232362	Enzo Doria	07/2016
721	2^771660+1866511	232293	Enzo Doria	02/2016
722	5^332150-18188	232163	Enzo Doria	06/2014
723	3^485977-2^485977	231870	Mike Oakes	09/2009
724	2^770082-114161	231818	Enzo Doria	01/2015
725	(20^177967+1)/21	231540	Paul Bourdelais	05/2013
726	2^767622-9221	231078	Lelio R Paula	01/2016
727	2^767344+1880311	230994	Enzo Doria	09/2016
728	(3^483611-1)/2	230741	Paul Bourdelais	02/2010
729	(10^230706+179)/9	230706	Serge Batalov	12/2014
730	2^766309+1875257	230682	Enzo Doria	06/2016
731	2^765635+1879883	230480	Enzo Doria	09/2016
732	2^764348-113697	230092	Enzo Doria	09/2014
733	2^764131+78863	230027	Enzo Doria	05/2016
734	2^763701+60197	229897	Enzo Doria	03/2016
735	2^762841-25905	229639	Enzo Doria	10/2013
736	2^761117-113569	229120	Enzo Doria	08/2014
737	(98^114859+1)/99	228709	Paul Bourdelais	12/2018
738	(2^758231+1)/(32714694297653973236839266867)	228223	Gord Palameta	12/2018
739	2^757985-2790013	228177	Enzo Doria	12/2015
740	2^757038-1862081	227892	Enzo Doria	12/2015
741	2^756839+95849	227832	Makoto Morimoto	10/2013
742	(2^756839+6989)/756091	227826	Makoto Morimoto	09/2016
743	(2^756839-50211)/(137*3203)	227826	Makoto Morimoto	08/2019
744	2^756773-112723	227812	Enzo Doria	07/2014
745	524309#+616367	227431	Makoto Morimoto	02/2016
746	2^755097-114193	227307	Enzo Doria	12/2014
747	2^754473-2791513	227120	Enzo Doria	01/2016
748	2^751426-764321	226202	Enzo Doria	12/2013
749	(18^180181-1)/17	226176	Andy Steward	04/2007
750	2^750740-3	225996	Paul Bourdelais	03/2012

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Probable Primes Top 10000

(277054 PRPs in the top)