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	2^1061095-1061095	319422	Henri Lifchitz	10/2013
502	2^1060950+653119	319378	Enzo Doria	12/2016
503	2^1060363+782753	319202	Enzo Doria	11/2016
504	(71^172259-1)/70	318895	Paul Bourdelais	08/2020
505	2^1054736+483061	317508	Enzo Doria	12/2016
506	2^1053965+1879667	317276	Enzo Doria	10/2016
507	(43^194119-1)/42	317086	Paul Bourdelais	08/2020
508	2^1052186-458165	316740	Enzo Doria	03/2015
509	2^1046613-114685	315062	Enzo Doria	04/2015
510	2^1045625-459373	314765	Enzo Doria	06/2015
511	(7*10^314564-61)/9	314564	Erik Branger	09/2016
512	2^1044206+7	314338	Stefano Morozzi	10/2022
513	(7^371669-1)/6	314096	Paul Bourdelais	02/2010
514	(53^181981-1)/52	313784	Paul Bourdelais	08/2020
515	2^1041944+283051	313657	Enzo Doria	12/2016
516	2^1041153-114391	313419	Enzo Doria	02/2015
517	(2^1039700+9)/5	312981	Stefano Morozzi	09/2022
518	(74^167311+1)/75	312742	Paul Bourdelais	12/2020
519	2^1038871+1866983	312732	Enzo Doria	04/2016
520	(55^179573-1)/54	312521	Paul Bourdelais	08/2020
521	2^1037647+1881263	312363	Enzo Doria	11/2016
522	2^1037226+1879699	312237	Enzo Doria	10/2016
523	2^1036867+1865843	312129	Enzo Doria	02/2016
524	(76^165947+1)/77	312114	Paul Bourdelais	01/2021
525	2^1036020-114539	311874	Enzo Doria	02/2015
526	(90^159463-1)/89	311628	Paul Bourdelais	08/2020
527	2^1032240+1883431	310736	Enzo Doria	01/2017
528	2^1030352+1870021	310167	Enzo Doria	06/2016
529	2^1030046+1882843	310075	Enzo Doria	11/2016
530	3^648872+16	309591	Robert Price	04/2020
531	5^442281+2	309142	Paul Bourdelais	01/2021
532	2^1026190+15	308914	Stefano Morozzi	10/2022
533	A352736(16)	306985	Kellen Shenton	05/2022
534	(11^293831-1)/10	305993	Paul Bourdelais	03/2010
535	(67^167449-1)/66	305773	Paul Bourdelais	08/2020
536	(62^170539+1)/63	305671	Paul Bourdelais	12/2020
537	2^1015321-1015321	305643	Henri Lifchitz	08/2013
538	2^1014450+7	305380	Stefano Morozzi	10/2022
539	2^1014224-2791229	305312	Enzo Doria	01/2016
540	(10^304986+7)/673	304984	Alfred Reich	11/2021
541	65473^45250+45250^65473	304818	Hans Havermann	02/2022
542	66012^41423+41423^66012	304794	Hans Havermann	03/2022
543	65073^48202+48202^65073	304742	Hans Havermann	04/2022
544	238176^19+19^238176	304569	Hans Havermann	03/2022
545	73122^14615+14615^73122	304539	Hans Havermann	05/2022
546	64492^52639+52639^64492	304487	Hans Havermann	03/2022
547	65955^41288+41288^65955	304437	Hans Havermann	04/2022
548	71729^17530+17530^71729	304403	Hans Havermann	03/2022
549	70170^21733+21733^70170	304336	Hans Havermann	03/2022
550	2^1010751-107709	304267	Enzo Doria	03/2014
551	84473^3994+3994^84473	304222	Hans Havermann	03/2022
552	(2^1010623-1)/12602017578957977	304212	Tony Prest / Never Odd Or Even	02/2014
553	74442^12125+12125^74442	303998	Hans Havermann	02/2022
554	77842^8039+8039^77842	303989	Hans Havermann	01/2022
555	64209^54140+54140^64209	303935	Hans Havermann	02/2022
556	2^1009577+1869587	303913	Enzo Doria	06/2016
557	67389^32338+32338^67389	303906	Hans Havermann	02/2022
558	8^336419-7^336419	303817	Jean-Louis Charton	01/2008
559	2^1009168+15	303790	Stefano Morozzi	10/2022
560	80766^5771+5771^80766	303782	Hans Havermann	01/2022
561	66094^39385+39385^66094	303724	Hans Havermann	01/2022
562	69147^24574+24574^69147	303589	Hans Havermann	02/2022
563	78390^7459+7459^78390	303580	Hans Havermann	01/2022
564	2^1008301+1869377	303529	Enzo Doria	06/2016
565	65008^46615+46615^65008	303492	Hans Havermann	02/2022
566	(2^1007838+5)/3	303389	Serge Batalov	08/2015
567	65018^46293+46293^65018	303343	Hans Havermann	01/2022
568	6^389756+5	303290	Paul Bourdelais	02/2021
569	71016^18649+18649^71016	303285	Hans Havermann	01/2022
570	80160^6047+6047^80160	303129	Hans Havermann	01/2022
571	67434^31237+31237^67434	303094	Hans Havermann	03/2022
572	65537^42102+42102^65537	303063	Hans Havermann	02/2022
573	71790^16553+16553^71790	302874	Hans Havermann	11/2021
574	65208^44129+44129^65208	302874	Hans Havermann	11/2021
575	84181^3960+3960^84181	302858	Hans Havermann	11/2021
576	71956^16087+16087^71956	302682	Hans Havermann	11/2021
577	2^1005326+383059	302634	Enzo Doria	12/2016
578	2^1004929+1877567	302514	Enzo Doria	08/2016
579	69341^22978+22978^69341	302418	Hans Havermann	12/2021
580	111443^516+516^111443	302306	Hans Havermann	12/2021
581	67638^29387+29387^67638	302218	Hans Havermann	11/2021
582	2^1003494+1874899	302082	Enzo Doria	06/2016
583	75189^10400+10400^75189	302037	Hans Havermann	12/2021
584	67237^31042+31042^67237	302026	Hans Havermann	12/2021
585	64540^47791+47791^64540	302005	Hans Havermann	11/2021
586	2^1003046+60529	301947	Enzo Doria	04/2016
587	83278^4209+4209^83278	301815	Hans Havermann	09/2021
588	64431^48250+48250^64431	301763	Hans Havermann	09/2021
589	67237^30714+30714^67237	301716	Hans Havermann	09/2021
590	64641^46288+46288^64641	301581	Hans Havermann	09/2021
591	71513^16482+16482^71513	301572	Hans Havermann	10/2021
592	72017^15396+15396^72017	301565	Hans Havermann	09/2021
593	65534^39927+39927^65534	301540	Hans Havermann	10/2021
594	(23^221411-1)/22	301501	Paul Bourdelais	08/2020
595	63169^59152+59152^63169	301441	Hans Havermann	09/2021
596	75055^10348+10348^75055	301336	Hans Havermann	09/2021
597	2^1000647+1881353	301225	Enzo Doria	11/2016
598	83686^3961+3961^83686	301086	Hans Havermann	10/2021
599	68529^24742+24742^68529	301078	Hans Havermann	09/2021
600	65207^41416+41416^65207	301072	Hans Havermann	10/2021
601	2^1000000+821751	301030	Tony Prest / Never Odd Or Even	10/2015
602	90762^2071+2071^90762	300984	Hans Havermann	06/2021
603	63909^51142+51142^63909	300934	Hans Havermann	08/2021
604	2^999646+1874029	300924	Enzo Doria	06/2016
605	66280^34607+34607^66280	300856	Hans Havermann	06/2021
606	65534^38925+38925^65534	300817	Hans Havermann	07/2021
607	63296^56517+56517^63296	300794	Hans Havermann	06/2021
608	110610^523+523^110610	300694	Hans Havermann	06/2021
609	66428^33609+33609^66428	300684	Hans Havermann	06/2021
610	74247^11210+11210^74247	300672	Hans Havermann	06/2021
611	(59^169777-1)/58	300649	Paul Bourdelais	08/2020
612	10^300476+3	300477	Ed Trice	10/2012
613	10^300476-530913	300476	Patrick De Geest	03/2016
614	66703^31960+31960^66703	300471	Hans Havermann	06/2021
615	63722^51915+51915^63722	300468	Hans Havermann	06/2021
616	2^998053+1879667	300444	Enzo Doria	09/2016
617	77018^7959+7959^77018	300437	Hans Havermann	07/2021
618	314738^9+9^314738	300337	Anatoly F. Selevich	02/2011
619	69478^20987+20987^69478	300281	Hans Havermann	07/2021
620	64088^48393+48393^64088	300239	Hans Havermann	07/2021
621	64605^44146+44146^64605	300084	Hans Havermann	08/2021
622	7^355039-6^355039	300043	Jean-Louis Charton	05/2011
623	67594^27465+27465^67594	300035	Hans Havermann	06/2021
624	10^300000+287389	300001	Patrick De Geest	10/2019
625	10^300000-83657	300000	Patrick De Geest	10/2019
626	70599^17756+17756^70599	300000	Hans Havermann	06/2021
627	numbpart(72526161452)	299999	Serge Batalov	04/2017
628	2^996182-114431	299881	Enzo Doria	02/2015
629	2^996034-17	299837	Stefano Morozzi	07/2022
630	2^995214-2788361	299590	Enzo Doria	12/2015
631	2^994791-114319	299462	Enzo Doria	01/2015
632	2^994490-1863791	299372	Enzo Doria	01/2016
633	2^993322+1885729	299020	Enzo Doria	03/2017
634	(36395^65536+36393^65536)/2	298913	Kellen Shenton	04/2022
635	2^992711-2788807	298836	Enzo Doria	12/2015
636	2^992525-114199	298780	Enzo Doria	12/2014
637	2^992329+1884707	298721	Enzo Doria	02/2017
638	2^991968-23	298613	Stefano Morozzi	07/2022
639	2^991715-19	298536	Stefano Morozzi	07/2022
640	(10^298414+7)/191/823/56921/1334467	298398	Alfred Reich	10/2021
641	2^989562+25	297888	Stefano Morozzi	05/2021
642	(2*10^297488-23)/3	297488	Robert Price	10/2022
643	(2^986191+1)/3	296873	Vincent Diepeveen	06/2008
644	2^985217-114553	296580	Enzo Doria	03/2015
645	(76^157649-1)/75	296507	Paul Bourdelais	07/2019
646	2^984131-1828009	296253	Enzo Doria	01/2015
647	2^983620+60451	296100	Phil Moore	03/2008
648	2^982721-2683	295829	Yves Minet	02/2016
649	2^981298-2788421	295401	Enzo Doria	12/2015
650	2^981163-2790967	295360	Enzo Doria	12/2015
651	2^981016-15	295316	Stefano Morozzi	07/2022
652	2^979594+1865839	294888	Enzo Doria	02/2016
653	2^976760+1885021	294035	Enzo Doria	02/2017
654	2^974441+1878407	293336	Enzo Doria	08/2016
655	2^974180+1876831	293258	Enzo Doria	07/2016
656	2^974170+453319	293255	Enzo Doria	01/2017
657	2^972744-114419	292826	Enzo Doria	03/2015
658	11^281143+6	292781	Paul Bourdelais	03/2021
659	(4*10^292619-91)/3	292620	Robert Price	12/2022
660	CopelandErdos(292447)	292447	Mark Rodenkirch	12/2015
661	3*10^292344-97	292345	Robert Price	01/2023
662	2^970911+1873373	292274	Enzo Doria	07/2016
663	2^970670+383059	292201	Enzo Doria	12/2016
664	2^970141-100363	292042	Enzo Doria	02/2014
665	2^969945+1874717	291983	Enzo Doria	06/2016
666	2^969384+1880701	291814	Enzo Doria	10/2016
667	(3^611333-2^611333)/(99035947*87109884549431)	291659	Mike Oakes	02/2017
668	2^962194+60139	289650	Enzo Doria	02/2016
669	2^959307-1861507	288781	Enzo Doria	11/2015
670	14^251797-3	288592	Paul Bourdelais	12/2020
671	(2*10^288371-23)/3	288371	Robert Price	10/2022
672	2^957372+283531	288198	Enzo Doria	02/2017
673	2^957192-1864049	288144	Enzo Doria	01/2016
674	2^956446+1875199	287919	Enzo Doria	06/2016
675	7*10^287854+39	287855	Robert Price	01/2023
676	(17^233689+1)/18	287542	Paul Bourdelais	09/2013
677	2^955178+1883587	287538	Enzo Doria	12/2016
678	2^954127-954127^2	287221	Henri Lifchitz	01/2021
679	2^954001+1875257	287183	Enzo Doria	07/2016
680	(23891^65536+1)/2	286932	Serge Batalov	03/2018
681	2^952268+1878601	286662	Enzo Doria	09/2016
682	2^950801+81557	286220	Enzo Doria	08/2016
683	22845^65536+22844^65536	285658	Kellen Shenton	03/2021
684	(11*2^948635-13)/15	285568	Renaud Lifchitz	11/2011
685	(54^164839+1)/55	285565	Paul Bourdelais	07/2019
686	2^948510+782569	285530	Enzo Doria	10/2016
687	2^948374-114137	285490	Enzo Doria	01/2015
688	2^947739+1872923	285298	Enzo Doria	06/2016
689	2^944561-21	284342	Stefano Morozzi	07/2022
690	(4*10^284330-31)/9	284330	Serge Batalov	11/2022
691	(32*10^283826-23)/9	283827	Serge Batalov	01/2023
692	2^942533+82067	283731	Enzo Doria	09/2016
693	2^940950+1874989	283255	Enzo Doria	06/2016
694	2^940426-2786141	283097	Enzo Doria	11/2015
695	(2*10^282948-11)/9	282948	Serge Batalov	11/2022
696	2^939881-114115	282933	Enzo Doria	12/2014
697	10^282493+632551	282494	Patrick De Geest	02/2017
699	10^282493-9^282493	282493	Jean-Louis Charton	03/2007
698	10^282493-132327	282493	Patrick De Geest	02/2017
700	3^591827-2^591827	282374	Mike Oakes	08/2009
701	Tau(509^18946)	282048	Nik Lygeros / Olivier Rozier	05/2015
702	2^936716-1835519	281980	Enzo Doria	04/2015
703	2^936588+79411	281942	Enzo Doria	06/2016
704	2^936047+1877423	281779	Enzo Doria	08/2016
705	2^935713+1869377	281678	Enzo Doria	05/2016
706	2^933082+1877059	280886	Enzo Doria	08/2016
707	(5*10^280710+1)/3	280711	Serge Batalov	10/2014
708	2^931976+25	280553	Stefano Morozzi	05/2021
709	(42^172663+1)/43	280274	Paul Bourdelais	07/2019
710	(10^279978+11)/3	279978	Serge Batalov	07/2015
711	2^929524-1864829	279815	Enzo Doria	01/2016
712	2^929152+60181	279703	Enzo Doria	02/2016
713	2^928621-2787883	279543	Enzo Doria	11/2015
714	(2^927763+lucasV(-1,2,927763)+1)/2	279285	Mike Oakes	04/2017
715	2^927429+1882277	279184	Enzo Doria	12/2016
716	2^926766-11	278985	Stefano Morozzi	07/2022
717	(71^150697-1)/70	278978	Paul Bourdelais	07/2019
718	(33^183661-1)/32	278891	Paul Bourdelais	12/2018
719	(2^925391+lucasV(-1,2,925391)+1)/2	278571	Mike Oakes	03/2017
720	2^925330-1301	278553	Yves Minet	06/2015
721	(299*10^278546+1)/3	278548	Robert Price	01/2023
722	(21^210599+1)/22	278457	Paul Bourdelais	08/2013
723	(266*10^278325+1)/3	278327	Robert Price	01/2023
724	2^923261-69175	277930	Enzo Doria	11/2015
725	757^96487-756^96487	277796	Jean-Louis Charton	12/2012
726	2^922301+57	277641	Stefano Morozzi	05/2021
727	((((((((((((((291487327^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2	277369	Serge Batalov	07/2016
728	(5^396413-1)/4	277081	Paul Bourdelais	06/2010
729	2^920318+2792299	277044	Enzo Doria	02/2016
730	2^918596-2786939	276525	Enzo Doria	11/2015
731	2^916639+60563	275936	Enzo Doria	04/2016
732	(2*10^275922+1)/3	275922	Serge Batalov	11/2022
733	2^916385-2786383	275860	Enzo Doria	11/2015
734	2^915928+82081	275722	Enzo Doria	09/2016
735	2^915576-114137	275616	Enzo Doria	01/2015
736	2^914828+1876741	275391	Enzo Doria	07/2016
737	2^914757-2203	275370	Yves Minet	12/2015
738	7*10^275157-27	275158	Robert Price	11/2022
739	2^911900+1871245	274510	Enzo Doria	05/2016
740	(16*10^274251-91)/3	274252	Robert Price	11/2022
741	2^910999+9	274239	Stefano Morozzi	05/2021
742	(2^910869-7)/5	274199	Stefano Morozzi	08/2022
743	2^910490+283429	274085	Enzo Doria	01/2017
744	7*10^273983+39	273984	Robert Price	01/2023
745	2^909988-1862249	273934	Enzo Doria	12/2015
746	2^909297+1879157	273726	Enzo Doria	08/2016
747	2^909257-1864423	273714	Enzo Doria	01/2016
748	2^908739-7	273558	Stefano Morozzi	07/2022
749	2^908579-1861747	273510	Enzo Doria	12/2015
750	2^907635-2791597	273226	Enzo Doria	01/2016

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