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 ?
5501	7*10^82509-47	82510	Robert Price	02/2017
5502	2^274081-6555	82507	Lelio R Paula	07/2013
5503	2^274074-274074+1	82505	Robert Price	10/2014
5504	14^71985+47	82505	Lelio R Paula	11/2015
5505	5*10^82504+21	82505	Robert Price	01/2017
5506	6^106014-139	82495	Lelio R Paula	12/2015
5507	(2^274046+47)/753	82494	Lelio R Paula	12/2012
5508	2^274008-1838099	82485	Enzo Doria	05/2015
5509	2^273981-110029	82477	Enzo Doria	04/2014
5510	19^64490-30	82467	Lelio R Paula	12/2015
5512	2^273785+11715	82418	Lelio R Paula	07/2013
5511	8*10^82417+51	82418	Robert Price	05/2017
5513	11^79133-10	82409	Theodore Burton	11/2005
5514	91^42063+90	82404	Norbert Schneider	01/2016
5515	2^273662-63	82381	Lelio R Paula	06/2012
5516	2^273661+255	82381	Lelio R Paula	07/2013
5517	(62*10^82377-17)/9	82378	Robert Price	09/2015
5518	2^273608+524287	82365	Paul Underwood	08/2018
5519	8*10^82360-51	82361	Robert Price	10/2017
5520	(79*10^82347-1)/3	82349	Robert Price	11/2017
5521	(11*10^82323+91)/3	82323	Robert Price	02/2017
5522	(189977#+19081)/(19081*17260483)	82317	Makoto Morimoto	10/2017
5523	(189977#+196924)/(271354128874441)	82316	Makoto Morimoto	10/2017
5524	15^69984+32	82308	Lelio R Paula	11/2015
5525	9*6^105746+7	82288	Lelio R Paula	10/2014
5526	89^42211-88	82286	Norbert Schneider	01/2016
5527	gcd(V(1476435),5F(295287)(F(295287)+1)+1)	82281	Serge Batalov	04/2015
5528	(19*10^82270-43)/3	82271	Robert Price	10/2017
5529	2^273282-110241	82267	Enzo Doria	05/2014
5530	(13^73849+4^73849)/17	82263	Robert Price	05/2013
5531	10^82254+9^(82254+1)	82255	Robert Price	08/2016
5532	10^82254+457773	82255	Patrick De Geest	12/2016
5533	10^82254-99609	82254	Patrick De Geest	12/2016
5534	(754*10^82250-7)/9	82252	Robert Price	11/2017
5535	18^65524+13	82251	Lelio R Paula	11/2015
5536	2^273206-107	82244	Lelio R Paula	06/2012
5537	2^273193-459145	82240	Enzo Doria	05/2015
5539	2^273126+36937	82220	Yves Minet	06/2010
5538	39505!2+128	82220	Robert Price	03/2015
5540	2^273053-112111	82198	Enzo Doria	06/2014
5541	2^273016+1185	82187	Lelio R Paula	07/2013
5542	(2^273008+3)/7	82183	Lelio R Paula	12/2012
5543	5^117554-15386	82167	Enzo Doria	02/2013
5544	(38*10^82161+403)/9	82162	Robert Price	11/2017
5545	2^272907-111439	82154	Enzo Doria	05/2014
5546	(67607*2^272901+1)/50790115	82149	Lelio R Paula	06/2014
5547	2^272875-69	82144	Lelio R Paula	06/2012
5548	7^97197+4	82141	Robert Price	01/2014
5549	(4*6^105554+1)/5	82137	Serge Batalov	10/2014
5550	6^105531-109	82120	Lelio R Paula	12/2015
5551	2^272766-65	82111	Lelio R Paula	06/2012
5552	19^64205-78	82103	Lelio R Paula	12/2015
5553	2^272702+1869979	82092	Enzo Doria	05/2016
5554	(29*2^272687-1)/9	82088	Lelio R Paula	02/2014
5555	(5*10^82085-119)/3	82086	Robert Price	04/2016
5556	2^272660-110049	82079	Enzo Doria	04/2014
5557	6^105474+67	82075	Lelio R Paula	12/2015
5558	2^272637+82875	82072	Lelio R Paula	07/2013
5559	2^272587-31	82057	Lelio R Paula	06/2012
5560	(41*10^82044-59)/9	82045	Robert Price	10/2017
5561	8*5^117368+9	82038	Lelio R Paula	10/2014
5562	(101525^16384+1)/131074	82023	Lelio R Paula	11/2011
5563	4*5^117343-7	82020	Lelio R Paula	10/2014
5564	(265*10^81990+17)/3	81992	Robert Price	05/2016
5565	3^171843+10	81990	Robert Price	10/2013
5566	(7*10^81985+107)/3	81986	Robert Price	02/2017
5567	(3*2^272356+1)/177163	81983	Lelio R Paula	12/2012
5568	2^272296-111149	81970	Enzo Doria	05/2014
5569	(9*2^272243-1)/7	81954	Lelio R Paula	02/2014
5570	2^272177-111223	81934	Enzo Doria	05/2014
5571	(151009^15817+1)/151010	81912	Faysal YAtim	06/2017
5572	(16*10^81896-19)/3	81897	Robert Price	03/2016
5573	(2^271922+78557)/63	81855	Lelio R Paula	12/2012
5574	(10^81848+77)/3	81848	Robert Price	01/2017
5575	(24737*2^271883+1)/3757	81846	Lelio R Paula	06/2014
5576	10^81778+39	81779	Robert Price	03/2011
5577	10^81778-171999	81778	Patrick De Geest	07/2013
5578	(14*10^81767-11)/3	81768	Erik Branger	09/2014
5579	2^271541+1868417	81742	Enzo Doria	04/2016
5580	(2^271549-1)/238749682487	81734	Jens K. Andersen	02/2009
5581	2^271484-167	81725	Lelio R Paula	06/2012
5582	(8*10^81709-611)/9	81709	Robert Price	11/2017
5583	2^271382+12909	81695	Lelio R Paula	07/2013
5584	49^48334+48	81694	Norbert Schneider	07/2014
5585	7^96668+48	81694	Lelio R Paula	10/2015
5586	11^78435-1410	81682	Enzo Doria	12/2012
5587	5*10^81653+9	81654	Dmitry Domanov	11/2010
5588	(2^271211-1)/613961495159	81631	Jens K. Andersen	02/2009
5589	3^171068+52	81621	Lelio R Paula	12/2015
5590	2^271115-110407	81614	Enzo Doria	05/2014
5591	2^271111-110635	81613	Enzo Doria	05/2014
5592	2^271098-111	81609	Lelio R Paula	06/2012
5593	(77*10^81606+13)/9	81607	Robert Price	10/2015
5594	2^271064-2790209	81599	Enzo Doria	03/2016
5595	(13*2^271053-1)/3095	81593	Lelio R Paula	02/2014
5596	2^271040-57	81592	Lelio R Paula	06/2012
5597	(14*10^81585+73)/3	81586	Robert Price	04/2016
5598	127^38779+126	81584	Norbert Schneider	02/2015
5599	18^64966-43	81551	Lelio R Paula	11/2015
5600	(2^270840+47)/591	81529	Lelio R Paula	12/2012
5601	20^62654+87	81515	Lelio R Paula	01/2016
5602	(19*10^81488+191)/3	81489	Robert Price	01/2017
5603	8*10^81487+21	81488	Robert Price	02/2017
5604	(73*10^81485+107)/9	81486	Robert Price	08/2016
5605	536^29847+29847^536	81458	Norbert Schneider	03/2017
5606	8*7^96378+9	81450	Lelio R Paula	10/2014
5607	2^270546-110345	81443	Enzo Doria	05/2014
5608	13^73105-60	81435	Lelio R Paula	11/2015
5609	44^49524+43	81391	Norbert Schneider	06/2014
5610	(3*2^270368-1)/13	81389	Lelio R Paula	02/2014
5611	(10^81363+719)/9	81363	Serge Batalov	12/2014
5612	(10^81353+449)/9	81353	Serge Batalov	12/2014
5613	14^70978-89	81350	Lelio R Paula	11/2015
5614	11^78108-2040	81342	Enzo Doria	12/2012
5615	3^170400-58	81302	Lelio R Paula	12/2015
5616	(17*10^81300-131)/3	81301	Robert Price	12/2017
5617	10^81297+36991	81298	Patrick De Geest	06/2013
5618	10^81297-57	81297	Robert Price	05/2011
5619	2^270055-113047	81295	Enzo Doria	07/2014
5620	18^64759-55	81291	Lelio R Paula	11/2015
5621	(2^269987+1)/3	81274	H.&R. Lifchitz	10/2000
5622	(31^54493-1)/30	81268	Alexander Zhirkov	10/2010
5623	(2^270059-1)/540119/6481417/7124976157756725967	81265	Dario Alpern	09/2014
5624	(2^269816+7)/424901	81218	Lelio R Paula	12/2012
5625	(23*10^81214+1)/3	81215	Serge Batalov	06/2009
5626	(17*2^269720+1)/303	81193	Lelio R Paula	07/2012
5627	56^46441-55^46441	81188	Robert Price	10/2013
5628	2^269664+177	81177	Lelio R Paula	06/2012
5629	(13*2^269665-1)/185	81177	Lelio R Paula	02/2014
5630	2^269539-112249	81140	Enzo Doria	06/2014
5631	((2170026-3)3^(170026-1)+1)/4	81128	Robert Price	01/2015
5632	(2^269495-5)/9	81126	Lelio R Paula	12/2012
5633	2^269490-3623	81125	Yves Minet	10/2009
5634	(55459*2^269444+1)/35	81114	Lelio R Paula	06/2014
5635	(2^269417+78557)/5257	81099	Lelio R Paula	12/2012
5636	4*5^116011-7	81089	Lelio R Paula	10/2014
5637	7*10^81058+79	81059	Robert Price	02/2017
5638	2^269236-109907	81049	Enzo Doria	04/2014
5639	(8*10^81029-11)/3	81030	Erik Branger	03/2014
5640	3*10^81021+7	81022	Erik Branger	11/2013
5641	6^104115+103	81018	Lelio R Paula	12/2015
5642	2^269120+1869151	81014	Enzo Doria	05/2016
5643	5^115901+12	81012	Lelio R Paula	10/2015
5644	(2^269083-9)/320369	80997	Lelio R Paula	12/2012
5645	17^65810-20	80976	Lelio R Paula	11/2015
5646	20^62236-23	80971	Lelio R Paula	01/2016
5647	2^268974-112181	80970	Enzo Doria	06/2014
5649	L(387433)	80969	Renaud Lifchitz	11/2003
5648	V(387433)	80969	Serge Batalov	03/2015
5650	(2^268955-509203)/5	80963	Lelio R Paula	12/2012
5651	(87398^16384+1)/65537	80957	Lelio R Paula	11/2011
5652	329^32160+32160^329	80954	Norbert Schneider	11/2014
5653	2^268859-159	80935	Lelio R Paula	05/2012
5654	(2^268841-lucasV(1,2,268841)+1)/2	80929	Mike Oakes	11/2016
5655	2^268827+5775	80925	Lelio R Paula	07/2013
5656	2^268824-110255	80925	Enzo Doria	05/2014
5657	2^268798-1868321	80917	Enzo Doria	04/2016
5658	2^268753-114621	80903	Enzo Doria	05/2015
5659	2^268743+1605	80900	Lelio R Paula	07/2013
5660	6^103954-139	80892	Lelio R Paula	12/2015
5661	10^80883+49	80884	Robert Price	03/2011
5662	10^80883-80327	80883	Patrick De Geest	07/2013
5663	6^103937+121	80879	Lelio R Paula	12/2015
5664	148^37266+147	80877	Norbert Schneider	12/2018
5665	(26*10^80875-119)/3	80876	Robert Price	07/2016
5666	(22699*2^268657+1)/6351	80875	Lelio R Paula	06/2014
5667	2^268581-869688105	80851	Lelio R Paula	05/2016
5668	(11*2^268521-1)/3	80834	Lelio R Paula	02/2014
5669	2^268516-249	80832	Yves Minet	02/2012
5670	2^268500+16095	80827	Lelio R Paula	07/2013
5671	3^169402+100	80826	Lelio R Paula	12/2015
5672	9^84698+8^(84698-1)	80823	Robert Price	03/2016
5673	2^268472-109739	80819	Enzo Doria	04/2014
5674	(9*2^268454+1)/37	80813	Lelio R Paula	12/2012
5675	(3*2^268502+1)/377902188435353647	80811	Lelio R Paula	12/2012
5676	134^37987-133^37987	80803	Jean-Louis Charton	12/2005
5677	15^68702-76	80800	Lelio R Paula	11/2015
5678	2^268408+7	80799	Lelio R Paula	05/2012
5679	2^268375+141	80789	Lelio R Paula	05/2012
5680	12^74856-47	80784	Lelio R Paula	11/2015
5681	2^268346+524287	80781	Paul Underwood	08/2018
5682	6^103770-107	80749	Lelio R Paula	12/2015
5684	3^169224-62	80741	Lelio R Paula	12/2015
5683	p(16866)#/2+64	80741	Robert Price	03/2017
5685	5^115502-72	80733	Lelio R Paula	10/2015
5686	2^268079-1927	80700	Yves Minet	10/2009
5687	2^268028+117	80685	Lelio R Paula	05/2012
5688	121^38738+120	80683	Norbert Schneider	01/2015
5689	(3^169097-8)/835	80677	Lelio R Paula	12/2012
5690	2^267918+67	80652	Lelio R Paula	05/2012
5691	(89*10^80650-179)/9	80651	Robert Price	11/2017
5692	(302*10^80638+13)/9	80640	Robert Price	01/2017
5693	3^169004+2660	80636	Lelio R Paula	12/2015
5694	2^267860-112859	80634	Enzo Doria	06/2014
5695	2^267828-110705	80625	Enzo Doria	05/2014
5696	2^267743+12705	80599	Lelio R Paula	07/2013
5697	(22*10^80595+23)/9	80596	Robert Price	03/2015
5698	2^267674-51	80578	Lelio R Paula	05/2012
5699	(86*10^80571-41)/9	80572	Robert Price	11/2015
5700	2^267612-1965	80560	Lelio R Paula	07/2013
5701	2^267553+4097	80542	Lelio R Paula	07/2013
5702	7^95276-8	80518	Robert Price	01/2014
5703	(15185*2^267457-1)/47829	80513	Lelio R Paula	04/2015
5704	6^103467+163	80513	Lelio R Paula	12/2015
5705	(7*10^80490+143)/3	80491	Robert Price	04/2016
5706	86^41597-85^41597	80470	Robert Price	04/2015
5707	13^72237+30	80468	Lelio R Paula	11/2015
5708	17^65389+14	80458	Lelio R Paula	11/2015
5709	423^30634+30634^423	80456	Norbert Schneider	05/2017
5710	2^267232+105	80445	Lelio R Paula	05/2012
5711	11^77237-3072000	80435	Enzo Doria	01/2013
5712	2^267116-459959	80410	Enzo Doria	06/2015
5713	38715!2+8	80406	Robert Price	01/2015
5714	(2^267017+1)/3	80380	H.&R. Lifchitz	09/2000
5715	2^266968-45	80366	Lelio R Paula	05/2012
5716	20^61768-63	80363	Lelio R Paula	01/2016
5717	2^266920-112967	80351	Enzo Doria	06/2014
5718	8*10^80342+87	80343	Robert Price	10/2017
5719	12^74428-13	80322	Lelio R Paula	11/2015
5720	2^266680+27	80279	Lelio R Paula	05/2012
5721	2^266630-131	80264	Lelio R Paula	05/2012
5722	2^266598+76819	80254	Enzo Doria	05/2016
5723	2^266587+1880633	80251	Enzo Doria	10/2016
5724	2^266541-110049	80237	Enzo Doria	04/2014
5725	38635!2-8	80222	Robert Price	06/2015
5726	3^168111+168111^3-1	80210	Robert Price	04/2014
5727	2^266443+513	80208	Lelio R Paula	07/2013
5728	(26*10^80200+61)/3	80201	Robert Price	06/2017
5729	2^266412-109913	80199	Enzo Doria	04/2014
5730	(10223*2^266417+1)/45091	80199	Lelio R Paula	06/2014
5731	13^71988+66	80191	Lelio R Paula	11/2015
5732	11^77002-4320	80190	Enzo Doria	01/2013
5733	18^63879-13	80186	Lelio R Paula	11/2015
5734	2^266368-112295	80185	Enzo Doria	06/2014
5735	(3^168050+5)/1021454	80175	Lelio R Paula	10/2012
5736	(22*10^80167+41)/9	80168	Robert Price	02/2015
5737	(34*10^80162-43)/9	80163	Ray Chandler	12/2010
5738	(38*10^80150-11)/9	80151	Robert Price	05/2015
5739	(598*10^80149-31)/9	80151	Robert Price	02/2017
5740	19^62678-80	80150	Lelio R Paula	12/2015
5741	10^80139+32343	80140	Patrick De Geest	02/2011
5742	10^80139-9	80139	Alexander Gramolin	01/2011
5743	3^167955-106	80135	Lelio R Paula	12/2015
5744	(197*10^80089-11)/3	80091	Robert Price	10/2017
5745	2^265998+75559	80074	Enzo Doria	04/2016
5746	2^265969-109801	80065	Enzo Doria	04/2014
5747	2^265888-112757	80041	Enzo Doria	06/2014
5748	2^265809+1701	80017	Lelio R Paula	07/2013
5749	gcd(V(957175),5F(191435)(F(191435)+1)+1)	80014	Serge Batalov	04/2015
5750	3^167687-104	80008	Lelio R Paula	02/2015

Find by discoverer :

PRP Records

Probable Primes Top 10000

(252538 PRPs in the top)