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 ?
5029	25206!+p(4114)	100001	Henri Lifchitz	09/2005
5030	25206!-p(5447)	100001	Henri Lifchitz	10/2005
5031	25206!-p(12402)	100001	Henri Lifchitz	04/2006
5032	25206!-p(16290)	100001	Henri Lifchitz	09/2006
5033	25206!-p(19647)	100001	Henri Lifchitz	02/2007
5034	2^332194+11473	100001	Henri Lifchitz	03/2007
5024	10^100000+342909	100001	Milton L. Brown	12/2007
5025	10^100000+346579	100001	Robert Price	04/2012
5026	10^100000+829767	100001	Robert Price	05/2012
5027	10^100000+871899	100001	Robert Price	05/2012
5028	10^100000+1475997	100001	Robert Price	07/2012
5017	10^100000+1751769	100001	Robert Price	08/2012
5018	10^100000+2155489	100001	Robert Price	10/2012
5019	10^100000+2483527	100001	Robert Price	12/2012
5020	10^100000+2503087	100001	Robert Price	12/2012
5021	10^100000+2686179	100001	Robert Price	12/2012
5022	10^100000+2688933	100001	Robert Price	12/2012
5023	10^100000+3667159	100001	Robert Price	08/2013
5004	10^100000+7867333	100001	Robert Price	12/2016
5005	10^100000+8743093	100001	Robert Price	02/2017
5006	10^100000+8955391	100001	Robert Price	03/2017
5007	10^100000+9180019	100001	Robert Price	03/2017
5008	10^100000+9225987	100001	Robert Price	04/2017
5009	10^100000+9265587	100001	Robert Price	04/2017
5010	10^100000+9287049	100001	Robert Price	04/2017
5011	10^100000+9425053	100001	Robert Price	05/2017
5012	10^100000+9450769	100001	Robert Price	05/2017
5013	10^100000+9528747	100001	Robert Smith	05/2017
5014	10^100000+9548071	100001	Robert Price	06/2017
5015	10^100000+10064287	100001	Robert Price	08/2017
5016	10^100000+10229569	100001	Robert Price	10/2017
5001	10^100000+19495699	100001	Robert Price	09/2020
5002	10^100000+19668927	100001	Robert Price	09/2020
5003	10^100000+19704313	100001	Robert Price	09/2020
5035	10^99999+309403	100000	Daniel Heuer	01/2004
5036	10^100000-260199	100000	Patrick De Geest	01/2010
5037	10^99999-59511	99999	Patrick De Geest	07/2009
5038	10^99998+235437	99999	Patrick De Geest	02/2020
5039	10^99998-286587	99998	Patrick De Geest	02/2020
5040	10^99997+72297	99998	Patrick De Geest	02/2020
5041	10^99997-402627	99997	Patrick De Geest	02/2020
5042	10^99996+279853	99997	Patrick De Geest	02/2020
5043	10^99997-500000001	99997	Robert Price	12/2020
5044	10^99996-94961	99996	Patrick De Geest	02/2020
5045	10^99995+54633	99996	Patrick De Geest	02/2020
5046	10^99995-101429	99995	Patrick De Geest	02/2020
5047	10^99994+117271	99995	Patrick De Geest	02/2020
5048	10^99994-452289	99994	Patrick De Geest	02/2020
5049	10^99993+371311	99994	Patrick De Geest	02/2020
5050	10^99993-186491	99993	Patrick De Geest	02/2020
5051	10^99992+17431	99993	Patrick De Geest	02/2020
5052	10^99992-28607	99992	Patrick De Geest	02/2020
5053	10^99991+125391	99992	Patrick De Geest	02/2020
5054	10^99991-204573	99991	Patrick De Geest	02/2020
5055	10^99990+13899	99991	Patrick De Geest	02/2020
5056	10^99990-8111	99990	Patrick De Geest	02/2020
5057	2^332141-113073	99985	Enzo Doria	07/2014
5059	(3^209561+2)/728101255	99978	Lelio R Paula	09/2013
5058	23827^15702+15702^23827	99978	Hans Havermann	04/2018
5060	2^332085+1865897	99968	Enzo Doria	03/2016
5061	(9787*2^332070-1)/936402369	99959	Lelio R Paula	05/2015
5062	2^332023+191	99949	Lelio R Paula	02/2011
5063	7*10^99944+27	99945	Robert Price	11/2020
5064	2^331938+71149	99924	Enzo Doria	04/2016
5065	2^331932-78795	99922	Lelio R Paula	09/2016
5066	2^331921+771	99919	Lelio R Paula	01/2013
5067	(3^209419-2)/5132755	99912	Lelio R Paula	09/2013
5068	2^331860-114989	99900	Enzo Doria	05/2015
5069	2^331746-11655	99866	Lelio R Paula	09/2016
5070	11^95891-28	99861	Lelio R Paula	08/2016
5071	(2^331694-5)/11	99849	Lelio R Paula	10/2013
5072	(3^209246+7)/64	99834	Lelio R Paula	09/2013
5073	25062^9617+9617^25062	99823	Hans Havermann	04/2018
5074	15^84866-52	99811	Lelio R Paula	08/2016
5075	13^89600+30	99810	Lelio R Paula	08/2016
5076	22950^22309+22309^22950	99798	Hans Havermann	03/2018
5077	5^142772-38	99794	Lelio R Paula	08/2016
5078	(23*2^331459+1)/475	99778	Lelio R Paula	11/2013
5079	2^331416-331416+1	99767	Robert Price	10/2014
5080	2^331256-57	99718	Lelio R Paula	12/2012
5081	28192^3443+3443^28192	99714	Hans Havermann	03/2018
5082	2^331185+737	99697	Lelio R Paula	01/2013
5083	(4*10^99693+149)/9	99693	Robert Price	03/2017
5084	2^331154+1880527	99688	Enzo Doria	10/2016
5086	(19^77951+1)/20	99679	Paul Bourdelais	03/2010
5085	24354^12385+12385^24354	99679	Hans Havermann	03/2018
5087	2^331110+1870459	99675	Enzo Doria	05/2016
5088	5*2^331075+7	99665	Lelio R Paula	08/2014
5089	25776^7351+7351^25776	99659	Hans Havermann	02/2018
5090	(16*10^99656-31)/3	99657	Robert Price	03/2016
5091	2^330968+345	99632	Lelio R Paula	09/2016
5092	(2^330969+690)/2	99632	Stefano Morozzi	09/2020
5093	2*5^142528-7	99624	Lelio R Paula	11/2014
5094	2^330942+77329	99624	Enzo Doria	05/2016
5095	14^86914-99	99615	Lelio R Paula	08/2016
5096	(19*2^330902+1)/77	99611	Lelio R Paula	11/2013
5097	22971^21692+21692^22971	99610	Hans Havermann	03/2018
5098	2^330845+71687	99595	Enzo Doria	04/2016
5099	(23*2^330770+1)/3	99573	Lelio R Paula	11/2013
5100	24494^11613+11613^24494	99567	Hans Havermann	03/2018
5101	2^330735+8415	99562	Lelio R Paula	09/2016
5102	2^330720+74071	99557	Enzo Doria	04/2016
5103	31^66738-2	99531	Lelio R Paula	09/2013
5104	7*3^208567+4	99513	Lelio R Paula	08/2014
5105	(13*10^99508+47)/3	99509	Robert Price	01/2017
5106	2^330553+779	99507	Lelio R Paula	01/2013
5107	15^84606-94	99505	Lelio R Paula	08/2016
5108	6^127858+47	99493	Lelio R Paula	08/2016
5109	5^142337+48	99490	Lelio R Paula	08/2016
5110	7^117724-20	99489	Lelio R Paula	08/2016
5111	(29*10^99474-17)/3	99475	Erik Branger	09/2014
5112	(185*10^99466-11)/3	99468	Robert Price	10/2020
5113	(2^330410+2038)/2	99464	Stefano Morozzi	09/2020
5114	(9*2^330407-1)/7	99463	Lelio R Paula	03/2014
5115	(2^330373+2114)/2	99452	Stefano Morozzi	09/2020
5116	(68*10^99441+7)/3	99443	Robert Price	03/2016
5117	10^99434+155571	99435	Patrick De Geest	04/2020
5118	10^99434-123456789	99434	Robert Price	02/2020
5119	10^99434-191237	99434	Patrick De Geest	04/2020
5120	46^59791-45^59791	99418	Jean-Louis Charton	01/2013
5121	23839^14802+14802^23839	99417	Hans Havermann	02/2018
5122	(2*10^99408+529)/9	99408	Robert Price	01/2017
5123	(2^330216+3510)/2	99405	Stefano Morozzi	09/2020
5124	53^57646-2	99398	Lelio R Paula	09/2013
5125	2^330165+1870025	99390	Enzo Doria	05/2016
5126	2^330142-155	99383	Lelio R Paula	12/2012
5127	2^330088-115259	99367	Enzo Doria	06/2015
5128	24216^12671+12671^24216	99354	Hans Havermann	01/2018
5129	Phi(200548,10)/3208769	99354	Makoto Kamada	04/2019
5130	(746*10^99303+1)/9	99305	Robert Price	02/2017
5131	3^208107+40	99293	Lelio R Paula	08/2016
5132	(5*2^329833-1)/369	99288	Lelio R Paula	02/2014
5133	8*3^208093+5	99287	Lelio R Paula	08/2014
5134	5^142043+56	99284	Lelio R Paula	08/2016
5135	22*10^99275+7	99277	Robert Price	04/2016
5136	2^329778+1876189	99274	Enzo Doria	07/2016
5137	(10^99239-13)/3	99239	Robert Price	02/2017
5138	3^207987+62	99236	Lelio R Paula	08/2016
5139	2^329638+49	99231	Lelio R Paula	12/2012
5140	7^117413-18	99226	Lelio R Paula	08/2016
5141	2^329586-458903	99216	Enzo Doria	04/2015
5142	2^329553+101	99206	Lelio R Paula	12/2012
5143	2^329551-112897	99205	Enzo Doria	06/2014
5144	(3^207925+7)/50	99204	Lelio R Paula	09/2013
5145	6^127458-17993	99182	Enzo Doria	03/2013
5146	27197^4428+4428^27197	99166	Hans Havermann	10/2017
5147	(46*10^99143-1)/9	99144	Robert Price	12/2014
5148	7*10^99133+69	99134	Robert Price	10/2017
5149	18^78968-3065	99127	Enzo Doria	03/2013
5151	25927^6654+6654^25927	99122	Hans Havermann	10/2017
5150	87915!4+16	99122	Robert Price	09/2019
5152	2^329259+189	99117	Lelio R Paula	12/2012
5153	8*10^99113+39	99114	Robert Price	01/2017
5154	6^127364+77	99109	Lelio R Paula	08/2016
5155	(2^329135+1110)/2	99080	Stefano Morozzi	09/2020
5156	6^127285+13	99047	Lelio R Paula	08/2016
5157	(228581#+235862)/(2^31171*151)	99044	Makoto Morimoto	10/2017
5158	2^329007+73283	99041	Enzo Doria	04/2016
5159	5*3^207543-8	99024	Lelio R Paula	08/2014
5160	(2^328930+570)/2	99018	Stefano Morozzi	09/2020
5161	2^328885+149	99005	Lelio R Paula	12/2012
5162	23392^17075+17075^23392	99004	Hans Havermann	09/2017
5163	(2^328879-9)/119	99001	Lelio R Paula	10/2013
5164	5^141618+54	98987	Lelio R Paula	08/2016
5165	8*10^98982+51	98983	Robert Price	05/2017
5166	(21*2^328809-1)/7709	98979	Lelio R Paula	03/2014
5167	2^328794-2797601	98977	Enzo Doria	04/2016
5168	6^127176+5	98963	Lelio R Paula	11/2014
5169	2*10^98961-21	98962	Robert Price	09/2020
5170	24262^11989+11989^24262	98960	Hans Havermann	09/2017
5171	2^328700-109709	98949	Enzo Doria	04/2014
5172	(2^328698+1810)/2	98948	Stefano Morozzi	01/2021
5173	87771!4-128	98944	Robert Price	11/2019
5174	(2^328658+3042)/2	98936	Stefano Morozzi	09/2020
5175	46711!2-2^46711	98916	Robert Price	09/2015
5176	9*7^117037+4	98909	Lelio R Paula	11/2014
5177	127^47012+126	98905	Norbert Schneider	01/2019
5178	(2^328525+1250)/2	98896	Stefano Morozzi	09/2020
5179	(10^98890+149)/3	98890	Serge Batalov	12/2014
5180	22775^21978+21978^22775	98889	Hans Havermann	08/2017
5181	2^328497-216933	98888	Enzo Doria	05/2014
5182	2^328487+32769	98885	Lelio R Paula	08/2016
5183	3^207250-112358	98884	Enzo Doria	06/2014
5184	13^88754-90	98867	Lelio R Paula	08/2016
5186	2^328406+709	98861	Lelio R Paula	02/2013
5185	2*10^98860-21	98861	Robert Price	09/2020
5187	(17*2^328413-1)/16173	98860	Lelio R Paula	03/2014
5188	7^116976+76	98857	Lelio R Paula	08/2016
5189	(2^328378+2710)/2	98852	Stefano Morozzi	09/2020
5190	2^328335+1155	98839	Lelio R Paula	08/2016
5192	(3*2^328311+1)/5	98832	Lelio R Paula	11/2013
5191	287^40210+40210^287	98832	Norbert Schneider	11/2014
5193	(2^328284+9)/1325	98821	Lelio R Paula	10/2013
5194	(21*2^328258+1)/2125	98814	Lelio R Paula	11/2013
5195	24746^9825+9825^24746	98795	Hans Havermann	07/2020
5196	26620^5143+5143^26620	98793	Hans Havermann	07/2020
5197	65^54491+48	98788	Lelio R Paula	04/2016
5198	3^207042+98	98785	Lelio R Paula	08/2016
5199	(2^328121+3110)/2	98774	Stefano Morozzi	09/2020
5201	3^206977-112756	98754	Enzo Doria	07/2014
5200	10^98754-40000000001	98754	Robert Price	09/2020
5202	7^116846-50	98747	Lelio R Paula	08/2016
5203	23267^17512+17512^23267	98730	Hans Havermann	04/2020
5204	2^327967-28635	98728	Lelio R Paula	08/2016
5205	707^34642+34642^707	98710	Norbert Schneider	12/2017
5206	6^126850-47	98709	Lelio R Paula	08/2016
5207	(2^327886+2170)/2	98704	Stefano Morozzi	09/2020
5208	8*6^126830-7	98694	Lelio R Paula	11/2014
5209	11^94770-270	98693	Enzo Doria	08/2012
5210	(2^327846+3250)/2	98692	Stefano Morozzi	01/2021
5211	2^327832+43	98688	Lelio R Paula	12/2012
5212	2^327795+761	98677	Lelio R Paula	02/2013
5213	(2^327796+1522)/2	98677	Stefano Morozzi	09/2020
5214	10^98669+147411	98670	Patrick De Geest	11/2016
5216	10^98669-9^(98669-1)	98669	Robert Price	05/2016
5215	10^98669-105249	98669	Patrick De Geest	11/2016
5217	2^327671-109801	98639	Enzo Doria	04/2014
5218	24398^11037+11037^24398	98638	Hans Havermann	10/2019
5219	5^141090-14	98618	Lelio R Paula	08/2016
5220	20^75799+47	98617	Lelio R Paula	08/2016
5221	28101^3226+3226^28101	98597	Hans Havermann	07/2020
5222	2^327515-1017	98592	Lelio R Paula	08/2016
5223	6^126692+97681	98586	Mike Oakes	04/2011
5224	2^327467-741	98578	Lelio R Paula	08/2016
5225	22713^21800+21800^22713	98540	Hans Havermann	05/2020
5226	(2^327329+9)/19	98535	Lelio R Paula	10/2013
5227	7^116577-66	98519	Lelio R Paula	08/2016
5229	(3*2^327250+1)/7	98512	Lelio R Paula	11/2013
5228	23220^17479+17479^23220	98512	Hans Havermann	03/2020
5230	(19*2^327192+1)/275	98494	Lelio R Paula	11/2013
5231	2^327162-66945	98486	Lelio R Paula	08/2016
5232	30139^1852+1852^30139	98484	Hans Havermann	02/2020
5233	23182^17703+17703^23182	98479	Hans Havermann	01/2020
5234	4*10^98472-3	98473	Erik Branger	11/2013
5235	26167^5794+5794^26167	98466	Hans Havermann	01/2020
5236	(6883*2^327047-1)/77	98453	Lelio R Paula	05/2015
5237	(71*10^98446+1)/9	98447	Serge Batalov	11/2010
5238	13^88363+94	98432	Lelio R Paula	08/2016
5239	48^58543-47^58543	98425	Jean-Louis Charton	11/2005
5240	6^126481+41	98422	Lelio R Paula	08/2016
5241	78*10^98413-7	98415	Robert Price	05/2017
5242	22634^22263+22263^22634	98404	Hans Havermann	07/2020
5243	7^116416+46	98383	Lelio R Paula	08/2016
5244	7^116407-24	98376	Lelio R Paula	07/2016
5245	439^37228+37228^439	98374	Norbert Schneider	08/2018
5247	2^326782-1860671	98372	Enzo Doria	03/2016
5246	17^79948+58	98372	Lelio R Paula	08/2016
5248	22499^22602-22602^22499	98368	Norbert Schneider	08/2020
5249	3^206143-98	98356	Lelio R Paula	08/2016
5250	8*5^140705+7	98350	Lelio R Paula	11/2014

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PRP Records

Probable Primes Top 10000

(277034 PRPs in the top)