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 ?
4751	2^271064-2790209	81599	Enzo Doria	03/2016
4752	(13*2^271053-1)/3095	81593	Lelio R Paula	02/2014
4753	2^271040-57	81592	Lelio R Paula	06/2012
4754	(14*10^81585+73)/3	81586	Robert Price	04/2016
4755	127^38779+126	81584	Norbert Schneider	02/2015
4756	18^64966-43	81551	Lelio R Paula	11/2015
4757	(2^270840+47)/591	81529	Lelio R Paula	12/2012
4758	20^62654+87	81515	Lelio R Paula	01/2016
4759	(19*10^81488+191)/3	81489	Robert Price	01/2017
4760	8*10^81487+21	81488	Robert Price	02/2017
4761	(73*10^81485+107)/9	81486	Robert Price	08/2016
4762	536^29847+29847^536	81458	Norbert Schneider	03/2017
4763	8*7^96378+9	81450	Lelio R Paula	10/2014
4764	2^270546-110345	81443	Enzo Doria	05/2014
4765	13^73105-60	81435	Lelio R Paula	11/2015
4766	44^49524+43	81391	Norbert Schneider	06/2014
4767	(3*2^270368-1)/13	81389	Lelio R Paula	02/2014
4768	(10^81363+719)/9	81363	Serge Batalov	12/2014
4769	(10^81353+449)/9	81353	Serge Batalov	12/2014
4770	14^70978-89	81350	Lelio R Paula	11/2015
4771	11^78108-2040	81342	Enzo Doria	12/2012
4772	3^170400-58	81302	Lelio R Paula	12/2015
4773	10^81297+36991	81298	Patrick De Geest	06/2013
4774	10^81297-57	81297	Robert Price	05/2011
4775	2^270055-113047	81295	Enzo Doria	07/2014
4776	18^64759-55	81291	Lelio R Paula	11/2015
4777	(2^269987+1)/3	81274	H.&R. Lifchitz	10/2000
4778	(31^54493-1)/30	81268	Alexander Zhirkov	10/2010
4779	(2^270059-1)/540119/6481417/7124976157756725967	81265	Dario Alpern	09/2014
4780	(2^269816+7)/424901	81218	Lelio R Paula	12/2012
4781	(23*10^81214+1)/3	81215	Serge Batalov	06/2009
4782	(17*2^269720+1)/303	81193	Lelio R Paula	07/2012
4783	56^46441-55^46441	81188	Robert Price	10/2013
4785	2^269664+177	81177	Lelio R Paula	06/2012
4784	(13*2^269665-1)/185	81177	Lelio R Paula	02/2014
4786	2^269539-112249	81140	Enzo Doria	06/2014
4787	((2170026-3)3^(170026-1)+1)/4	81128	Robert Price	01/2015
4788	(2^269495-5)/9	81126	Lelio R Paula	12/2012
4789	2^269490-3623	81125	Yves Minet	10/2009
4790	(55459*2^269444+1)/35	81114	Lelio R Paula	06/2014
4791	(2^269417+78557)/5257	81099	Lelio R Paula	12/2012
4792	4*5^116011-7	81089	Lelio R Paula	10/2014
4793	7*10^81058+79	81059	Robert Price	02/2017
4794	2^269236-109907	81049	Enzo Doria	04/2014
4795	(8*10^81029-11)/3	81030	Erik Branger	03/2014
4796	3*10^81021+7	81022	Erik Branger	11/2013
4797	6^104115+103	81018	Lelio R Paula	12/2015
4798	2^269120+1869151	81014	Enzo Doria	05/2016
4799	5^115901+12	81012	Lelio R Paula	10/2015
4800	(2^269083-9)/320369	80997	Lelio R Paula	12/2012
4801	17^65810-20	80976	Lelio R Paula	11/2015
4802	20^62236-23	80971	Lelio R Paula	01/2016
4803	2^268974-112181	80970	Enzo Doria	06/2014
4805	L(387433)	80969	Renaud Lifchitz	11/2003
4804	V(387433)	80969	Serge Batalov	03/2015
4806	(2^268955-509203)/5	80963	Lelio R Paula	12/2012
4807	(87398^16384+1)/65537	80957	Lelio R Paula	11/2011
4808	329^32160+32160^329	80954	Norbert Schneider	11/2014
4809	2^268859-159	80935	Lelio R Paula	05/2012
4810	(2^268841-lucasV(1,2,268841)+1)/2	80929	Mike Oakes	11/2016
4811	2^268827+5775	80925	Lelio R Paula	07/2013
4812	2^268824-110255	80925	Enzo Doria	05/2014
4813	2^268798-1868321	80917	Enzo Doria	04/2016
4814	2^268753-114621	80903	Enzo Doria	05/2015
4815	2^268743+1605	80900	Lelio R Paula	07/2013
4816	6^103954-139	80892	Lelio R Paula	12/2015
4817	10^80883+49	80884	Robert Price	03/2011
4818	10^80883-80327	80883	Patrick De Geest	07/2013
4819	6^103937+121	80879	Lelio R Paula	12/2015
4820	(26*10^80875-119)/3	80876	Robert Price	07/2016
4821	(22699*2^268657+1)/6351	80875	Lelio R Paula	06/2014
4822	2^268581-869688105	80851	Lelio R Paula	05/2016
4823	(11*2^268521-1)/3	80834	Lelio R Paula	02/2014
4824	2^268516-249	80832	Yves Minet	02/2012
4825	2^268500+16095	80827	Lelio R Paula	07/2013
4826	3^169402+100	80826	Lelio R Paula	12/2015
4827	9^84698+8^(84698-1)	80823	Robert Price	03/2016
4828	2^268472-109739	80819	Enzo Doria	04/2014
4829	(9*2^268454+1)/37	80813	Lelio R Paula	12/2012
4830	(3*2^268502+1)/377902188435353647	80811	Lelio R Paula	12/2012
4831	134^37987-133^37987	80803	Jean-Louis Charton	12/2005
4832	15^68702-76	80800	Lelio R Paula	11/2015
4833	2^268408+7	80799	Lelio R Paula	05/2012
4834	2^268375+141	80789	Lelio R Paula	05/2012
4835	12^74856-47	80784	Lelio R Paula	11/2015
4836	6^103770-107	80749	Lelio R Paula	12/2015
4837	3^169224-62	80741	Lelio R Paula	12/2015
4838	p(16866)#/2+64	80741	Robert Price	03/2017
4839	5^115502-72	80733	Lelio R Paula	10/2015
4840	2^268079-1927	80700	Yves Minet	10/2009
4841	2^268028+117	80685	Lelio R Paula	05/2012
4842	121^38738+120	80683	Norbert Schneider	01/2015
4843	(3^169097-8)/835	80677	Lelio R Paula	12/2012
4844	2^267918+67	80652	Lelio R Paula	05/2012
4845	(302*10^80638+13)/9	80640	Robert Price	01/2017
4846	3^169004+2660	80636	Lelio R Paula	12/2015
4847	2^267860-112859	80634	Enzo Doria	06/2014
4848	2^267828-110705	80625	Enzo Doria	05/2014
4849	2^267743+12705	80599	Lelio R Paula	07/2013
4850	(22*10^80595+23)/9	80596	Robert Price	03/2015
4851	2^267674-51	80578	Lelio R Paula	05/2012
4852	(86*10^80571-41)/9	80572	Robert Price	11/2015
4853	2^267612-1965	80560	Lelio R Paula	07/2013
4854	2^267553+4097	80542	Lelio R Paula	07/2013
4855	7^95276-8	80518	Robert Price	01/2014
4856	(15185*2^267457-1)/47829	80513	Lelio R Paula	04/2015
4857	6^103467+163	80513	Lelio R Paula	12/2015
4858	(7*10^80490+143)/3	80491	Robert Price	04/2016
4859	86^41597-85^41597	80470	Robert Price	04/2015
4860	13^72237+30	80468	Lelio R Paula	11/2015
4861	17^65389+14	80458	Lelio R Paula	11/2015
4862	423^30634+30634^423	80456	Norbert Schneider	05/2017
4863	2^267232+105	80445	Lelio R Paula	05/2012
4864	11^77237-3072000	80435	Enzo Doria	01/2013
4865	2^267116-459959	80410	Enzo Doria	06/2015
4866	38715!2+8	80406	Robert Price	01/2015
4867	(2^267017+1)/3	80380	H.&R. Lifchitz	09/2000
4868	2^266968-45	80366	Lelio R Paula	05/2012
4869	20^61768-63	80363	Lelio R Paula	01/2016
4870	2^266920-112967	80351	Enzo Doria	06/2014
4871	12^74428-13	80322	Lelio R Paula	11/2015
4872	2^266680+27	80279	Lelio R Paula	05/2012
4873	2^266630-131	80264	Lelio R Paula	05/2012
4874	2^266598+76819	80254	Enzo Doria	05/2016
4875	2^266587+1880633	80251	Enzo Doria	10/2016
4876	2^266541-110049	80237	Enzo Doria	04/2014
4877	38635!2-8	80222	Robert Price	06/2015
4878	3^168111+168111^3-1	80210	Robert Price	04/2014
4879	2^266443+513	80208	Lelio R Paula	07/2013
4880	(26*10^80200+61)/3	80201	Robert Price	06/2017
4881	2^266412-109913	80199	Enzo Doria	04/2014
4882	(10223*2^266417+1)/45091	80199	Lelio R Paula	06/2014
4883	13^71988+66	80191	Lelio R Paula	11/2015
4884	11^77002-4320	80190	Enzo Doria	01/2013
4885	18^63879-13	80186	Lelio R Paula	11/2015
4886	2^266368-112295	80185	Enzo Doria	06/2014
4887	(3^168050+5)/1021454	80175	Lelio R Paula	10/2012
4888	(22*10^80167+41)/9	80168	Robert Price	02/2015
4889	(34*10^80162-43)/9	80163	Ray Chandler	12/2010
4890	(38*10^80150-11)/9	80151	Robert Price	05/2015
4891	(598*10^80149-31)/9	80151	Robert Price	02/2017
4892	19^62678-80	80150	Lelio R Paula	12/2015
4893	10^80139+32343	80140	Patrick De Geest	02/2011
4894	10^80139-9	80139	Alexander Gramolin	01/2011
4895	3^167955-106	80135	Lelio R Paula	12/2015
4896	2^265998+75559	80074	Enzo Doria	04/2016
4897	2^265969-109801	80065	Enzo Doria	04/2014
4898	2^265888-112757	80041	Enzo Doria	06/2014
4899	2^265809+1701	80017	Lelio R Paula	07/2013
4900	gcd(V(957175),5F(191435)(F(191435)+1)+1)	80014	Serge Batalov	04/2015
4901	3^167687-104	80008	Lelio R Paula	02/2015
4902	11^76826-5790	80007	Enzo Doria	01/2013
4903	10^80000+85731	80001	Patrick De Geest	10/2009
4904	10^80000-7169	80000	Patrick De Geest	09/2009
4905	10^79999+22399	80000	Patrick De Geest	09/2009
4906	10^79999-74873	79999	Patrick De Geest	09/2009
4907	3^167668+58	79998	Lelio R Paula	02/2015
4908	2^265612+4257	79958	Lelio R Paula	07/2013
4909	5*3^167577+4	79956	Lelio R Paula	06/2014
4910	(9179*2^265593-1)/9	79955	Lelio R Paula	04/2015
4911	6^102723-43	79935	Lelio R Paula	04/2015
4912	11^76748-3360	79925	Enzo Doria	12/2012
4913	(13*2^265498-1)/187119	79919	Lelio R Paula	02/2014
4914	2^265399-109855	79894	Enzo Doria	04/2014
4915	(20^61403-1)/19	79886	Paul Bourdelais	03/2010
4916	18^63635+59	79880	Lelio R Paula	02/2015
4917	(11*10^79867-107)/3	79868	Robert Price	11/2016
4918	3^167375+80	79859	Lelio R Paula	02/2015
4919	5^114240-14486	79851	Enzo Doria	02/2013
4920	49^47238+48	79842	Norbert Schneider	07/2014
4921	2^265212-3779	79837	Yves Minet	04/2017
4922	91^40746+40746^91	79824	Norbert Schneider	12/2014
4923	(68*10^79813-257)/9	79814	Robert Price	06/2017
4924	(5*2^265118-1)/61	79808	Lelio R Paula	02/2014
4925	2^265074+28425	79796	Lelio R Paula	07/2013
4926	2^265072+1185	79795	Lelio R Paula	07/2013
4927	p(16682)#/2-128	79771	Robert Price	05/2017
4928	3^167167-34	79759	Robert Price	11/2013
4929	12^73906+29	79758	Lelio R Paula	02/2015
4930	2^264934+255	79754	Lelio R Paula	07/2013
4931	4*10^79729-87	79730	Robert Price	03/2017
4932	2^264846-111701	79727	Enzo Doria	05/2014
4933	2^264831-112041	79723	Enzo Doria	06/2014
4934	2^264816-455	79718	Yves Minet	03/2012
4935	(55*10^79711+89)/9	79712	Robert Price	09/2017
4936	47^47667-46	79704	Theodore Burton	02/2007
4937	13^71547+96	79700	Lelio R Paula	03/2015
4938	2^264752-112883	79699	Enzo Doria	06/2014
4939	2^264732+133	79693	Lelio R Paula	05/2012
4940	8*3^167010+7	79685	Lelio R Paula	06/2014
4941	42^49087-41	79681	Norbert Schneider	06/2014
4942	(26*10^79678-119)/3	79679	Robert Price	07/2016
4943	2^264683-21	79678	Lelio R Paula	05/2012
4944	7^94279+18	79675	Lelio R Paula	02/2015
4945	2^264655-127	79670	Lelio R Paula	02/2012
4946	2^264597-459043	79652	Enzo Doria	05/2015
4947	(21*2^264566+1)/5	79643	Lelio R Paula	10/2012
4948	2^264536+1870021	79634	Enzo Doria	05/2016
4949	(17*2^264512-1)/359	79625	Lelio R Paula	02/2014
4950	2^264477-109783	79616	Enzo Doria	04/2014
4951	18^63419-1333	79609	Enzo Doria	03/2013
4952	13^71451-36	79593	Lelio R Paula	03/2015
4953	(2^264410-5)/128002609121	79585	Lelio R Paula	10/2012
4954	19^62234+90	79582	Lelio R Paula	03/2015
4955	12^73714+49	79551	Lelio R Paula	02/2015
4956	(3*2^264184-1)/1433339	79522	Lelio R Paula	02/2014
4957	2^264103-112531	79503	Enzo Doria	06/2014
4958	19^62170+78	79501	Lelio R Paula	03/2015
4959	11^76340-2580	79500	Enzo Doria	12/2012
4960	(23*10^79492-11)/3	79493	Robert Price	10/2015
4961	((2^132049+13650)^2+(2^132049+13650)+41)/2003/23841473	79491	Makoto Morimoto	05/2016
4962	2^264060-112133	79490	Enzo Doria	06/2014
4963	((2^132049+4641)^2+(2^132049+4641)+41)/487/8537/10426147	79488	Makoto Morimoto	05/2016
4964	9^83298+6^83298-2^83298	79487	Mike Oakes	08/2010
4965	18^63319+35	79483	Lelio R Paula	02/2015
4966	38303!2+256	79461	Robert Price	01/2015
4967	(29*10^79445+61)/9	79446	Robert Price	04/2015
4968	2^263902-195	79443	Lelio R Paula	05/2012
4969	3^166499-112696	79441	Enzo Doria	06/2014
4970	11^76279-2760	79437	Enzo Doria	12/2012
4971	6^102077-25	79432	Lelio R Paula	03/2015
4972	2^263852-1017	79428	Lelio R Paula	07/2013
4973	2^263842-33	79425	Lelio R Paula	05/2012
4974	12^73584-55	79411	Lelio R Paula	02/2015
4975	2^263772-185	79404	Lelio R Paula	05/2012
4976	(15^67489+1)/16	79373	Paul Bourdelais	03/2010
4977	2^263664+15015	79371	Lelio R Paula	07/2013
4978	10^79362+3^79363	79363	Mike Oakes	06/2010
4979	Phi(163244,10)/2448661/6856249	79331	Maksym Voznyy	11/2015
4980	3^166262+44	79328	Lelio R Paula	02/2015
4981	4*10^79327-63	79328	Robert Price	12/2016
4982	2^263486+513	79318	Lelio R Paula	07/2013
4983	2^263448-519509	79306	Paul Bourdelais	03/2013
4984	21^59971-20^59971	79295	Robert Price	05/2012
4985	2^263372+123	79283	Lelio R Paula	05/2012
4986	17^64429+84	79277	Lelio R Paula	03/2015
4987	11^76124-11430	79275	Enzo Doria	12/2012
4988	(206*10^79268-17)/9	79270	Robert Price	03/2017
4989	13^71157+18	79265	Lelio R Paula	03/2015
4990	2^263297+65835	79261	Lelio R Paula	07/2013
4991	19^61980-18	79258	Theodore Burton	12/2005
4992	2*10^79242+93	79243	Robert Price	07/2016
4993	(88^40751-1)/87	79238	Paul Bourdelais	08/2017
4994	(103*29^54179-39)/4	79233	Curtis Bright	05/2015
4995	9^83024-83024^9	79226	Norbert Schneider	08/2017
4996	17^64382-26	79219	Lelio R Paula	03/2015
4997	7^93733-74	79214	Lelio R Paula	02/2015
4998	15^67352+38	79213	Lelio R Paula	02/2015
4999	2^263135-110235	79212	Enzo Doria	05/2014
5000	2^263044+4257	79185	Lelio R Paula	07/2013

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PRP Records

Probable Primes Top 10000

(181746 PRPs in the top)