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 (> 50000)	Who ?	When ?
5001	6^115840-55	90142	Lelio R Paula	05/2016
5002	(5*10^90142-473)/9	90142	Robert Price	12/2017
5003	8*7^106659+5	90139	Lelio R Paula	10/2014
5004	2^299406-16653	90131	Enzo Doria	05/2013
5005	10^90128+288673	90129	Patrick De Geest	07/2019
5007	208049#+(216091#)/(208049#)	90128	Makoto Morimoto	04/2016
5006	10^90128-8387	90128	Patrick De Geest	09/2018
5008	(F(5)^128941-F(4)^128941)/F(3)	90126	Wayne Halsdorf	03/2012
5009	6^115819-53	90125	Lelio R Paula	05/2016
5010	10^90123+6313	90124	Patrick De Geest	09/2018
5012	6^115816-16853	90123	Enzo Doria	02/2013
5011	10^90123-22617	90123	Patrick De Geest	07/2019
5013	6^115813-23	90121	Lelio R Paula	05/2016
5014	(22*10^90110+161)/3	90111	Robert Price	02/2017
5015	(2^299330-509203)/69	90106	Lelio R Paula	01/2013
5016	10^90105+915759	90106	Patrick De Geest	07/2019
5018	10^90105-767	90105	Patrick De Geest	09/2018
5017	10^90104+48189	90105	Patrick De Geest	07/2019
5019	10^90104-7703	90104	Patrick De Geest	09/2018
5020	10^90103+9159	90104	Patrick De Geest	09/2018
5021	10^90103-208457	90103	Patrick De Geest	07/2019
5022	10^90102+73011	90103	Patrick De Geest	07/2019
5023	10^90102-602433	90102	Patrick De Geest	07/2019
5024	10^90101+1225537	90102	Patrick De Geest	07/2019
5025	10^90101-3207	90101	Patrick De Geest	09/2018
5026	(29*10^90096-17)/3	90097	Erik Branger	09/2014
5027	10^90089+143181	90090	Patrick De Geest	07/2019
5028	10^90089-3573	90089	Patrick De Geest	09/2018
5029	2^299247+1870529	90083	Enzo Doria	05/2016
5030	10^90079+1609	90080	Patrick De Geest	09/2018
5031	10^90079-230043	90079	Patrick De Geest	07/2019
5032	2^299229-2797783	90077	Enzo Doria	04/2016
5033	2^299220-16317	90075	Enzo Doria	04/2013
5034	11^86491-1350	90072	Enzo Doria	12/2012
5035	10^90071+52333	90072	Patrick De Geest	07/2019
5036	10^90071-1233	90071	Patrick De Geest	09/2018
5037	10^90069+158527	90070	Patrick De Geest	07/2019
5038	10^90069-7841	90069	Patrick De Geest	09/2018
5039	(31*10^90064-1)/3	90066	Robert Price	03/2017
5040	10^90060+149431	90061	Patrick De Geest	07/2019
5041	10^90060-839	90060	Patrick De Geest	09/2018
5042	10^90052+2361	90053	Patrick De Geest	09/2018
5043	10^90052-90929	90052	Patrick De Geest	07/2019
5044	10^90047+619	90048	Patrick De Geest	09/2018
5045	10^90047-151071	90047	Patrick De Geest	07/2019
5046	L(430949)/861899/1440387561539	90045	Serge Batalov	07/2017
5047	2^299112+73951	90042	Enzo Doria	04/2016
5048	8^99702+7^(99702-1)	90040	Robert Price	02/2016
5049	10^90038+157803	90039	Patrick De Geest	07/2019
5050	10^90038-9687	90038	Patrick De Geest	09/2018
5051	5*10^90033+3	90034	Dmitry Domanov	11/2010
5052	10^90030+225813	90031	Patrick De Geest	07/2019
5053	10^90030-1461	90030	Patrick De Geest	09/2018
5054	243^37738+37738^243	90029	Norbert Schneider	01/2015
5055	10^90025+70569	90026	Patrick De Geest	07/2019
5056	10^90025-8703	90025	Patrick De Geest	09/2018
5057	2^299048-113297	90023	Enzo Doria	07/2014
5058	10^90015+849	90016	Patrick De Geest	09/2018
5059	10^90015-228387	90015	Patrick De Geest	07/2019
5060	10^90010+6811	90011	Patrick De Geest	09/2018
5061	10^90010-183597	90010	Patrick De Geest	11/2018
5062	10^90009+58321	90010	Patrick De Geest	11/2018
5063	10^90008+847	90009	Patrick De Geest	09/2018
5064	10^90009-356013	90009	Patrick De Geest	11/2018
5066	3^188648+92	90008	Lelio R Paula	12/2015
5065	10^90008-706049	90008	Patrick De Geest	11/2018
5067	5*2^298991+7	90006	Lelio R Paula	08/2014
5068	(25*2^298997+1)/3267	90005	Lelio R Paula	01/2013
5069	10^90000+8869	90001	Patrick De Geest	12/2009
5071	10^89999+82939	90000	Dirk Augustin	04/2007
5070	10^90000-140343	90000	Patrick De Geest	12/2009
5072	10^89999-194891	89999	Patrick De Geest	11/2009
5073	19^70365-78	89980	Lelio R Paula	12/2015
5074	NaturalLogarithmOf2(89973)	89973	Eric W. Weisstein	10/2015
5075	2^298852-64875	89964	Lelio R Paula	11/2013
5076	18^71659+37	89952	Lelio R Paula	12/2015
5077	(2908*29^61501-3)/7	89942	Curtis Bright	05/2015
5078	17^73067+20	89906	Lelio R Paula	11/2015
5079	2^298637-99	89899	Lelio R Paula	10/2012
5080	9^94188+38^94188-24^94188-3*2^94188	89879	Mike Oakes	01/2011
5081	9*10^89858+19	89859	Robert Price	05/2016
5082	2^298501+1870067	89858	Enzo Doria	05/2016
5083	11^86280-98	89852	Lelio R Paula	11/2015
5084	2^298473-110059	89850	Enzo Doria	04/2014
5085	19^70263-32	89850	Lelio R Paula	12/2015
5086	(299*10^89836-17)/3	89838	Robert Price	01/2017
5087	3^188286+14	89836	Robert Price	09/2013
5088	gcd(V(1091095),5F(218219)(F(218219)+1)+1)	89822	Serge Batalov	04/2015
5089	2^298367+58905	89818	Lelio R Paula	11/2013
5090	2^298319-109657	89803	Enzo Doria	04/2014
5091	8*10^89800+81	89801	Robert Price	05/2017
5092	18^71505-91	89759	Lelio R Paula	12/2015
5093	(7^106187+1)/8	89738	Paul Bourdelais	04/2008
5094	2^298079-109531	89731	Enzo Doria	04/2014
5095	117^43380+116	89718	Norbert Schneider	08/2018
5096	(22699*2^298016+1)/385	89714	Lelio R Paula	06/2014
5097	156(10^(422427)-1)/101-1	89709	Robert Price	05/2014
5098	2^298003-66945	89708	Lelio R Paula	11/2013
5099	(23*10^89705-83)/3	89706	Robert Price	09/2017
5100	17^72900-54	89700	Lelio R Paula	11/2015
5101	3*2^297956+5	89695	Lelio R Paula	08/2014
5102	20^68938-11	89691	Lelio R Paula	01/2016
5103	89*10^89687-7	89689	Robert Price	03/2017
5104	2^297923+77783	89684	Enzo Doria	05/2016
5105	11^86107-24576000	89672	Enzo Doria	02/2013
5106	2^297878-111911	89671	Enzo Doria	05/2014
5107	7^106084+40	89652	Lelio R Paula	10/2015
5108	(86*10^89640-311)/9	89641	Robert Price	10/2017
5109	3*10^89608-59	89609	Robert Price	10/2017
5110	3^187780-11038	89594	Enzo Doria	05/2014
5111	(13*2^297560-1)/49151787	89568	Lelio R Paula	02/2014
5112	5^128141-36	89567	Lelio R Paula	10/2015
5113	4*7^105951+9	89540	Lelio R Paula	10/2014
5114	(7*10^89539-439)/9	89539	Robert Price	09/2017
5115	2^297397+177257	89526	Enzo Doria	05/2016
5116	2^297346-16241	89511	Enzo Doria	04/2013
5117	(5*10^89510+79)/3	89511	Robert Price	11/2017
5118	4^148663-3^148663	89505	Jean-Louis Charton	11/2005
5119	2^297328-869688105	89505	Lelio R Paula	07/2016
5120	2^297325-459043	89504	Enzo Doria	05/2015
5121	2^297310-112391	89500	Enzo Doria	06/2014
5122	2^297296-112157	89496	Enzo Doria	06/2014
5123	57^50966-2	89490	Lelio R Paula	08/2013
5124	(266*10^89482+1)/3	89484	Robert Price	02/2016
5125	(14*10^89480-101)/3	89481	Robert Price	04/2017
5126	2^297122+99	89443	Lelio R Paula	10/2012
5127	(3^187435-5)/1286	89427	Lelio R Paula	01/2013
5128	(25*10^89413+161)/3	89414	Robert Price	01/2017
5129	2^296990+1870699	89403	Enzo Doria	05/2016
5130	2^296972-1017	89398	Lelio R Paula	11/2013
5131	(7*10^89383+167)/3	89384	Robert Kinser	10/2017
5132	(85*10^89375-31)/9	89376	Robert Price	11/2015
5133	9*2^296870+7	89368	Lelio R Paula	08/2014
5134	100^44683-99^44683	89366	Robert Price	07/2013
5135	2^296810+76519	89349	Enzo Doria	05/2016
5136	8^98928+7^(98928+1)	89341	Robert Price	06/2016
5137	(3^187247+4)/1027	89337	Lelio R Paula	01/2013
5138	(3^187235-2)/2045	89331	Lelio R Paula	01/2013
5139	2^296736-432149	89327	Paul Bourdelais	05/2013
5140	2^296737-112519	89327	Enzo Doria	06/2014
5141	2^296718-3645	89322	Lelio R Paula	11/2013
5142	2^296681-16221	89310	Enzo Doria	04/2013
5143	2^296669-16513	89307	Enzo Doria	04/2013
5144	2^296619-16357	89292	Enzo Doria	04/2013
5145	2^296614-110051	89290	Enzo Doria	04/2014
5146	(3^187138+8)/83147	89283	Lelio R Paula	01/2013
5147	(2*10^89279+457)/9	89279	Robert Price	01/2017
5148	15^75907-28	89274	Lelio R Paula	11/2015
5149	2^296547-37	89270	Yves Minet	01/2012
5150	2^296485+191	89251	Lelio R Paula	10/2012
5151	2^296467-75	89246	Lelio R Paula	10/2012
5152	2^296416-109535	89231	Enzo Doria	04/2014
5153	(23*2^296406+1)/3	89228	Lelio R Paula	01/2013
5154	66^49037-65	89225	Norbert Schneider	11/2014
5155	2^296377-16245	89219	Enzo Doria	04/2013
5156	2^296372-64875	89217	Lelio R Paula	11/2013
5157	5*6^114648-7	89215	Lelio R Paula	10/2014
5158	3*10^89206+13	89207	Robert Price	08/2017
5159	7*3^186960-4	89204	Lelio R Paula	08/2014
5160	2^296290-112133	89193	Enzo Doria	06/2014
5161	6^114620-17003	89192	Enzo Doria	02/2013
5162	(4*10^89189+41)/9	89189	Robert Price	11/2014
5163	2^296261-161181	89184	Enzo Doria	04/2013
5164	(19*2^296269-1)/530623	89182	Lelio R Paula	02/2014
5165	3^186903-10	89176	Robert Price	09/2013
5167	7*10^89169-3	89170	Dmitry Domanov	11/2010
5166	(2^296221-1017)/35	89170	Lelio R Paula	01/2013
5168	(43*10^89169+47)/9	89170	Robert Price	12/2017
5169	(10^89160+29)/3	89160	Serge Batalov	12/2014
5170	(28*10^89141-97)/3	89142	Robert Price	07/2016
5171	2^296116-734639	89140	Paul Bourdelais	04/2013
5172	6^114544-133	89133	Lelio R Paula	12/2015
5173	2^296076-113297	89128	Enzo Doria	07/2014
5174	(11*2^296060-1)/215	89122	Lelio R Paula	02/2014
5175	5*10^89118+81	89119	Robert Price	08/2017
5176	2^296037-1411	89117	Yves Minet	01/2013
5177	2^296020-2604809	89111	Enzo Doria	05/2015
5178	2^296016+81	89110	Henri Lifchitz	02/2007
5179	2^296010-11	89108	Lelio R Paula	10/2012
5180	2^295998-111911	89105	Enzo Doria	05/2014
5181	(2^296014+47)/93991149	89102	Lelio R Paula	01/2013
5182	2^295939-16621	89087	Enzo Doria	04/2013
5183	2^295934-109691	89086	Enzo Doria	04/2014
5184	(185*10^89063+7)/3	89065	Robert Price	02/2017
5185	2^295831+143	89055	Lelio R Paula	10/2012
5186	31^59713-30	89054	Theodore Burton	02/2007
5187	(7*2^295834-1)/27663	89052	Lelio R Paula	02/2014
5188	123^42608+2	89047	Lelio R Paula	05/2013
5189	6^114433-114433^6	89047	Norbert Schneider	04/2017
5190	2^295800-459659	89045	Enzo Doria	05/2015
5191	(52*10^89037-1)/3	89039	Robert Price	02/2017
5192	(6^114398-11)/5	89019	Paul Bourdelais	11/2011
5193	11^85470-5850	89008	Enzo Doria	02/2013
5194	(27*2^295634+1)/4687	88993	Lelio R Paula	01/2013
5195	(p(18424)#-4)/2	88985	Robert Price	09/2017
5196	2^295564-189	88974	Lelio R Paula	10/2012
5197	2^295557+73097	88972	Enzo Doria	04/2016
5198	11^85433-5760	88970	Enzo Doria	01/2013
5199	6*10^88938-91	88939	Robert Price	11/2017
5200	15^75619-88	88935	Lelio R Paula	11/2015
5201	2^295385-85	88920	Lelio R Paula	10/2012
5202	2^295385-16333	88920	Enzo Doria	04/2013
5203	2^295309+59	88897	Lelio R Paula	10/2012
5204	2^295288-109799	88891	Enzo Doria	04/2014
5205	10^88888+170373	88889	Stefano Morozzi	07/2018
5206	10^88888+271399	88889	Stefano Morozzi	07/2018
5207	10^88888+375397	88889	Stefano Morozzi	07/2018
5208	10^88888+548823	88889	Stefano Morozzi	07/2018
5209	10^88888+820861	88889	Stefano Morozzi	07/2018
5210	10^88888+1206349	88889	Stefano Morozzi	07/2018
5211	10^88888+1292047	88889	Stefano Morozzi	07/2018
5212	10^88888+1456029	88889	Stefano Morozzi	07/2018
5213	10^88888-490287	88888	Patrick De Geest	09/2018
5214	2^295245+65	88878	Lelio R Paula	10/2012
5215	Padovan(727734)	88874	Eric W. Weisstein	04/2011
5216	18^70793-17	88865	Lelio R Paula	11/2015
5217	6^114196-17573	88862	Enzo Doria	02/2013
5218	302^35829+35829^302	88857	Norbert Schneider	12/2014
5219	3^186223+16	88851	Robert Price	10/2013
5220	3*2^295139+7	88847	Lelio R Paula	08/2014
5221	3^186212-113008	88846	Enzo Doria	07/2014
5222	87^45803-86	88836	Norbert Schneider	11/2015
5223	2^295094-110273	88833	Enzo Doria	05/2014
5224	2^295080+1869151	88828	Enzo Doria	05/2016
5225	2^295027-113407	88812	Enzo Doria	07/2014
5226	(2*10^88808-71)/3	88808	Robert Price	01/2017
5227	13^79722-80	88806	Lelio R Paula	11/2015
5228	3^186103+104	88794	Lelio R Paula	12/2015
5229	(3*2^294971+1)/25565	88792	Lelio R Paula	01/2013
5230	2^294937-115003	88785	Enzo Doria	06/2015
5231	2^294868-109709	88765	Enzo Doria	04/2014
5232	2^294864-2985	88763	Yves Minet	09/2014
5233	(17*10^88761-41)/3	88762	Robert Price	09/2017
5234	2^294754+15015	88730	Lelio R Paula	10/2013
5235	(3^185951-7)/20	88720	Lelio R Paula	01/2013
5236	(2^294661+5)/443693383	88694	Lelio R Paula	01/2013
5237	(10^88680+11)/3	88680	Robert Price	11/2014
5238	2*7^104928-9	88675	Lelio R Paula	10/2014
5239	11^85150+12	88675	Lelio R Paula	11/2015
5240	8*6^113951+5	88673	Lelio R Paula	10/2014
5241	6^113940-18563	88663	Enzo Doria	03/2013
5242	38^56123-56123^38	88663	Norbert Schneider	02/2017
5243	2^294492-65	88651	Lelio R Paula	10/2012
5244	20^68120-53	88627	Lelio R Paula	01/2016
5245	122^42477-121	88623	Norbert Schneider	10/2018
5246	2^294391-113257	88621	Enzo Doria	07/2014
5247	5^126784-15476	88619	Enzo Doria	02/2013
5248	2^294327+9	88602	Lelio R Paula	10/2012
5249	2^294320+18915	88600	Lelio R Paula	10/2013
5250	(98*10^88595-89)/99	88595	Ray Chandler	07/2011

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Probable Primes Top 10000

(253466 PRPs in the top)