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	(22699*2^268657+1)/6351	80875	Lelio R Paula	06/2014
4752	2^268581-869688105	80851	Lelio R Paula	05/2016
4753	(11*2^268521-1)/3	80834	Lelio R Paula	02/2014
4754	2^268516-249	80832	Yves Minet	02/2012
4755	2^268500+16095	80827	Lelio R Paula	07/2013
4756	3^169402+100	80826	Lelio R Paula	12/2015
4757	9^84698+8^(84698-1)	80823	Robert Price	03/2016
4758	2^268472-109739	80819	Enzo Doria	04/2014
4759	(9*2^268454+1)/37	80813	Lelio R Paula	12/2012
4760	(3*2^268502+1)/377902188435353647	80811	Lelio R Paula	12/2012
4761	134^37987-133^37987	80803	Jean-Louis Charton	12/2005
4762	15^68702-76	80800	Lelio R Paula	11/2015
4763	2^268408+7	80799	Lelio R Paula	05/2012
4764	2^268375+141	80789	Lelio R Paula	05/2012
4765	12^74856-47	80784	Lelio R Paula	11/2015
4766	6^103770-107	80749	Lelio R Paula	12/2015
4767	3^169224-62	80741	Lelio R Paula	12/2015
4768	p(16866)#/2+64	80741	Robert Price	03/2017
4769	5^115502-72	80733	Lelio R Paula	10/2015
4770	2^268079-1927	80700	Yves Minet	10/2009
4771	2^268028+117	80685	Lelio R Paula	05/2012
4772	121^38738+120	80683	Norbert Schneider	01/2015
4773	(3^169097-8)/835	80677	Lelio R Paula	12/2012
4774	2^267918+67	80652	Lelio R Paula	05/2012
4775	(302*10^80638+13)/9	80640	Robert Price	01/2017
4776	3^169004+2660	80636	Lelio R Paula	12/2015
4777	2^267860-112859	80634	Enzo Doria	06/2014
4778	2^267828-110705	80625	Enzo Doria	05/2014
4779	2^267743+12705	80599	Lelio R Paula	07/2013
4780	(22*10^80595+23)/9	80596	Robert Price	03/2015
4781	2^267674-51	80578	Lelio R Paula	05/2012
4782	(86*10^80571-41)/9	80572	Robert Price	11/2015
4783	2^267612-1965	80560	Lelio R Paula	07/2013
4784	2^267553+4097	80542	Lelio R Paula	07/2013
4785	7^95276-8	80518	Robert Price	01/2014
4786	(15185*2^267457-1)/47829	80513	Lelio R Paula	04/2015
4787	6^103467+163	80513	Lelio R Paula	12/2015
4788	(7*10^80490+143)/3	80491	Robert Price	04/2016
4789	86^41597-85^41597	80470	Robert Price	04/2015
4790	13^72237+30	80468	Lelio R Paula	11/2015
4791	17^65389+14	80458	Lelio R Paula	11/2015
4792	423^30634+30634^423	80456	Norbert Schneider	05/2017
4793	2^267232+105	80445	Lelio R Paula	05/2012
4794	11^77237-3072000	80435	Enzo Doria	01/2013
4795	2^267116-459959	80410	Enzo Doria	06/2015
4796	38715!2+8	80406	Robert Price	01/2015
4797	(2^267017+1)/3	80380	H.&R. Lifchitz	09/2000
4798	2^266968-45	80366	Lelio R Paula	05/2012
4799	20^61768-63	80363	Lelio R Paula	01/2016
4800	2^266920-112967	80351	Enzo Doria	06/2014
4801	12^74428-13	80322	Lelio R Paula	11/2015
4802	2^266680+27	80279	Lelio R Paula	05/2012
4803	2^266630-131	80264	Lelio R Paula	05/2012
4804	2^266598+76819	80254	Enzo Doria	05/2016
4805	2^266587+1880633	80251	Enzo Doria	10/2016
4806	2^266541-110049	80237	Enzo Doria	04/2014
4807	38635!2-8	80222	Robert Price	06/2015
4808	3^168111+168111^3-1	80210	Robert Price	04/2014
4809	2^266443+513	80208	Lelio R Paula	07/2013
4810	(26*10^80200+61)/3	80201	Robert Price	06/2017
4811	2^266412-109913	80199	Enzo Doria	04/2014
4812	(10223*2^266417+1)/45091	80199	Lelio R Paula	06/2014
4813	13^71988+66	80191	Lelio R Paula	11/2015
4814	11^77002-4320	80190	Enzo Doria	01/2013
4815	18^63879-13	80186	Lelio R Paula	11/2015
4816	2^266368-112295	80185	Enzo Doria	06/2014
4817	(3^168050+5)/1021454	80175	Lelio R Paula	10/2012
4818	(22*10^80167+41)/9	80168	Robert Price	02/2015
4819	(34*10^80162-43)/9	80163	Ray Chandler	12/2010
4820	(38*10^80150-11)/9	80151	Robert Price	05/2015
4821	(598*10^80149-31)/9	80151	Robert Price	02/2017
4822	19^62678-80	80150	Lelio R Paula	12/2015
4823	10^80139+32343	80140	Patrick De Geest	02/2011
4824	10^80139-9	80139	Alexander Gramolin	01/2011
4825	3^167955-106	80135	Lelio R Paula	12/2015
4826	2^265998+75559	80074	Enzo Doria	04/2016
4827	2^265969-109801	80065	Enzo Doria	04/2014
4828	2^265888-112757	80041	Enzo Doria	06/2014
4829	2^265809+1701	80017	Lelio R Paula	07/2013
4830	gcd(V(957175),5F(191435)(F(191435)+1)+1)	80014	Serge Batalov	04/2015
4831	3^167687-104	80008	Lelio R Paula	02/2015
4832	11^76826-5790	80007	Enzo Doria	01/2013
4833	10^80000+85731	80001	Patrick De Geest	10/2009
4834	10^80000-7169	80000	Patrick De Geest	09/2009
4835	10^79999+22399	80000	Patrick De Geest	09/2009
4836	10^79999-74873	79999	Patrick De Geest	09/2009
4837	3^167668+58	79998	Lelio R Paula	02/2015
4838	2^265612+4257	79958	Lelio R Paula	07/2013
4839	5*3^167577+4	79956	Lelio R Paula	06/2014
4840	(9179*2^265593-1)/9	79955	Lelio R Paula	04/2015
4841	6^102723-43	79935	Lelio R Paula	04/2015
4842	11^76748-3360	79925	Enzo Doria	12/2012
4843	(13*2^265498-1)/187119	79919	Lelio R Paula	02/2014
4844	2^265399-109855	79894	Enzo Doria	04/2014
4845	(20^61403-1)/19	79886	Paul Bourdelais	03/2010
4846	18^63635+59	79880	Lelio R Paula	02/2015
4847	(11*10^79867-107)/3	79868	Robert Price	11/2016
4848	3^167375+80	79859	Lelio R Paula	02/2015
4849	5^114240-14486	79851	Enzo Doria	02/2013
4850	49^47238+48	79842	Norbert Schneider	07/2014
4851	2^265212-3779	79837	Yves Minet	04/2017
4852	91^40746+40746^91	79824	Norbert Schneider	12/2014
4853	(68*10^79813-257)/9	79814	Robert Price	06/2017
4854	(5*2^265118-1)/61	79808	Lelio R Paula	02/2014
4855	2^265074+28425	79796	Lelio R Paula	07/2013
4856	2^265072+1185	79795	Lelio R Paula	07/2013
4857	p(16682)#/2-128	79771	Robert Price	05/2017
4858	3^167167-34	79759	Robert Price	11/2013
4859	12^73906+29	79758	Lelio R Paula	02/2015
4860	2^264934+255	79754	Lelio R Paula	07/2013
4861	4*10^79729-87	79730	Robert Price	03/2017
4862	2^264846-111701	79727	Enzo Doria	05/2014
4863	2^264831-112041	79723	Enzo Doria	06/2014
4864	2^264816-455	79718	Yves Minet	03/2012
4865	47^47667-46	79704	Theodore Burton	02/2007
4866	13^71547+96	79700	Lelio R Paula	03/2015
4867	2^264752-112883	79699	Enzo Doria	06/2014
4868	2^264732+133	79693	Lelio R Paula	05/2012
4869	8*3^167010+7	79685	Lelio R Paula	06/2014
4870	42^49087-41	79681	Norbert Schneider	06/2014
4871	(26*10^79678-119)/3	79679	Robert Price	07/2016
4872	2^264683-21	79678	Lelio R Paula	05/2012
4873	7^94279+18	79675	Lelio R Paula	02/2015
4874	2^264655-127	79670	Lelio R Paula	02/2012
4875	2^264597-459043	79652	Enzo Doria	05/2015
4876	(21*2^264566+1)/5	79643	Lelio R Paula	10/2012
4877	2^264536+1870021	79634	Enzo Doria	05/2016
4878	(17*2^264512-1)/359	79625	Lelio R Paula	02/2014
4879	2^264477-109783	79616	Enzo Doria	04/2014
4880	18^63419-1333	79609	Enzo Doria	03/2013
4881	13^71451-36	79593	Lelio R Paula	03/2015
4882	(2^264410-5)/128002609121	79585	Lelio R Paula	10/2012
4883	19^62234+90	79582	Lelio R Paula	03/2015
4884	12^73714+49	79551	Lelio R Paula	02/2015
4885	(3*2^264184-1)/1433339	79522	Lelio R Paula	02/2014
4886	2^264103-112531	79503	Enzo Doria	06/2014
4887	19^62170+78	79501	Lelio R Paula	03/2015
4888	11^76340-2580	79500	Enzo Doria	12/2012
4889	(23*10^79492-11)/3	79493	Robert Price	10/2015
4890	((2^132049+13650)^2+(2^132049+13650)+41)/2003/23841473	79491	Makoto Morimoto	05/2016
4891	2^264060-112133	79490	Enzo Doria	06/2014
4892	((2^132049+4641)^2+(2^132049+4641)+41)/487/8537/10426147	79488	Makoto Morimoto	05/2016
4893	9^83298+6^83298-2^83298	79487	Mike Oakes	08/2010
4894	18^63319+35	79483	Lelio R Paula	02/2015
4895	38303!2+256	79461	Robert Price	01/2015
4896	(29*10^79445+61)/9	79446	Robert Price	04/2015
4897	2^263902-195	79443	Lelio R Paula	05/2012
4898	3^166499-112696	79441	Enzo Doria	06/2014
4899	11^76279-2760	79437	Enzo Doria	12/2012
4900	6^102077-25	79432	Lelio R Paula	03/2015
4901	2^263852-1017	79428	Lelio R Paula	07/2013
4902	2^263842-33	79425	Lelio R Paula	05/2012
4903	12^73584-55	79411	Lelio R Paula	02/2015
4904	2^263772-185	79404	Lelio R Paula	05/2012
4905	(15^67489+1)/16	79373	Paul Bourdelais	03/2010
4906	2^263664+15015	79371	Lelio R Paula	07/2013
4907	10^79362+3^79363	79363	Mike Oakes	06/2010
4908	Phi(163244,10)/2448661/6856249	79331	Maksym Voznyy	11/2015
4909	3^166262+44	79328	Lelio R Paula	02/2015
4910	4*10^79327-63	79328	Robert Price	12/2016
4911	2^263486+513	79318	Lelio R Paula	07/2013
4912	2^263448-519509	79306	Paul Bourdelais	03/2013
4913	21^59971-20^59971	79295	Robert Price	05/2012
4914	2^263372+123	79283	Lelio R Paula	05/2012
4915	17^64429+84	79277	Lelio R Paula	03/2015
4916	11^76124-11430	79275	Enzo Doria	12/2012
4917	(206*10^79268-17)/9	79270	Robert Price	03/2017
4918	13^71157+18	79265	Lelio R Paula	03/2015
4919	2^263297+65835	79261	Lelio R Paula	07/2013
4920	19^61980-18	79258	Theodore Burton	12/2005
4921	2*10^79242+93	79243	Robert Price	07/2016
4922	(103*29^54179-39)/4	79233	Curtis Bright	05/2015
4923	17^64382-26	79219	Lelio R Paula	03/2015
4924	7^93733-74	79214	Lelio R Paula	02/2015
4925	15^67352+38	79213	Lelio R Paula	02/2015
4926	2^263135-110235	79212	Enzo Doria	05/2014
4927	2^263044+4257	79185	Lelio R Paula	07/2013
4929	2^263032+87517	79181	Yves Minet	11/2010
4928	6^101755+95	79181	Lelio R Paula	03/2015
4930	4^131497-3^131497	79170	Jean-Louis Charton	05/2004
4931	5*7^93674+8	79165	Lelio R Paula	10/2014
4932	lucasU(486,25,29457)-5*lucasU(486,25,29456)	79137	Mike Oakes	05/2009
4933	11^75978-42	79123	Lelio R Paula	02/2015
4934	8*5^113180+9	79111	Lelio R Paula	10/2014
4935	(6883*2^262741-1)/4835	79094	Lelio R Paula	04/2015
4936	(9*2^262745+1)/137	79093	Lelio R Paula	10/2012
4937	12^73285+85	79088	Lelio R Paula	02/2015
4938	19^61840+52	79079	Lelio R Paula	03/2015
4939	(10^79067+77)/3	79067	Robert Price	01/2017
4940	(1017*2^262640-1)/11557	79062	Lelio R Paula	04/2015
4941	10^79040+137949	79041	Patrick De Geest	02/2016
4943	10^79040-1007297	79040	Robert Price	02/2015
4942	10^79040-77427	79040	Patrick De Geest	02/2016
4944	2^262551-17295	79036	Lelio R Paula	07/2013
4945	3^165597+340	79010	Lelio R Paula	02/2015
4946	(23*2^262435+1)/55	79001	Lelio R Paula	10/2012
4947	11^75860-2100	79001	Enzo Doria	12/2012
4948	8*7^93463+9	78987	Lelio R Paula	10/2014
4949	67^43240-2	78960	Lelio R Paula	09/2013
4950	1000001^13159-1000000^13159	78953	Jean-Louis Charton	10/2003
4951	2^262199-110287	78930	Enzo Doria	05/2014
4952	(19*2^262180-1)/177	78924	Lelio R Paula	02/2014
4953	(3^165403+4)/7	78917	Lelio R Paula	10/2012
4955	2^21068*(2^241076+1)-1	78914	Makoto Morimoto	03/2014
4956	2^29258*(2^232886+1)-1	78914	Makoto Morimoto	03/2014
4954	2^262144+18531	78914	Makoto Morimoto	12/2015
4957	14^68837+75	78897	Lelio R Paula	02/2015
4958	106^38949+105	78884	Norbert Schneider	12/2016
4959	(25*2^261917-1)/20927	78842	Lelio R Paula	02/2014
4960	2^261881-1859713	78835	Enzo Doria	03/2016
4961	2^261874+1915	78832	Lelio R Paula	07/2013
4962	2^261856+98765331	78827	Jason Earls	01/2009
4963	(5*2^261857-1)/20501277	78821	Lelio R Paula	02/2014
4964	2^261724+92691	78787	Tony Prest / Never Odd Or Even	03/2014
4965	2^261724+285111	78787	Tony Prest / Never Odd Or Even	04/2014
4966	2^261724+293713	78787	Tony Prest / Never Odd Or Even	04/2014
4967	(2^261724+381949)/5	78787	Tony Prest / Never Odd Or Even	04/2014
4968	2^261724+572971	78787	Tony Prest / Never Odd Or Even	05/2014
4969	(2^261724+392705)/3/7	78786	Tony Prest / Never Odd Or Even	04/2014
4970	(2^261724+629709)/5/5	78786	Tony Prest / Never Odd Or Even	05/2014
4971	(2^261724+67397)/3/103	78785	Tony Prest / Never Odd Or Even	04/2014
4972	(2^261724+323043)/11/103	78784	Tony Prest / Never Odd Or Even	04/2014
4973	(2^261724+370143)/1289	78784	Tony Prest / Never Odd Or Even	04/2014
4974	(2^261724+560259)/5/5/73	78784	Tony Prest / Never Odd Or Even	05/2014
4975	(2^261724+64109)/3/3/3/5/5/19	78783	Tony Prest / Never Odd Or Even	04/2014
4976	(2^261724+394491)/55787	78783	Tony Prest / Never Odd Or Even	04/2014
4977	(2^261724+625897)/23/883	78783	Tony Prest / Never Odd Or Even	05/2014
4978	(2^261724+292471)/13/97/151	78782	Tony Prest / Never Odd Or Even	04/2014
4979	(2^261724+154303)/11/67/127	78782	Tony Prest / Never Odd Or Even	04/2014
4980	(2^261724+313319)/3/3/3/3/5/11/113	78782	Tony Prest / Never Odd Or Even	04/2014
4981	(2^261724+383949)/5/41/43/83	78781	Tony Prest / Never Odd Or Even	04/2014
4982	(2^261724+626567)/3/331/631	78781	Tony Prest / Never Odd Or Even	05/2014
4983	(2^261724+32987)/3/3/19/223/1031	78780	Tony Prest / Never Odd Or Even	04/2014
4984	(2^261724+5813)/3/5991397	78780	Tony Prest / Never Odd Or Even	04/2014
4985	(2^261724+13481)/3/11/239/2087	78780	Tony Prest / Never Odd Or Even	04/2014
4986	(2^261724+103399)/5/13/37/10607	78780	Tony Prest / Never Odd Or Even	04/2014
4987	(2^261724+18477)/367/65111	78780	Tony Prest / Never Odd Or Even	04/2014
4988	(2^261724+121285)/167/227/1217	78780	Tony Prest / Never Odd Or Even	04/2014
4989	(2^261724+262037)/3/3/11/23/18517	78780	Tony Prest / Never Odd Or Even	04/2014
4990	(2^261724+586157)/3/7/457/1259	78780	Tony Prest / Never Odd Or Even	05/2014
4991	(2^261724+315287)/3/45822541	78779	Tony Prest / Never Odd Or Even	04/2014
4992	(2^261724+605675)/3/3/3/103/207481	78779	Tony Prest / Never Odd Or Even	05/2014
4993	(2^261724+60031)/13/31/7024877	78778	Tony Prest / Never Odd Or Even	04/2014
4994	(2^261724+121879)/5/789433217	78778	Tony Prest / Never Odd Or Even	04/2014
4995	(2^261724+290135)/3/3/8467/9059	78778	Tony Prest / Never Odd Or Even	04/2014
4996	(2^261724+79857)/59/3847/165331	78777	Tony Prest / Never Odd Or Even	04/2014
4997	(2^261724+22883)/3/17/23/2351/10079	78777	Tony Prest / Never Odd Or Even	04/2014
4998	(2^261724+154799)/3/5/3655653719	78777	Tony Prest / Never Odd Or Even	04/2014
4999	(2^261724+391001)/3/11/17/41/43/24071	78777	Tony Prest / Never Odd Or Even	04/2014
5000	(2^261724+622383)/34843/550717	78777	Tony Prest / Never Odd Or Even	05/2014

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Probable Primes Top 10000

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