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 (> 30000)	Who ?	When ?
5001	2^275879-109807	83048	Enzo Doria	04/2014
5003	F(397379)	83047	Henri Lifchitz	08/2003
5002	U(397379)	83047	Serge Batalov	03/2015
5005	3^174040-14	83039	Robert Price	08/2013
5004	(86*10^83038-221)/9	83039	Robert Price	06/2017
5006	2^275841-6883	83037	Lelio R Paula	07/2011
5007	3^174002-140	83021	Lelio R Paula	12/2015
5008	6^106681+77	83014	Lelio R Paula	12/2015
5009	187^36539-2	83011	Lelio R Paula	10/2017
5010	11^79701-3150	83001	Enzo Doria	12/2012
5011	(55459*2^275657+1)/21	82985	Lelio R Paula	06/2014
5012	(7*10^82960-457)/9	82960	Robert Price	09/2017
5013	2^275535-6855	82945	Lelio R Paula	08/2013
5014	3^173828-14	82938	Robert Price	08/2013
5015	2^275512-109677	82938	Enzo Doria	04/2014
5016	2^275446-110045	82918	Enzo Doria	04/2014
5017	(2^275473+47)/29526097447	82916	Lelio R Paula	12/2012
5018	3^173755-14	82903	Robert Price	08/2013
5019	(182*10^82898+43)/9	82900	Robert Price	11/2017
5020	2^275363-112309	82893	Enzo Doria	06/2014
5021	61^46427-60	82888	Norbert Schneider	10/2014
5022	3*10^82880-7^82880	82881	Mike Oakes	02/2010
5024	2^275290+90195	82871	Lelio R Paula	07/2013
5023	(35*10^82870-71)/9	82871	Robert Price	05/2015
5025	2^275270-1859621	82865	Enzo Doria	03/2016
5026	2^275259+81	82862	Henri Lifchitz	01/2007
5027	(113703^16384+1)/2	82834	Richard Fischer	04/2018
5028	7^98003+98003^7+1	82823	Robert Price	05/2014
5029	10^82790+126043	82791	Patrick De Geest	07/2013
5030	10^82790-47	82790	Robert Price	05/2011
5031	2^274985-112663	82779	Enzo Doria	06/2014
5032	2^274935+15015	82764	Lelio R Paula	07/2013
5033	(17*2^274922+1)/3	82761	Lelio R Paula	12/2012
5034	(43*10^82752-61)/9	82753	Robert Price	06/2015
5035	(3*2^274862+1)/1027	82740	Lelio R Paula	12/2012
5036	(31*2^274848-1)/4065	82736	Lelio R Paula	02/2014
5037	(4^137405+23)/3	82726	Robert Price	02/2017
5038	2^274791-110491	82721	Enzo Doria	05/2014
5039	(11*2^274776-1)/95	82715	Lelio R Paula	02/2014
5040	(47*10^82706-119)/9	82707	Robert Price	09/2017
5041	2^274704-111395	82695	Enzo Doria	05/2014
5042	2^274686-3911	82689	Yves Minet	04/2017
5043	(2^274663-1017)/48871318292279	82669	Lelio R Paula	12/2012
5044	(3^173263-5)/14498	82664	Lelio R Paula	12/2012
5045	2^274511-64875	82637	Lelio R Paula	08/2013
5046	12^76572-83	82636	Lelio R Paula	11/2015
5047	3^173191-2^173191	82634	Mike Oakes	02/2004
5048	14^72072-15	82604	Lelio R Paula	11/2015
5049	(55459*2^274339+1)/3	82589	Lelio R Paula	06/2014
5050	2^274351+123	82588	Lelio R Paula	06/2012
5051	(1017*2^274339-1)/3515	82584	Lelio R Paula	04/2015
5052	6^106086+113	82551	Lelio R Paula	12/2015
5053	(17*10^82540-377)/9	82541	Robert Price	11/2017
5054	2^274093-58695	82511	Lelio R Paula	07/2013
5055	7*10^82509-47	82510	Robert Price	02/2017
5056	2^274081-6555	82507	Lelio R Paula	07/2013
5058	2^274074-274074+1	82505	Robert Price	10/2014
5059	14^71985+47	82505	Lelio R Paula	11/2015
5057	5*10^82504+21	82505	Robert Price	01/2017
5060	6^106014-139	82495	Lelio R Paula	12/2015
5061	(2^274046+47)/753	82494	Lelio R Paula	12/2012
5062	2^274008-1838099	82485	Enzo Doria	05/2015
5063	2^273981-110029	82477	Enzo Doria	04/2014
5064	19^64490-30	82467	Lelio R Paula	12/2015
5065	2^273785+11715	82418	Lelio R Paula	07/2013
5066	8*10^82417+51	82418	Robert Price	05/2017
5067	11^79133-10	82409	Theodore Burton	11/2005
5068	91^42063+90	82404	Norbert Schneider	01/2016
5070	2^273662-63	82381	Lelio R Paula	06/2012
5069	2^273661+255	82381	Lelio R Paula	07/2013
5071	(62*10^82377-17)/9	82378	Robert Price	09/2015
5072	8*10^82360-51	82361	Robert Price	10/2017
5073	(79*10^82347-1)/3	82349	Robert Price	11/2017
5074	(11*10^82323+91)/3	82323	Robert Price	02/2017
5075	(189977#+19081)/(19081*17260483)	82317	Makoto Morimoto	10/2017
5076	(189977#+196924)/(271354128874441)	82316	Makoto Morimoto	10/2017
5077	15^69984+32	82308	Lelio R Paula	11/2015
5078	9*6^105746+7	82288	Lelio R Paula	10/2014
5079	89^42211-88	82286	Norbert Schneider	01/2016
5080	gcd(V(1476435),5F(295287)(F(295287)+1)+1)	82281	Serge Batalov	04/2015
5081	(19*10^82270-43)/3	82271	Robert Price	10/2017
5082	2^273282-110241	82267	Enzo Doria	05/2014
5083	(13^73849+4^73849)/17	82263	Robert Price	05/2013
5084	10^82254+9^(82254+1)	82255	Robert Price	08/2016
5085	10^82254+457773	82255	Patrick De Geest	12/2016
5086	10^82254-99609	82254	Patrick De Geest	12/2016
5087	(754*10^82250-7)/9	82252	Robert Price	11/2017
5088	18^65524+13	82251	Lelio R Paula	11/2015
5089	2^273206-107	82244	Lelio R Paula	06/2012
5090	2^273193-459145	82240	Enzo Doria	05/2015
5092	2^273126+36937	82220	Yves Minet	06/2010
5091	39505!2+128	82220	Robert Price	03/2015
5093	2^273053-112111	82198	Enzo Doria	06/2014
5094	2^273016+1185	82187	Lelio R Paula	07/2013
5095	(2^273008+3)/7	82183	Lelio R Paula	12/2012
5096	5^117554-15386	82167	Enzo Doria	02/2013
5097	(38*10^82161+403)/9	82162	Robert Price	11/2017
5098	2^272907-111439	82154	Enzo Doria	05/2014
5099	(67607*2^272901+1)/50790115	82149	Lelio R Paula	06/2014
5100	2^272875-69	82144	Lelio R Paula	06/2012
5101	7^97197+4	82141	Robert Price	01/2014
5102	(4*6^105554+1)/5	82137	Serge Batalov	10/2014
5103	6^105531-109	82120	Lelio R Paula	12/2015
5104	2^272766-65	82111	Lelio R Paula	06/2012
5105	19^64205-78	82103	Lelio R Paula	12/2015
5106	2^272702+1869979	82092	Enzo Doria	05/2016
5107	(29*2^272687-1)/9	82088	Lelio R Paula	02/2014
5108	(5*10^82085-119)/3	82086	Robert Price	04/2016
5109	2^272660-110049	82079	Enzo Doria	04/2014
5110	6^105474+67	82075	Lelio R Paula	12/2015
5111	2^272637+82875	82072	Lelio R Paula	07/2013
5112	2^272587-31	82057	Lelio R Paula	06/2012
5113	(41*10^82044-59)/9	82045	Robert Price	10/2017
5114	8*5^117368+9	82038	Lelio R Paula	10/2014
5115	(101525^16384+1)/131074	82023	Lelio R Paula	11/2011
5116	4*5^117343-7	82020	Lelio R Paula	10/2014
5117	(265*10^81990+17)/3	81992	Robert Price	05/2016
5118	3^171843+10	81990	Robert Price	10/2013
5119	(7*10^81985+107)/3	81986	Robert Price	02/2017
5120	(3*2^272356+1)/177163	81983	Lelio R Paula	12/2012
5121	2^272296-111149	81970	Enzo Doria	05/2014
5122	(9*2^272243-1)/7	81954	Lelio R Paula	02/2014
5123	2^272177-111223	81934	Enzo Doria	05/2014
5124	(151009^15817+1)/151010	81912	Faysal YAtim	06/2017
5125	(16*10^81896-19)/3	81897	Robert Price	03/2016
5126	(2^271922+78557)/63	81855	Lelio R Paula	12/2012
5127	(10^81848+77)/3	81848	Robert Price	01/2017
5128	(24737*2^271883+1)/3757	81846	Lelio R Paula	06/2014
5129	10^81778+39	81779	Robert Price	03/2011
5130	10^81778-171999	81778	Patrick De Geest	07/2013
5131	(14*10^81767-11)/3	81768	Erik Branger	09/2014
5132	2^271541+1868417	81742	Enzo Doria	04/2016
5133	(2^271549-1)/238749682487	81734	Jens K. Andersen	02/2009
5134	2^271484-167	81725	Lelio R Paula	06/2012
5135	(8*10^81709-611)/9	81709	Robert Price	11/2017
5136	2^271382+12909	81695	Lelio R Paula	07/2013
5137	49^48334+48	81694	Norbert Schneider	07/2014
5138	7^96668+48	81694	Lelio R Paula	10/2015
5139	11^78435-1410	81682	Enzo Doria	12/2012
5140	5*10^81653+9	81654	Dmitry Domanov	11/2010
5141	(2^271211-1)/613961495159	81631	Jens K. Andersen	02/2009
5142	3^171068+52	81621	Lelio R Paula	12/2015
5143	2^271115-110407	81614	Enzo Doria	05/2014
5144	2^271111-110635	81613	Enzo Doria	05/2014
5145	2^271098-111	81609	Lelio R Paula	06/2012
5146	(77*10^81606+13)/9	81607	Robert Price	10/2015
5147	2^271064-2790209	81599	Enzo Doria	03/2016
5148	(13*2^271053-1)/3095	81593	Lelio R Paula	02/2014
5149	2^271040-57	81592	Lelio R Paula	06/2012
5150	(14*10^81585+73)/3	81586	Robert Price	04/2016
5151	127^38779+126	81584	Norbert Schneider	02/2015
5152	18^64966-43	81551	Lelio R Paula	11/2015
5153	(2^270840+47)/591	81529	Lelio R Paula	12/2012
5154	20^62654+87	81515	Lelio R Paula	01/2016
5155	(19*10^81488+191)/3	81489	Robert Price	01/2017
5156	8*10^81487+21	81488	Robert Price	02/2017
5157	(73*10^81485+107)/9	81486	Robert Price	08/2016
5158	536^29847+29847^536	81458	Norbert Schneider	03/2017
5159	8*7^96378+9	81450	Lelio R Paula	10/2014
5160	2^270546-110345	81443	Enzo Doria	05/2014
5161	13^73105-60	81435	Lelio R Paula	11/2015
5162	44^49524+43	81391	Norbert Schneider	06/2014
5163	(3*2^270368-1)/13	81389	Lelio R Paula	02/2014
5164	(10^81363+719)/9	81363	Serge Batalov	12/2014
5165	(10^81353+449)/9	81353	Serge Batalov	12/2014
5166	14^70978-89	81350	Lelio R Paula	11/2015
5167	11^78108-2040	81342	Enzo Doria	12/2012
5168	3^170400-58	81302	Lelio R Paula	12/2015
5169	(17*10^81300-131)/3	81301	Robert Price	12/2017
5170	10^81297+36991	81298	Patrick De Geest	06/2013
5171	10^81297-57	81297	Robert Price	05/2011
5172	2^270055-113047	81295	Enzo Doria	07/2014
5173	18^64759-55	81291	Lelio R Paula	11/2015
5174	(2^269987+1)/3	81274	H.&R. Lifchitz	10/2000
5175	(31^54493-1)/30	81268	Alexander Zhirkov	10/2010
5176	(2^270059-1)/540119/6481417/7124976157756725967	81265	Dario Alpern	09/2014
5177	(2^269816+7)/424901	81218	Lelio R Paula	12/2012
5178	(23*10^81214+1)/3	81215	Serge Batalov	06/2009
5179	(17*2^269720+1)/303	81193	Lelio R Paula	07/2012
5180	56^46441-55^46441	81188	Robert Price	10/2013
5182	2^269664+177	81177	Lelio R Paula	06/2012
5181	(13*2^269665-1)/185	81177	Lelio R Paula	02/2014
5183	2^269539-112249	81140	Enzo Doria	06/2014
5184	((2170026-3)3^(170026-1)+1)/4	81128	Robert Price	01/2015
5185	(2^269495-5)/9	81126	Lelio R Paula	12/2012
5186	2^269490-3623	81125	Yves Minet	10/2009
5187	(55459*2^269444+1)/35	81114	Lelio R Paula	06/2014
5188	(2^269417+78557)/5257	81099	Lelio R Paula	12/2012
5189	4*5^116011-7	81089	Lelio R Paula	10/2014
5190	7*10^81058+79	81059	Robert Price	02/2017
5191	2^269236-109907	81049	Enzo Doria	04/2014
5192	(8*10^81029-11)/3	81030	Erik Branger	03/2014
5193	3*10^81021+7	81022	Erik Branger	11/2013
5194	6^104115+103	81018	Lelio R Paula	12/2015
5195	2^269120+1869151	81014	Enzo Doria	05/2016
5196	5^115901+12	81012	Lelio R Paula	10/2015
5197	(2^269083-9)/320369	80997	Lelio R Paula	12/2012
5198	17^65810-20	80976	Lelio R Paula	11/2015
5199	20^62236-23	80971	Lelio R Paula	01/2016
5200	2^268974-112181	80970	Enzo Doria	06/2014
5202	L(387433)	80969	Renaud Lifchitz	11/2003
5201	V(387433)	80969	Serge Batalov	03/2015
5203	(2^268955-509203)/5	80963	Lelio R Paula	12/2012
5204	(87398^16384+1)/65537	80957	Lelio R Paula	11/2011
5205	329^32160+32160^329	80954	Norbert Schneider	11/2014
5206	2^268859-159	80935	Lelio R Paula	05/2012
5207	(2^268841-lucasV(1,2,268841)+1)/2	80929	Mike Oakes	11/2016
5208	2^268827+5775	80925	Lelio R Paula	07/2013
5209	2^268824-110255	80925	Enzo Doria	05/2014
5210	2^268798-1868321	80917	Enzo Doria	04/2016
5211	2^268753-114621	80903	Enzo Doria	05/2015
5212	2^268743+1605	80900	Lelio R Paula	07/2013
5213	6^103954-139	80892	Lelio R Paula	12/2015
5214	10^80883+49	80884	Robert Price	03/2011
5215	10^80883-80327	80883	Patrick De Geest	07/2013
5216	6^103937+121	80879	Lelio R Paula	12/2015
5217	(26*10^80875-119)/3	80876	Robert Price	07/2016
5218	(22699*2^268657+1)/6351	80875	Lelio R Paula	06/2014
5219	2^268581-869688105	80851	Lelio R Paula	05/2016
5220	(11*2^268521-1)/3	80834	Lelio R Paula	02/2014
5221	2^268516-249	80832	Yves Minet	02/2012
5222	2^268500+16095	80827	Lelio R Paula	07/2013
5223	3^169402+100	80826	Lelio R Paula	12/2015
5224	9^84698+8^(84698-1)	80823	Robert Price	03/2016
5225	2^268472-109739	80819	Enzo Doria	04/2014
5226	(9*2^268454+1)/37	80813	Lelio R Paula	12/2012
5227	(3*2^268502+1)/377902188435353647	80811	Lelio R Paula	12/2012
5228	134^37987-133^37987	80803	Jean-Louis Charton	12/2005
5229	15^68702-76	80800	Lelio R Paula	11/2015
5230	2^268408+7	80799	Lelio R Paula	05/2012
5231	2^268375+141	80789	Lelio R Paula	05/2012
5232	12^74856-47	80784	Lelio R Paula	11/2015
5233	6^103770-107	80749	Lelio R Paula	12/2015
5234	3^169224-62	80741	Lelio R Paula	12/2015
5235	p(16866)#/2+64	80741	Robert Price	03/2017
5236	5^115502-72	80733	Lelio R Paula	10/2015
5237	2^268079-1927	80700	Yves Minet	10/2009
5238	2^268028+117	80685	Lelio R Paula	05/2012
5239	121^38738+120	80683	Norbert Schneider	01/2015
5240	(3^169097-8)/835	80677	Lelio R Paula	12/2012
5241	2^267918+67	80652	Lelio R Paula	05/2012
5242	(89*10^80650-179)/9	80651	Robert Price	11/2017
5243	(302*10^80638+13)/9	80640	Robert Price	01/2017
5244	3^169004+2660	80636	Lelio R Paula	12/2015
5245	2^267860-112859	80634	Enzo Doria	06/2014
5246	2^267828-110705	80625	Enzo Doria	05/2014
5247	2^267743+12705	80599	Lelio R Paula	07/2013
5248	(22*10^80595+23)/9	80596	Robert Price	03/2015
5249	2^267674-51	80578	Lelio R Paula	05/2012
5250	(86*10^80571-41)/9	80572	Robert Price	11/2015

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PRP Records

Probable Primes Top 10000

(211563 PRPs in the top)