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) !!!

Submit your PRPs

See the Top discoverers
See the Latest PRPs
Search by form


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	6^389756+5	303290	Paul Bourdelais	02/2021
502	71016^18649+18649^71016	303285	Hans Havermann	01/2022
503	80160^6047+6047^80160	303129	Hans Havermann	01/2022
504	67434^31237+31237^67434	303094	Hans Havermann	03/2022
505	65537^42102+42102^65537	303063	Hans Havermann	02/2022
506	71790^16553+16553^71790	302874	Hans Havermann	11/2021
507	65208^44129+44129^65208	302874	Hans Havermann	11/2021
508	84181^3960+3960^84181	302858	Hans Havermann	11/2021
509	71956^16087+16087^71956	302682	Hans Havermann	11/2021
510	2^1005326+383059	302634	Enzo Doria	12/2016
511	2^1004929+1877567	302514	Enzo Doria	08/2016
512	69341^22978+22978^69341	302418	Hans Havermann	12/2021
513	111443^516+516^111443	302306	Hans Havermann	12/2021
514	67638^29387+29387^67638	302218	Hans Havermann	11/2021
515	2^1003494+1874899	302082	Enzo Doria	06/2016
516	75189^10400+10400^75189	302037	Hans Havermann	12/2021
517	67237^31042+31042^67237	302026	Hans Havermann	12/2021
518	64540^47791+47791^64540	302005	Hans Havermann	11/2021
519	2^1003046+60529	301947	Enzo Doria	04/2016
520	83278^4209+4209^83278	301815	Hans Havermann	09/2021
521	64431^48250+48250^64431	301763	Hans Havermann	09/2021
522	67237^30714+30714^67237	301716	Hans Havermann	09/2021
523	64641^46288+46288^64641	301581	Hans Havermann	09/2021
524	71513^16482+16482^71513	301572	Hans Havermann	10/2021
525	72017^15396+15396^72017	301565	Hans Havermann	09/2021
526	65534^39927+39927^65534	301540	Hans Havermann	10/2021
527	(23^221411-1)/22	301501	Paul Bourdelais	08/2020
528	63169^59152+59152^63169	301441	Hans Havermann	09/2021
529	75055^10348+10348^75055	301336	Hans Havermann	09/2021
530	2^1000647+1881353	301225	Enzo Doria	11/2016
531	83686^3961+3961^83686	301086	Hans Havermann	10/2021
532	68529^24742+24742^68529	301078	Hans Havermann	09/2021
533	65207^41416+41416^65207	301072	Hans Havermann	10/2021
534	2^1000000+821751	301030	Tony Prest / Never Odd Or Even	10/2015
535	90762^2071+2071^90762	300984	Hans Havermann	06/2021
536	63909^51142+51142^63909	300934	Hans Havermann	08/2021
537	2^999646+1874029	300924	Enzo Doria	06/2016
538	66280^34607+34607^66280	300856	Hans Havermann	06/2021
539	65534^38925+38925^65534	300817	Hans Havermann	07/2021
540	63296^56517+56517^63296	300794	Hans Havermann	06/2021
541	110610^523+523^110610	300694	Hans Havermann	06/2021
542	66428^33609+33609^66428	300684	Hans Havermann	06/2021
543	74247^11210+11210^74247	300672	Hans Havermann	06/2021
544	(59^169777-1)/58	300649	Paul Bourdelais	08/2020
545	10^300476+3	300477	Ed Trice	10/2012
546	10^300476-530913	300476	Patrick De Geest	03/2016
547	66703^31960+31960^66703	300471	Hans Havermann	06/2021
548	63722^51915+51915^63722	300468	Hans Havermann	06/2021
549	2^998053+1879667	300444	Enzo Doria	09/2016
550	77018^7959+7959^77018	300437	Hans Havermann	07/2021
551	314738^9+9^314738	300337	Anatoly F. Selevich	02/2011
552	69478^20987+20987^69478	300281	Hans Havermann	07/2021
553	64088^48393+48393^64088	300239	Hans Havermann	07/2021
554	64605^44146+44146^64605	300084	Hans Havermann	08/2021
555	7^355039-6^355039	300043	Jean-Louis Charton	05/2011
556	67594^27465+27465^67594	300035	Hans Havermann	06/2021
557	10^300000+287389	300001	Patrick De Geest	10/2019
558	10^300000-83657	300000	Patrick De Geest	10/2019
559	70599^17756+17756^70599	300000	Hans Havermann	06/2021
560	numbpart(72526161452)	299999	Serge Batalov	04/2017
561	2^996182-114431	299881	Enzo Doria	02/2015
562	2^995214-2788361	299590	Enzo Doria	12/2015
563	2^994791-114319	299462	Enzo Doria	01/2015
564	2^994490-1863791	299372	Enzo Doria	01/2016
565	2^993322+1885729	299020	Enzo Doria	03/2017
566	(36395^65536+36393^65536)/2	298913	Kellen Shenton	04/2022
567	2^992711-2788807	298836	Enzo Doria	12/2015
568	2^992525-114199	298780	Enzo Doria	12/2014
569	2^992329+1884707	298721	Enzo Doria	02/2017
570	(10^298414+7)/191/823/56921/1334467	298398	Alfred Reich	10/2021
571	2^989562+25	297888	Stefano Morozzi	05/2021
572	(2^986191+1)/3	296873	Vincent Diepeveen	06/2008
573	2^985217-114553	296580	Enzo Doria	03/2015
574	(76^157649-1)/75	296507	Paul Bourdelais	07/2019
575	2^984131-1828009	296253	Enzo Doria	01/2015
576	2^983620+60451	296100	Phil Moore	03/2008
577	2^982721-2683	295829	Yves Minet	02/2016
578	2^981298-2788421	295401	Enzo Doria	12/2015
579	2^981163-2790967	295360	Enzo Doria	12/2015
580	2^979594+1865839	294888	Enzo Doria	02/2016
581	2^976760+1885021	294035	Enzo Doria	02/2017
582	2^974441+1878407	293336	Enzo Doria	08/2016
583	2^974180+1876831	293258	Enzo Doria	07/2016
584	2^974170+453319	293255	Enzo Doria	01/2017
585	2^972744-114419	292826	Enzo Doria	03/2015
586	11^281143+6	292781	Paul Bourdelais	03/2021
587	CopelandErdos(292447)	292447	Mark Rodenkirch	12/2015
588	2^970911+1873373	292274	Enzo Doria	07/2016
589	2^970670+383059	292201	Enzo Doria	12/2016
590	2^970141-100363	292042	Enzo Doria	02/2014
591	2^969945+1874717	291983	Enzo Doria	06/2016
592	2^969384+1880701	291814	Enzo Doria	10/2016
593	(3^611333-2^611333)/(99035947*87109884549431)	291659	Mike Oakes	02/2017
594	2^962194+60139	289650	Enzo Doria	02/2016
595	2^959307-1861507	288781	Enzo Doria	11/2015
596	14^251797-3	288592	Paul Bourdelais	12/2020
597	2^957372+283531	288198	Enzo Doria	02/2017
598	2^957192-1864049	288144	Enzo Doria	01/2016
599	2^956446+1875199	287919	Enzo Doria	06/2016
600	(17^233689+1)/18	287542	Paul Bourdelais	09/2013
601	2^955178+1883587	287538	Enzo Doria	12/2016
602	2^954127-954127^2	287221	Henri Lifchitz	01/2021
603	2^954001+1875257	287183	Enzo Doria	07/2016
604	(23891^65536+1)/2	286932	Serge Batalov	03/2018
605	2^952268+1878601	286662	Enzo Doria	09/2016
606	2^950801+81557	286220	Enzo Doria	08/2016
607	22845^65536+22844^65536	285658	Kellen Shenton	03/2021
608	(11*2^948635-13)/15	285568	Renaud Lifchitz	11/2011
609	(54^164839+1)/55	285565	Paul Bourdelais	07/2019
610	2^948510+782569	285530	Enzo Doria	10/2016
611	2^948374-114137	285490	Enzo Doria	01/2015
612	2^947739+1872923	285298	Enzo Doria	06/2016
613	2^942533+82067	283731	Enzo Doria	09/2016
614	2^940950+1874989	283255	Enzo Doria	06/2016
615	2^940426-2786141	283097	Enzo Doria	11/2015
616	2^939881-114115	282933	Enzo Doria	12/2014
617	10^282493+632551	282494	Patrick De Geest	02/2017
619	10^282493-9^282493	282493	Jean-Louis Charton	03/2007
618	10^282493-132327	282493	Patrick De Geest	02/2017
620	3^591827-2^591827	282374	Mike Oakes	08/2009
621	Tau(509^18946)	282048	Nik Lygeros / Olivier Rozier	05/2015
622	2^936716-1835519	281980	Enzo Doria	04/2015
623	2^936588+79411	281942	Enzo Doria	06/2016
624	2^936047+1877423	281779	Enzo Doria	08/2016
625	2^935713+1869377	281678	Enzo Doria	05/2016
626	2^933082+1877059	280886	Enzo Doria	08/2016
627	(5*10^280710+1)/3	280711	Serge Batalov	10/2014
628	2^931976+25	280553	Stefano Morozzi	05/2021
629	(42^172663+1)/43	280274	Paul Bourdelais	07/2019
630	(10^279978+11)/3	279978	Serge Batalov	07/2015
631	2^929524-1864829	279815	Enzo Doria	01/2016
632	2^929152+60181	279703	Enzo Doria	02/2016
633	2^928621-2787883	279543	Enzo Doria	11/2015
634	(2^927763+lucasV(-1,2,927763)+1)/2	279285	Mike Oakes	04/2017
635	2^927429+1882277	279184	Enzo Doria	12/2016
636	(71^150697-1)/70	278978	Paul Bourdelais	07/2019
637	(33^183661-1)/32	278891	Paul Bourdelais	12/2018
638	(2^925391+lucasV(-1,2,925391)+1)/2	278571	Mike Oakes	03/2017
639	2^925330-1301	278553	Yves Minet	06/2015
640	(21^210599+1)/22	278457	Paul Bourdelais	08/2013
641	2^923261-69175	277930	Enzo Doria	11/2015
642	757^96487-756^96487	277796	Jean-Louis Charton	12/2012
643	2^922301+57	277641	Stefano Morozzi	05/2021
644	((((((((((((((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
645	(5^396413-1)/4	277081	Paul Bourdelais	06/2010
646	2^920318+2792299	277044	Enzo Doria	02/2016
647	2^918596-2786939	276525	Enzo Doria	11/2015
648	2^916639+60563	275936	Enzo Doria	04/2016
649	2^916385-2786383	275860	Enzo Doria	11/2015
650	2^915928+82081	275722	Enzo Doria	09/2016
651	2^915576-114137	275616	Enzo Doria	01/2015
652	2^914828+1876741	275391	Enzo Doria	07/2016
653	2^914757-2203	275370	Yves Minet	12/2015
654	2^911900+1871245	274510	Enzo Doria	05/2016
655	2^910999+9	274239	Stefano Morozzi	05/2021
656	2^910490+283429	274085	Enzo Doria	01/2017
657	2^909988-1862249	273934	Enzo Doria	12/2015
658	2^909297+1879157	273726	Enzo Doria	08/2016
659	2^909257-1864423	273714	Enzo Doria	01/2016
660	2^908579-1861747	273510	Enzo Doria	12/2015
661	2^907635-2791597	273226	Enzo Doria	01/2016
662	(53^158341+1)/54	273022	Paul Bourdelais	07/2019
663	2^906594-113201	272912	Enzo Doria	08/2014
664	2^904773+1872167	272364	Enzo Doria	06/2016
665	6^349903+5	272278	Paul Bourdelais	02/2021
666	2^904149-1862473	272176	Enzo Doria	12/2015
667	(7*10^271757-61)/9	271757	Erik Branger	03/2012
668	2^902497+1880117	271679	Enzo Doria	09/2016
669	2^901858+77689	271487	Enzo Doria	06/2016
670	2^901372+1875301	271341	Enzo Doria	06/2016
671	2^899121-115033	270663	Enzo Doria	07/2015
672	2^898900+883021	270596	Enzo Doria	12/2016
673	2^898762-251511	270555	Enzo Doria	12/2013
674	2^898589+47	270503	Lelio R Paula	03/2016
675	187322*10^270343-187321	270349	Danilo Nitsche	09/2013
676	48358*10^270343-48357	270348	Danilo Nitsche	09/2013
677	(10^270343-1)/9	270343	Maksym Voznyy	07/2007
678	2^897867-3217	270285	Yves Minet	12/2016
679	2^897849-115273	270280	Enzo Doria	07/2015
680	2^896616-114179	269909	Enzo Doria	12/2014
681	2^894928+583561	269401	Enzo Doria	04/2017
682	2^894673-39343	269324	Enzo Doria	08/2015
683	F(1285607)	268676	Henri Lifchitz	11/2008
684	2^892112+187663	268553	Enzo Doria	08/2016
685	(10^268207+1)/11	268206	Paul Bourdelais	02/2010
686	2^890957-69583	268205	Enzo Doria	12/2015
687	32841!^2+32840!^2+...+2!^2+1!^2	268128	Serge Batalov	07/2017
688	2^890122-351401	267954	Enzo Doria	07/2015
689	(19^209359-1)/18	267718	Paul Bourdelais	08/2010
690	(85^138647+1)/86	267507	Paul Bourdelais	07/2019
691	(485^99523-1)/484	267291	Michael Stocker	05/2020
692	2^886324+77791	266811	Enzo Doria	06/2016
693	2^884714+1880527	266326	Enzo Doria	10/2016
694	11^255426+255426^11	265999	Serge Batalov	05/2014
695	2^883462-343421	265949	Enzo Doria	07/2015
696	2^883442+1875019	265943	Enzo Doria	06/2016
697	2^883333-291583	265910	Enzo Doria	07/2015
698	2^880411+1882673	265031	Enzo Doria	12/2016
699	2^879530-2788031	264765	Enzo Doria	12/2015
700	2^878118+2793079	264340	Enzo Doria	02/2016
701	(37^168527-1)/36	264283	Paul Bourdelais	08/2019
702	2^875748-461129	263627	Enzo Doria	07/2015
703	2^875181-2789923	263456	Enzo Doria	12/2015
704	2^875101-350083	263432	Enzo Doria	08/2015
705	2^874684+1883587	263307	Enzo Doria	01/2017
706	2^874616+1872211	263286	Enzo Doria	05/2016
707	3^551491+16	263129	Robert Price	04/2020
708	2^874073+2792957	263123	Enzo Doria	02/2016
709	2^873628+1878751	262989	Enzo Doria	08/2016
710	2^873288-269	262886	Yves Minet	01/2015
711	2^871991-4207	262496	Yves Minet	03/2021
712	2^871146-3173	262242	Yves Minet	07/2016
713	2^869601-163	261776	Yves Minet	01/2015
714	2^869326+282859	261694	Enzo Doria	11/2016
715	2^869035-114181	261606	Enzo Doria	12/2014
716	2^865715+80303	260607	Enzo Doria	07/2016
717	2^865048+1882411	260406	Enzo Doria	12/2016
718	2^864899-113871	260361	Enzo Doria	10/2014
719	(7*10^260198-61)/9	260198	Erik Branger	11/2011
720	2^864298-2788421	260180	Enzo Doria	12/2015
721	2^864039-2791357	260102	Enzo Doria	01/2016
722	2^863621-113833	259976	Enzo Doria	10/2014
723	2^862837+75767	259740	Enzo Doria	05/2016
724	2^862637-31	259680	Jorge Menendez	05/2019
725	2^862088+1874941	259515	Enzo Doria	06/2016
726	2^861987-134557	259484	Hans Havermann	10/2018
727	2^861516-1854029	259343	Enzo Doria	09/2015
728	2^860975-1853977	259180	Enzo Doria	09/2015
729	3^543128+16	259138	Robert Price	04/2020
730	2^860625-1858843	259074	Enzo Doria	10/2015
731	2^860110+77689	258919	Enzo Doria	05/2016
732	2^859600+1880371	258766	Enzo Doria	10/2016
733	2^859433+494711	258716	Makoto Morimoto	10/2013
734	(2^859433-44)/(2^2*3)	258715	Makoto Morimoto	08/2019
735	(2^859433+39899)/(73390746301)	258705	Makoto Morimoto	10/2016
736	2^859240+1875271	258658	Enzo Doria	06/2016
737	Tau(971^15738)	258571	Nik Lygeros / Olivier Rozier	05/2015
738	(144^119671+1)/145	258292	Paul Bourdelais	08/2019
739	2^857608+105	258166	Stefano Morozzi	05/2021
740	(11*2^857159-13)/15	258031	Renaud Lifchitz	08/2011
741	2^857016-633113	257988	Enzo Doria	12/2013
742	2^855732-113969	257602	Enzo Doria	10/2014
743	2^853682-3911	256984	Enzo Doria	05/2014
744	11^246668-90	256879	Enzo Doria	12/2012
745	2^851904-113939	256449	Enzo Doria	10/2014
746	2^851725-851725^2	256395	Henri Lifchitz	03/2019
747	11^246167-90	256357	Enzo Doria	12/2012
748	(10^256187+7)/63443/148782853	256175	Alfred Reich	10/2021
749	2^850700-569049	256087	Enzo Doria	11/2013
750	2^850675+153	256079	Stefano Morozzi	05/2021

Find by discoverer :

PRP Records

Probable Primes Top 10000

(290751 PRPs in the top)