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	(11*10^82323+91)/3	82323	Robert Price	02/2017
5002	(189977#+19081)/(19081*17260483)	82317	Makoto Morimoto	10/2017
5003	(189977#+196924)/(271354128874441)	82316	Makoto Morimoto	10/2017
5004	15^69984+32	82308	Lelio R Paula	11/2015
5005	9*6^105746+7	82288	Lelio R Paula	10/2014
5006	89^42211-88	82286	Norbert Schneider	01/2016
5007	gcd(V(1476435),5F(295287)(F(295287)+1)+1)	82281	Serge Batalov	04/2015
5008	(19*10^82270-43)/3	82271	Robert Price	10/2017
5009	2^273282-110241	82267	Enzo Doria	05/2014
5010	(13^73849+4^73849)/17	82263	Robert Price	05/2013
5012	10^82254+9^(82254+1)	82255	Robert Price	08/2016
5011	10^82254+457773	82255	Patrick De Geest	12/2016
5013	10^82254-99609	82254	Patrick De Geest	12/2016
5014	(754*10^82250-7)/9	82252	Robert Price	11/2017
5015	18^65524+13	82251	Lelio R Paula	11/2015
5016	2^273206-107	82244	Lelio R Paula	06/2012
5017	2^273193-459145	82240	Enzo Doria	05/2015
5019	2^273126+36937	82220	Yves Minet	06/2010
5018	39505!2+128	82220	Robert Price	03/2015
5020	2^273053-112111	82198	Enzo Doria	06/2014
5021	2^273016+1185	82187	Lelio R Paula	07/2013
5022	(2^273008+3)/7	82183	Lelio R Paula	12/2012
5023	5^117554-15386	82167	Enzo Doria	02/2013
5024	(38*10^82161+403)/9	82162	Robert Price	11/2017
5025	2^272907-111439	82154	Enzo Doria	05/2014
5026	(67607*2^272901+1)/50790115	82149	Lelio R Paula	06/2014
5027	2^272875-69	82144	Lelio R Paula	06/2012
5028	7^97197+4	82141	Robert Price	01/2014
5029	(4*6^105554+1)/5	82137	Serge Batalov	10/2014
5030	6^105531-109	82120	Lelio R Paula	12/2015
5031	2^272766-65	82111	Lelio R Paula	06/2012
5032	19^64205-78	82103	Lelio R Paula	12/2015
5033	2^272702+1869979	82092	Enzo Doria	05/2016
5034	(29*2^272687-1)/9	82088	Lelio R Paula	02/2014
5035	(5*10^82085-119)/3	82086	Robert Price	04/2016
5036	2^272660-110049	82079	Enzo Doria	04/2014
5037	6^105474+67	82075	Lelio R Paula	12/2015
5038	2^272637+82875	82072	Lelio R Paula	07/2013
5039	2^272587-31	82057	Lelio R Paula	06/2012
5040	(41*10^82044-59)/9	82045	Robert Price	10/2017
5041	8*5^117368+9	82038	Lelio R Paula	10/2014
5042	(101525^16384+1)/131074	82023	Lelio R Paula	11/2011
5043	4*5^117343-7	82020	Lelio R Paula	10/2014
5044	(265*10^81990+17)/3	81992	Robert Price	05/2016
5045	3^171843+10	81990	Robert Price	10/2013
5046	(7*10^81985+107)/3	81986	Robert Price	02/2017
5047	(3*2^272356+1)/177163	81983	Lelio R Paula	12/2012
5048	2^272296-111149	81970	Enzo Doria	05/2014
5049	(9*2^272243-1)/7	81954	Lelio R Paula	02/2014
5050	2^272177-111223	81934	Enzo Doria	05/2014
5051	(151009^15817+1)/151010	81912	Faysal YAtim	06/2017
5052	(16*10^81896-19)/3	81897	Robert Price	03/2016
5053	(2^271922+78557)/63	81855	Lelio R Paula	12/2012
5054	(10^81848+77)/3	81848	Robert Price	01/2017
5055	(24737*2^271883+1)/3757	81846	Lelio R Paula	06/2014
5056	10^81778+39	81779	Robert Price	03/2011
5057	10^81778-171999	81778	Patrick De Geest	07/2013
5058	(14*10^81767-11)/3	81768	Erik Branger	09/2014
5059	2^271541+1868417	81742	Enzo Doria	04/2016
5060	(2^271549-1)/238749682487	81734	Jens K. Andersen	02/2009
5061	2^271484-167	81725	Lelio R Paula	06/2012
5062	(8*10^81709-611)/9	81709	Robert Price	11/2017
5063	2^271382+12909	81695	Lelio R Paula	07/2013
5064	49^48334+48	81694	Norbert Schneider	07/2014
5065	7^96668+48	81694	Lelio R Paula	10/2015
5066	11^78435-1410	81682	Enzo Doria	12/2012
5067	5*10^81653+9	81654	Dmitry Domanov	11/2010
5068	(2^271211-1)/613961495159	81631	Jens K. Andersen	02/2009
5069	3^171068+52	81621	Lelio R Paula	12/2015
5070	2^271115-110407	81614	Enzo Doria	05/2014
5071	2^271111-110635	81613	Enzo Doria	05/2014
5072	2^271098-111	81609	Lelio R Paula	06/2012
5073	(77*10^81606+13)/9	81607	Robert Price	10/2015
5074	2^271064-2790209	81599	Enzo Doria	03/2016
5075	(13*2^271053-1)/3095	81593	Lelio R Paula	02/2014
5076	2^271040-57	81592	Lelio R Paula	06/2012
5077	(14*10^81585+73)/3	81586	Robert Price	04/2016
5078	127^38779+126	81584	Norbert Schneider	02/2015
5079	18^64966-43	81551	Lelio R Paula	11/2015
5080	(2^270840+47)/591	81529	Lelio R Paula	12/2012
5081	20^62654+87	81515	Lelio R Paula	01/2016
5082	(19*10^81488+191)/3	81489	Robert Price	01/2017
5083	8*10^81487+21	81488	Robert Price	02/2017
5084	(73*10^81485+107)/9	81486	Robert Price	08/2016
5085	536^29847+29847^536	81458	Norbert Schneider	03/2017
5086	8*7^96378+9	81450	Lelio R Paula	10/2014
5087	2^270546-110345	81443	Enzo Doria	05/2014
5088	13^73105-60	81435	Lelio R Paula	11/2015
5089	44^49524+43	81391	Norbert Schneider	06/2014
5090	(3*2^270368-1)/13	81389	Lelio R Paula	02/2014
5091	(10^81363+719)/9	81363	Serge Batalov	12/2014
5092	(10^81353+449)/9	81353	Serge Batalov	12/2014
5093	14^70978-89	81350	Lelio R Paula	11/2015
5094	11^78108-2040	81342	Enzo Doria	12/2012
5095	3^170400-58	81302	Lelio R Paula	12/2015
5096	(17*10^81300-131)/3	81301	Robert Price	12/2017
5097	10^81297+36991	81298	Patrick De Geest	06/2013
5098	10^81297-57	81297	Robert Price	05/2011
5099	2^270055-113047	81295	Enzo Doria	07/2014
5100	18^64759-55	81291	Lelio R Paula	11/2015
5101	(2^269987+1)/3	81274	H.&R. Lifchitz	10/2000
5102	(31^54493-1)/30	81268	Alexander Zhirkov	10/2010
5103	(2^270059-1)/540119/6481417/7124976157756725967	81265	Dario Alpern	09/2014
5104	(2^269816+7)/424901	81218	Lelio R Paula	12/2012
5105	(23*10^81214+1)/3	81215	Serge Batalov	06/2009
5106	(17*2^269720+1)/303	81193	Lelio R Paula	07/2012
5107	56^46441-55^46441	81188	Robert Price	10/2013
5108	2^269664+177	81177	Lelio R Paula	06/2012
5109	(13*2^269665-1)/185	81177	Lelio R Paula	02/2014
5110	2^269539-112249	81140	Enzo Doria	06/2014
5111	((2170026-3)3^(170026-1)+1)/4	81128	Robert Price	01/2015
5112	(2^269495-5)/9	81126	Lelio R Paula	12/2012
5113	2^269490-3623	81125	Yves Minet	10/2009
5114	(55459*2^269444+1)/35	81114	Lelio R Paula	06/2014
5115	(2^269417+78557)/5257	81099	Lelio R Paula	12/2012
5116	4*5^116011-7	81089	Lelio R Paula	10/2014
5117	7*10^81058+79	81059	Robert Price	02/2017
5118	2^269236-109907	81049	Enzo Doria	04/2014
5119	(8*10^81029-11)/3	81030	Erik Branger	03/2014
5120	3*10^81021+7	81022	Erik Branger	11/2013
5121	6^104115+103	81018	Lelio R Paula	12/2015
5122	2^269120+1869151	81014	Enzo Doria	05/2016
5123	5^115901+12	81012	Lelio R Paula	10/2015
5124	(2^269083-9)/320369	80997	Lelio R Paula	12/2012
5125	17^65810-20	80976	Lelio R Paula	11/2015
5126	20^62236-23	80971	Lelio R Paula	01/2016
5127	2^268974-112181	80970	Enzo Doria	06/2014
5129	L(387433)	80969	Renaud Lifchitz	11/2003
5128	V(387433)	80969	Serge Batalov	03/2015
5130	(2^268955-509203)/5	80963	Lelio R Paula	12/2012
5131	(87398^16384+1)/65537	80957	Lelio R Paula	11/2011
5132	329^32160+32160^329	80954	Norbert Schneider	11/2014
5133	2^268859-159	80935	Lelio R Paula	05/2012
5134	(2^268841-lucasV(1,2,268841)+1)/2	80929	Mike Oakes	11/2016
5135	2^268827+5775	80925	Lelio R Paula	07/2013
5136	2^268824-110255	80925	Enzo Doria	05/2014
5137	2^268798-1868321	80917	Enzo Doria	04/2016
5138	2^268753-114621	80903	Enzo Doria	05/2015
5139	2^268743+1605	80900	Lelio R Paula	07/2013
5140	6^103954-139	80892	Lelio R Paula	12/2015
5141	10^80883+49	80884	Robert Price	03/2011
5142	10^80883-80327	80883	Patrick De Geest	07/2013
5143	6^103937+121	80879	Lelio R Paula	12/2015
5144	(26*10^80875-119)/3	80876	Robert Price	07/2016
5145	(22699*2^268657+1)/6351	80875	Lelio R Paula	06/2014
5146	2^268581-869688105	80851	Lelio R Paula	05/2016
5147	(11*2^268521-1)/3	80834	Lelio R Paula	02/2014
5148	2^268516-249	80832	Yves Minet	02/2012
5149	2^268500+16095	80827	Lelio R Paula	07/2013
5150	3^169402+100	80826	Lelio R Paula	12/2015
5151	9^84698+8^(84698-1)	80823	Robert Price	03/2016
5152	2^268472-109739	80819	Enzo Doria	04/2014
5153	(9*2^268454+1)/37	80813	Lelio R Paula	12/2012
5154	(3*2^268502+1)/377902188435353647	80811	Lelio R Paula	12/2012
5155	134^37987-133^37987	80803	Jean-Louis Charton	12/2005
5156	15^68702-76	80800	Lelio R Paula	11/2015
5157	2^268408+7	80799	Lelio R Paula	05/2012
5158	2^268375+141	80789	Lelio R Paula	05/2012
5159	12^74856-47	80784	Lelio R Paula	11/2015
5160	6^103770-107	80749	Lelio R Paula	12/2015
5161	3^169224-62	80741	Lelio R Paula	12/2015
5162	p(16866)#/2+64	80741	Robert Price	03/2017
5163	5^115502-72	80733	Lelio R Paula	10/2015
5164	2^268079-1927	80700	Yves Minet	10/2009
5165	2^268028+117	80685	Lelio R Paula	05/2012
5166	121^38738+120	80683	Norbert Schneider	01/2015
5167	(3^169097-8)/835	80677	Lelio R Paula	12/2012
5168	2^267918+67	80652	Lelio R Paula	05/2012
5169	(89*10^80650-179)/9	80651	Robert Price	11/2017
5170	(302*10^80638+13)/9	80640	Robert Price	01/2017
5171	3^169004+2660	80636	Lelio R Paula	12/2015
5172	2^267860-112859	80634	Enzo Doria	06/2014
5173	2^267828-110705	80625	Enzo Doria	05/2014
5174	2^267743+12705	80599	Lelio R Paula	07/2013
5175	(22*10^80595+23)/9	80596	Robert Price	03/2015
5176	2^267674-51	80578	Lelio R Paula	05/2012
5177	(86*10^80571-41)/9	80572	Robert Price	11/2015
5178	2^267612-1965	80560	Lelio R Paula	07/2013
5179	2^267553+4097	80542	Lelio R Paula	07/2013
5180	7^95276-8	80518	Robert Price	01/2014
5181	(15185*2^267457-1)/47829	80513	Lelio R Paula	04/2015
5182	6^103467+163	80513	Lelio R Paula	12/2015
5183	(7*10^80490+143)/3	80491	Robert Price	04/2016
5184	86^41597-85^41597	80470	Robert Price	04/2015
5185	13^72237+30	80468	Lelio R Paula	11/2015
5186	17^65389+14	80458	Lelio R Paula	11/2015
5187	423^30634+30634^423	80456	Norbert Schneider	05/2017
5188	2^267232+105	80445	Lelio R Paula	05/2012
5189	11^77237-3072000	80435	Enzo Doria	01/2013
5190	2^267116-459959	80410	Enzo Doria	06/2015
5191	38715!2+8	80406	Robert Price	01/2015
5192	(2^267017+1)/3	80380	H.&R. Lifchitz	09/2000
5193	2^266968-45	80366	Lelio R Paula	05/2012
5194	20^61768-63	80363	Lelio R Paula	01/2016
5195	2^266920-112967	80351	Enzo Doria	06/2014
5196	8*10^80342+87	80343	Robert Price	10/2017
5197	12^74428-13	80322	Lelio R Paula	11/2015
5198	2^266680+27	80279	Lelio R Paula	05/2012
5199	2^266630-131	80264	Lelio R Paula	05/2012
5200	2^266598+76819	80254	Enzo Doria	05/2016
5201	2^266587+1880633	80251	Enzo Doria	10/2016
5202	2^266541-110049	80237	Enzo Doria	04/2014
5203	38635!2-8	80222	Robert Price	06/2015
5204	3^168111+168111^3-1	80210	Robert Price	04/2014
5205	2^266443+513	80208	Lelio R Paula	07/2013
5206	(26*10^80200+61)/3	80201	Robert Price	06/2017
5207	2^266412-109913	80199	Enzo Doria	04/2014
5208	(10223*2^266417+1)/45091	80199	Lelio R Paula	06/2014
5209	13^71988+66	80191	Lelio R Paula	11/2015
5210	11^77002-4320	80190	Enzo Doria	01/2013
5211	18^63879-13	80186	Lelio R Paula	11/2015
5212	2^266368-112295	80185	Enzo Doria	06/2014
5213	(3^168050+5)/1021454	80175	Lelio R Paula	10/2012
5214	(22*10^80167+41)/9	80168	Robert Price	02/2015
5215	(34*10^80162-43)/9	80163	Ray Chandler	12/2010
5217	(38*10^80150-11)/9	80151	Robert Price	05/2015
5216	(598*10^80149-31)/9	80151	Robert Price	02/2017
5218	19^62678-80	80150	Lelio R Paula	12/2015
5219	10^80139+32343	80140	Patrick De Geest	02/2011
5220	10^80139-9	80139	Alexander Gramolin	01/2011
5221	3^167955-106	80135	Lelio R Paula	12/2015
5222	(197*10^80089-11)/3	80091	Robert Price	10/2017
5223	2^265998+75559	80074	Enzo Doria	04/2016
5224	2^265969-109801	80065	Enzo Doria	04/2014
5225	2^265888-112757	80041	Enzo Doria	06/2014
5226	2^265809+1701	80017	Lelio R Paula	07/2013
5227	gcd(V(957175),5F(191435)(F(191435)+1)+1)	80014	Serge Batalov	04/2015
5228	3^167687-104	80008	Lelio R Paula	02/2015
5229	11^76826-5790	80007	Enzo Doria	01/2013
5230	10^80000+85731	80001	Patrick De Geest	10/2009
5231	10^80000-7169	80000	Patrick De Geest	09/2009
5232	10^79999+22399	80000	Patrick De Geest	09/2009
5233	10^79999-74873	79999	Patrick De Geest	09/2009
5234	3^167668+58	79998	Lelio R Paula	02/2015
5235	155^36506-2	79961	Lelio R Paula	10/2017
5236	2^265612+4257	79958	Lelio R Paula	07/2013
5237	5*3^167577+4	79956	Lelio R Paula	06/2014
5238	(9179*2^265593-1)/9	79955	Lelio R Paula	04/2015
5239	6^102723-43	79935	Lelio R Paula	04/2015
5240	11^76748-3360	79925	Enzo Doria	12/2012
5241	(13*2^265498-1)/187119	79919	Lelio R Paula	02/2014
5242	2^265399-109855	79894	Enzo Doria	04/2014
5243	(20^61403-1)/19	79886	Paul Bourdelais	03/2010
5244	18^63635+59	79880	Lelio R Paula	02/2015
5245	(11*10^79867-107)/3	79868	Robert Price	11/2016
5246	3^167375+80	79859	Lelio R Paula	02/2015
5247	5^114240-14486	79851	Enzo Doria	02/2013
5248	49^47238+48	79842	Norbert Schneider	07/2014
5249	2^265212-3779	79837	Yves Minet	04/2017
5250	91^40746+40746^91	79824	Norbert Schneider	12/2014

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Probable Primes Top 10000

(205869 PRPs in the top)