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	238176^19+19^238176	304569	Hans Havermann	03/2022
502	73122^14615+14615^73122	304539	Hans Havermann	05/2022
503	64492^52639+52639^64492	304487	Hans Havermann	03/2022
504	65955^41288+41288^65955	304437	Hans Havermann	04/2022
505	71729^17530+17530^71729	304403	Hans Havermann	03/2022
506	70170^21733+21733^70170	304336	Hans Havermann	03/2022
507	2^1010751-107709	304267	Enzo Doria	03/2014
508	84473^3994+3994^84473	304222	Hans Havermann	03/2022
509	(2^1010623-1)/12602017578957977	304212	Tony Prest / Never Odd Or Even	02/2014
510	74442^12125+12125^74442	303998	Hans Havermann	02/2022
511	77842^8039+8039^77842	303989	Hans Havermann	01/2022
512	64209^54140+54140^64209	303935	Hans Havermann	02/2022
513	2^1009577+1869587	303913	Enzo Doria	06/2016
514	67389^32338+32338^67389	303906	Hans Havermann	02/2022
515	8^336419-7^336419	303817	Jean-Louis Charton	01/2008
516	80766^5771+5771^80766	303782	Hans Havermann	01/2022
517	66094^39385+39385^66094	303724	Hans Havermann	01/2022
518	69147^24574+24574^69147	303589	Hans Havermann	02/2022
519	78390^7459+7459^78390	303580	Hans Havermann	01/2022
520	2^1008301+1869377	303529	Enzo Doria	06/2016
521	65008^46615+46615^65008	303492	Hans Havermann	02/2022
522	(2^1007838+5)/3	303389	Serge Batalov	08/2015
523	65018^46293+46293^65018	303343	Hans Havermann	01/2022
524	6^389756+5	303290	Paul Bourdelais	02/2021
525	71016^18649+18649^71016	303285	Hans Havermann	01/2022
526	80160^6047+6047^80160	303129	Hans Havermann	01/2022
527	67434^31237+31237^67434	303094	Hans Havermann	03/2022
528	65537^42102+42102^65537	303063	Hans Havermann	02/2022
529	71790^16553+16553^71790	302874	Hans Havermann	11/2021
530	65208^44129+44129^65208	302874	Hans Havermann	11/2021
531	84181^3960+3960^84181	302858	Hans Havermann	11/2021
532	71956^16087+16087^71956	302682	Hans Havermann	11/2021
533	2^1005326+383059	302634	Enzo Doria	12/2016
534	2^1004929+1877567	302514	Enzo Doria	08/2016
535	69341^22978+22978^69341	302418	Hans Havermann	12/2021
536	111443^516+516^111443	302306	Hans Havermann	12/2021
537	67638^29387+29387^67638	302218	Hans Havermann	11/2021
538	2^1003494+1874899	302082	Enzo Doria	06/2016
539	75189^10400+10400^75189	302037	Hans Havermann	12/2021
540	67237^31042+31042^67237	302026	Hans Havermann	12/2021
541	64540^47791+47791^64540	302005	Hans Havermann	11/2021
542	2^1003046+60529	301947	Enzo Doria	04/2016
543	83278^4209+4209^83278	301815	Hans Havermann	09/2021
544	64431^48250+48250^64431	301763	Hans Havermann	09/2021
545	67237^30714+30714^67237	301716	Hans Havermann	09/2021
546	64641^46288+46288^64641	301581	Hans Havermann	09/2021
547	71513^16482+16482^71513	301572	Hans Havermann	10/2021
548	72017^15396+15396^72017	301565	Hans Havermann	09/2021
549	65534^39927+39927^65534	301540	Hans Havermann	10/2021
550	(23^221411-1)/22	301501	Paul Bourdelais	08/2020
551	63169^59152+59152^63169	301441	Hans Havermann	09/2021
552	75055^10348+10348^75055	301336	Hans Havermann	09/2021
553	2^1000647+1881353	301225	Enzo Doria	11/2016
554	83686^3961+3961^83686	301086	Hans Havermann	10/2021
555	68529^24742+24742^68529	301078	Hans Havermann	09/2021
556	65207^41416+41416^65207	301072	Hans Havermann	10/2021
557	2^1000000+821751	301030	Tony Prest / Never Odd Or Even	10/2015
558	90762^2071+2071^90762	300984	Hans Havermann	06/2021
559	63909^51142+51142^63909	300934	Hans Havermann	08/2021
560	2^999646+1874029	300924	Enzo Doria	06/2016
561	66280^34607+34607^66280	300856	Hans Havermann	06/2021
562	65534^38925+38925^65534	300817	Hans Havermann	07/2021
563	63296^56517+56517^63296	300794	Hans Havermann	06/2021
564	110610^523+523^110610	300694	Hans Havermann	06/2021
565	66428^33609+33609^66428	300684	Hans Havermann	06/2021
566	74247^11210+11210^74247	300672	Hans Havermann	06/2021
567	(59^169777-1)/58	300649	Paul Bourdelais	08/2020
568	10^300476+3	300477	Ed Trice	10/2012
569	10^300476-530913	300476	Patrick De Geest	03/2016
570	66703^31960+31960^66703	300471	Hans Havermann	06/2021
571	63722^51915+51915^63722	300468	Hans Havermann	06/2021
572	2^998053+1879667	300444	Enzo Doria	09/2016
573	77018^7959+7959^77018	300437	Hans Havermann	07/2021
574	314738^9+9^314738	300337	Anatoly F. Selevich	02/2011
575	69478^20987+20987^69478	300281	Hans Havermann	07/2021
576	64088^48393+48393^64088	300239	Hans Havermann	07/2021
577	64605^44146+44146^64605	300084	Hans Havermann	08/2021
578	7^355039-6^355039	300043	Jean-Louis Charton	05/2011
579	67594^27465+27465^67594	300035	Hans Havermann	06/2021
580	10^300000+287389	300001	Patrick De Geest	10/2019
581	10^300000-83657	300000	Patrick De Geest	10/2019
582	70599^17756+17756^70599	300000	Hans Havermann	06/2021
583	numbpart(72526161452)	299999	Serge Batalov	04/2017
584	2^996182-114431	299881	Enzo Doria	02/2015
585	2^996034-17	299837	Stefano Morozzi	07/2022
586	2^995214-2788361	299590	Enzo Doria	12/2015
587	2^994791-114319	299462	Enzo Doria	01/2015
588	2^994490-1863791	299372	Enzo Doria	01/2016
589	2^993322+1885729	299020	Enzo Doria	03/2017
590	(36395^65536+36393^65536)/2	298913	Kellen Shenton	04/2022
591	2^992711-2788807	298836	Enzo Doria	12/2015
592	2^992525-114199	298780	Enzo Doria	12/2014
593	2^992329+1884707	298721	Enzo Doria	02/2017
594	2^991968-23	298613	Stefano Morozzi	07/2022
595	2^991715-19	298536	Stefano Morozzi	07/2022
596	(10^298414+7)/191/823/56921/1334467	298398	Alfred Reich	10/2021
597	2^989562+25	297888	Stefano Morozzi	05/2021
598	(2^986191+1)/3	296873	Vincent Diepeveen	06/2008
599	2^985217-114553	296580	Enzo Doria	03/2015
600	(76^157649-1)/75	296507	Paul Bourdelais	07/2019
601	2^984131-1828009	296253	Enzo Doria	01/2015
602	2^983620+60451	296100	Phil Moore	03/2008
603	2^982721-2683	295829	Yves Minet	02/2016
604	2^981298-2788421	295401	Enzo Doria	12/2015
605	2^981163-2790967	295360	Enzo Doria	12/2015
606	2^981016-15	295316	Stefano Morozzi	07/2022
607	2^979594+1865839	294888	Enzo Doria	02/2016
608	2^976760+1885021	294035	Enzo Doria	02/2017
609	2^974441+1878407	293336	Enzo Doria	08/2016
610	2^974180+1876831	293258	Enzo Doria	07/2016
611	2^974170+453319	293255	Enzo Doria	01/2017
612	2^972744-114419	292826	Enzo Doria	03/2015
613	11^281143+6	292781	Paul Bourdelais	03/2021
614	CopelandErdos(292447)	292447	Mark Rodenkirch	12/2015
615	2^970911+1873373	292274	Enzo Doria	07/2016
616	2^970670+383059	292201	Enzo Doria	12/2016
617	2^970141-100363	292042	Enzo Doria	02/2014
618	2^969945+1874717	291983	Enzo Doria	06/2016
619	2^969384+1880701	291814	Enzo Doria	10/2016
620	(3^611333-2^611333)/(99035947*87109884549431)	291659	Mike Oakes	02/2017
621	2^962194+60139	289650	Enzo Doria	02/2016
622	2^959307-1861507	288781	Enzo Doria	11/2015
623	14^251797-3	288592	Paul Bourdelais	12/2020
624	2^957372+283531	288198	Enzo Doria	02/2017
625	2^957192-1864049	288144	Enzo Doria	01/2016
626	2^956446+1875199	287919	Enzo Doria	06/2016
627	(17^233689+1)/18	287542	Paul Bourdelais	09/2013
628	2^955178+1883587	287538	Enzo Doria	12/2016
629	2^954127-954127^2	287221	Henri Lifchitz	01/2021
630	2^954001+1875257	287183	Enzo Doria	07/2016
631	(23891^65536+1)/2	286932	Serge Batalov	03/2018
632	2^952268+1878601	286662	Enzo Doria	09/2016
633	2^950801+81557	286220	Enzo Doria	08/2016
634	22845^65536+22844^65536	285658	Kellen Shenton	03/2021
635	(11*2^948635-13)/15	285568	Renaud Lifchitz	11/2011
636	(54^164839+1)/55	285565	Paul Bourdelais	07/2019
637	2^948510+782569	285530	Enzo Doria	10/2016
638	2^948374-114137	285490	Enzo Doria	01/2015
639	2^947739+1872923	285298	Enzo Doria	06/2016
640	2^944561-21	284342	Stefano Morozzi	07/2022
641	2^942533+82067	283731	Enzo Doria	09/2016
642	2^940950+1874989	283255	Enzo Doria	06/2016
643	2^940426-2786141	283097	Enzo Doria	11/2015
644	2^939881-114115	282933	Enzo Doria	12/2014
645	10^282493+632551	282494	Patrick De Geest	02/2017
647	10^282493-9^282493	282493	Jean-Louis Charton	03/2007
646	10^282493-132327	282493	Patrick De Geest	02/2017
648	3^591827-2^591827	282374	Mike Oakes	08/2009
649	Tau(509^18946)	282048	Nik Lygeros / Olivier Rozier	05/2015
650	2^936716-1835519	281980	Enzo Doria	04/2015
651	2^936588+79411	281942	Enzo Doria	06/2016
652	2^936047+1877423	281779	Enzo Doria	08/2016
653	2^935713+1869377	281678	Enzo Doria	05/2016
654	2^933082+1877059	280886	Enzo Doria	08/2016
655	(5*10^280710+1)/3	280711	Serge Batalov	10/2014
656	2^931976+25	280553	Stefano Morozzi	05/2021
657	(42^172663+1)/43	280274	Paul Bourdelais	07/2019
658	(10^279978+11)/3	279978	Serge Batalov	07/2015
659	2^929524-1864829	279815	Enzo Doria	01/2016
660	2^929152+60181	279703	Enzo Doria	02/2016
661	2^928621-2787883	279543	Enzo Doria	11/2015
662	(2^927763+lucasV(-1,2,927763)+1)/2	279285	Mike Oakes	04/2017
663	2^927429+1882277	279184	Enzo Doria	12/2016
664	2^926766-11	278985	Stefano Morozzi	07/2022
665	(71^150697-1)/70	278978	Paul Bourdelais	07/2019
666	(33^183661-1)/32	278891	Paul Bourdelais	12/2018
667	(2^925391+lucasV(-1,2,925391)+1)/2	278571	Mike Oakes	03/2017
668	2^925330-1301	278553	Yves Minet	06/2015
669	(21^210599+1)/22	278457	Paul Bourdelais	08/2013
670	2^923261-69175	277930	Enzo Doria	11/2015
671	757^96487-756^96487	277796	Jean-Louis Charton	12/2012
672	2^922301+57	277641	Stefano Morozzi	05/2021
673	((((((((((((((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
674	(5^396413-1)/4	277081	Paul Bourdelais	06/2010
675	2^920318+2792299	277044	Enzo Doria	02/2016
676	2^918596-2786939	276525	Enzo Doria	11/2015
677	2^916639+60563	275936	Enzo Doria	04/2016
678	2^916385-2786383	275860	Enzo Doria	11/2015
679	2^915928+82081	275722	Enzo Doria	09/2016
680	2^915576-114137	275616	Enzo Doria	01/2015
681	2^914828+1876741	275391	Enzo Doria	07/2016
682	2^914757-2203	275370	Yves Minet	12/2015
683	2^911900+1871245	274510	Enzo Doria	05/2016
684	2^910999+9	274239	Stefano Morozzi	05/2021
685	(2^910869-7)/5	274199	Stefano Morozzi	08/2022
686	2^910490+283429	274085	Enzo Doria	01/2017
687	2^909988-1862249	273934	Enzo Doria	12/2015
688	2^909297+1879157	273726	Enzo Doria	08/2016
689	2^909257-1864423	273714	Enzo Doria	01/2016
690	2^908739-7	273558	Stefano Morozzi	07/2022
691	2^908579-1861747	273510	Enzo Doria	12/2015
692	2^907635-2791597	273226	Enzo Doria	01/2016
693	(53^158341+1)/54	273022	Paul Bourdelais	07/2019
694	2^906594-113201	272912	Enzo Doria	08/2014
695	2^904773+1872167	272364	Enzo Doria	06/2016
696	6^349903+5	272278	Paul Bourdelais	02/2021
697	2^904149-1862473	272176	Enzo Doria	12/2015
698	(7*10^271757-61)/9	271757	Erik Branger	03/2012
699	2^902497+1880117	271679	Enzo Doria	09/2016
700	2^901858+77689	271487	Enzo Doria	06/2016
701	2^901372+1875301	271341	Enzo Doria	06/2016
702	2^899121-115033	270663	Enzo Doria	07/2015
703	2^898900+883021	270596	Enzo Doria	12/2016
704	2^898762-251511	270555	Enzo Doria	12/2013
705	2^898589+47	270503	Lelio R Paula	03/2016
706	187322*10^270343-187321	270349	Danilo Nitsche	09/2013
707	48358*10^270343-48357	270348	Danilo Nitsche	09/2013
708	(10^270343-1)/9	270343	Maksym Voznyy	07/2007
709	2^897867-3217	270285	Yves Minet	12/2016
710	2^897849-115273	270280	Enzo Doria	07/2015
711	2^896616-114179	269909	Enzo Doria	12/2014
712	2^894928+583561	269401	Enzo Doria	04/2017
713	2^894673-39343	269324	Enzo Doria	08/2015
714	F(1285607)	268676	Henri Lifchitz	11/2008
715	2^892112+187663	268553	Enzo Doria	08/2016
716	(10^268207+1)/11	268206	Paul Bourdelais	02/2010
717	2^890957-69583	268205	Enzo Doria	12/2015
718	32841!^2+32840!^2+...+2!^2+1!^2	268128	Serge Batalov	07/2017
719	2^890122-351401	267954	Enzo Doria	07/2015
720	(19^209359-1)/18	267718	Paul Bourdelais	08/2010
721	(85^138647+1)/86	267507	Paul Bourdelais	07/2019
722	(485^99523-1)/484	267291	Michael Stocker	05/2020
723	2^886324+77791	266811	Enzo Doria	06/2016
724	2^884714+1880527	266326	Enzo Doria	10/2016
725	11^255426+255426^11	265999	Serge Batalov	05/2014
726	2^883462-343421	265949	Enzo Doria	07/2015
727	2^883442+1875019	265943	Enzo Doria	06/2016
728	2^883333-291583	265910	Enzo Doria	07/2015
729	2^880411+1882673	265031	Enzo Doria	12/2016
730	(14*10^264791-11)/3	264792	Robert Price	08/2022
731	2^879530-2788031	264765	Enzo Doria	12/2015
732	2^878118+2793079	264340	Enzo Doria	02/2016
733	(2^878073-7)/5	264326	Stefano Morozzi	08/2022
734	(37^168527-1)/36	264283	Paul Bourdelais	08/2019
735	2^876202-17	263764	Stefano Morozzi	07/2022
736	(14*10^263720-11)/3	263721	Robert Price	08/2022
737	2^875748-461129	263627	Enzo Doria	07/2015
738	2^875518-15	263558	Stefano Morozzi	07/2022
739	2^875181-2789923	263456	Enzo Doria	12/2015
740	2^875101-350083	263432	Enzo Doria	08/2015
741	2^874684+1883587	263307	Enzo Doria	01/2017
742	2^874616+1872211	263286	Enzo Doria	05/2016
743	3^551491+16	263129	Robert Price	04/2020
744	2^874073+2792957	263123	Enzo Doria	02/2016
745	2^873628+1878751	262989	Enzo Doria	08/2016
746	2^873288-269	262886	Yves Minet	01/2015
747	2^871991-4207	262496	Yves Minet	03/2021
748	2^871146-3173	262242	Yves Minet	07/2016
749	2^869601-163	261776	Yves Minet	01/2015
750	2^869326+282859	261694	Enzo Doria	11/2016

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Probable Primes Top 10000

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