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	6^112054-47	87195	Lelio R Paula	12/2015
5002	(55459*2^289632+1)/55	87191	Lelio R Paula	06/2014
5003	15^74131-68	87185	Lelio R Paula	11/2015
5004	2^289583-741	87174	Lelio R Paula	10/2013
5005	7^103146+12	87169	Lelio R Paula	10/2015
5006	5*2^289556-3	87166	Lelio R Paula	08/2014
5007	2^289543-112735	87162	Enzo Doria	06/2014
5008	8*3^182655-7	87150	Lelio R Paula	08/2014
5009	2*10^87144+81	87145	Robert Price	01/2017
5010	7^103106+2*3^103106	87135	Mike Oakes	08/2010
5011	8*3^182614+7	87130	Lelio R Paula	08/2014
5012	(2^289368-509203)/9	87108	Lelio R Paula	01/2013
5013	3^182566+14	87107	Robert Price	09/2013
5014	(3^182385-5)/2	87020	Lelio R Paula	01/2013
5015	11^83534-8	86992	Lelio R Paula	11/2015
5016	4^144479-14267	86986	Mike Oakes	03/2011
5017	(145*10^86982-1)/9	86984	Serge Batalov	12/2014
5018	(151*10^86963-1)/3	86965	Robert Price	04/2017
5019	15^73940-58	86961	Lelio R Paula	11/2015
5020	2^288761-113143	86926	Enzo Doria	07/2014
5021	2^288747+3083	86922	Yves Minet	03/2011
5022	30^58842+29	86917	Norbert Schneider	03/2017
5023	(10^86906-13)/3	86906	Robert Price	02/2017
5024	2^288692-110027	86905	Enzo Doria	04/2014
5025	(2^288682+7)/259895449	86894	Lelio R Paula	01/2013
5026	(2^288636+47)/1293	86885	Lelio R Paula	01/2013
5027	3^182089-34	86879	Robert Price	11/2013
5028	2^288543-109801	86861	Enzo Doria	04/2014
5029	60^48847-59	86858	Norbert Schneider	10/2014
5030	2^288470-64875	86839	Lelio R Paula	10/2013
5031	10^86816+32997	86817	Patrick De Geest	07/2013
5032	10^86816-99	86816	Robert Price	05/2011
5033	(89*10^86802-539)/9	86803	Robert Price	11/2017
5034	41487!2+256	86786	Robert Price	01/2015
5035	(5*2^288301-1)/999	86785	Lelio R Paula	02/2014
5036	2^288243+76043	86770	Enzo Doria	04/2016
5037	(29*2^288232+1)/15	86767	Lelio R Paula	01/2013
5038	9*6^111495+5	86761	Lelio R Paula	10/2014
5039	(5*2^288202+1)/81	86757	Lelio R Paula	01/2013
5040	9*7^102654-2	86754	Lelio R Paula	10/2014
5041	2^288122-112841	86734	Enzo Doria	06/2014
5042	5^124062-68	86716	Lelio R Paula	10/2015
5043	(2^288007-3)/125	86697	Lelio R Paula	01/2013
5044	379*10^86691+9	86694	Arkadiusz Wesolowski	10/2011
5045	7^102555+48	86670	Lelio R Paula	10/2015
5046	77779!4+2	86660	Robert Price	08/2017
5047	2^287809-111355	86640	Enzo Doria	05/2014
5048	(47*2^287795+1)/7	86636	Lelio R Paula	04/2015
5049	9*7^102504+8	86627	Lelio R Paula	10/2014
5050	3^181551+32	86622	Robert Price	11/2013
5051	2^287735-521347	86617	Paul Bourdelais	05/2013
5052	(1017*2^287600-1)/91	86578	Lelio R Paula	04/2015
5053	2^287540-112967	86559	Enzo Doria	06/2014
5054	3^181407+20	86554	Robert Price	10/2013
5055	(13*10^86546+83)/3	86547	Robert Price	09/2016
5056	3^181378-2^(181378-1)	86540	Robert Price	01/2016
5057	83^45080-2	86513	Lelio R Paula	08/2013
5058	(78557*2^287351+1)/611	86504	Lelio R Paula	06/2014
5059	25*29^59147+20936	86498	Curtis Bright	05/2015
5060	2^287298+1871359	86486	Enzo Doria	05/2016
5061	118^41740-117	86481	Norbert Schneider	08/2018
5062	3*10^86478+89	86479	Robert Price	03/2017
5063	2^287272-79049	86478	Paul Bourdelais	02/2012
5064	9067052((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
5065	8118242((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
5066	7790642((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
5067	7683852((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
5068	7008912((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
5069	6523202((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
5070	3779202((10^86453-1)/9)+1	86458	Danilo Nitsche	01/2016
5071	2550602((10^86453-1)/9)+1	86458	Danilo Nitsche	01/2016
5072	1871112((10^86453-1)/9)+1	86458	Danilo Nitsche	01/2016
5073	(10^86453-1)/9	86453	Lew Baxter	10/2000
5074	87^44563-86^44563	86431	Robert Price	05/2015
5075	6^111057+61	86420	Lelio R Paula	12/2015
5076	2^287057-109909	86413	Enzo Doria	04/2014
5077	5^123608+22	86399	Lelio R Paula	10/2015
5078	(31*10^86364-121)/9	86365	Robert Price	06/2016
5079	2^286859+71663	86354	Enzo Doria	04/2016
5080	2^286740+29835	86318	Lelio R Paula	10/2013
5081	2*10^86310+9^86310	86311	Mike Oakes	05/2011
5082	11^82878-1860	86309	Enzo Doria	12/2012
5083	2^286547+16095	86260	Lelio R Paula	10/2013
5084	(58*10^86242+329)/9	86243	Robert Price	11/2017
5085	2^286455-110427	86232	Enzo Doria	05/2014
5086	(37*10^86230+53)/9	86231	Robert Price	05/2015
5087	8*3^180700+5	86217	Lelio R Paula	08/2014
5088	3^180697-40	86215	Lelio R Paula	12/2015
5089	(13*2^286318-1)/13257	86188	Lelio R Paula	02/2014
5090	2^286165+77	86145	Lelio R Paula	08/2012
5091	9*2^286140+7	86138	Lelio R Paula	08/2014
5092	(29*2^286108-1)/2002367	86123	Lelio R Paula	02/2014
5093	10^86110+161113	86111	Patrick De Geest	07/2013
5094	10^86110-69	86110	Robert Price	05/2011
5095	2^286036-869688105	86106	Lelio R Paula	07/2016
5096	(77*10^86072+31)/9	86073	Robert Price	10/2015
5097	2^285923+345	86072	Lelio R Paula	09/2013
5098	13^77266-90	86070	Lelio R Paula	11/2015
5099	2^285910-458903	86068	Enzo Doria	04/2015
5100	2^285904-125	86066	Lelio R Paula	08/2012
5101	2^285836+65835	86046	Lelio R Paula	09/2013
5102	(2^285766+78557)/3	86024	Lelio R Paula	01/2013
5103	(5*10^86011-107)/3	86012	Robert Price	01/2017
5104	6^110522+163	86003	Lelio R Paula	12/2015
5105	41^53323-40^53323	85999	Robert Price	07/2012
5106	2^285678-109617	85998	Enzo Doria	04/2014
5107	6^110506-16673	85991	Enzo Doria	02/2013
5109	2^285569-741	85965	Lelio R Paula	09/2013
5108	(32*10^85964+31)/9	85965	Robert Price	05/2015
5110	6*10^85910-7	85911	Dmitry Domanov	11/2010
5111	(412*10^85897-7)/9	85899	Robert Price	10/2017
5112	4*10^85881+63	85882	Robert Price	06/2016
5113	(10^85864+53)/9	85864	Robert Price	01/2015
5114	2^285230+345	85863	Lelio R Paula	09/2013
5115	(5*10^85855-473)/9	85855	Robert Price	12/2017
5116	2^285199+75683	85854	Enzo Doria	04/2016
5117	(76*10^85847-211)/9	85848	Robert Price	10/2017
5118	p(17832)#/2+512	85845	Robert Price	05/2017
5119	(16*10^85839+167)/3	85840	Robert Price	10/2017
5120	11^82426-1230	85838	Enzo Doria	11/2012
5121	2^285113-109881	85828	Enzo Doria	04/2014
5122	5^122746-92	85796	Lelio R Paula	10/2015
5123	2^285001-113461	85794	Enzo Doria	08/2014
5124	(11*10^85782-131)/3	85783	Robert Price	02/2017
5125	2^284913-110491	85768	Enzo Doria	05/2014
5126	6^110220+47	85768	Lelio R Paula	12/2015
5127	3*6^110202-5	85755	Lelio R Paula	10/2014
5128	(157^39047-1)/156	85742	Alexander Zhirkov	06/2016
5129	(3^179705+7)/250	85739	Lelio R Paula	12/2012
5130	2^284734-6555	85714	Lelio R Paula	09/2013
5131	(10^85712+53)/9	85712	Robert Price	01/2015
5132	3*10^85703+11	85704	Robert Price	11/2017
5133	(6883*2^284668-1)/3	85697	Lelio R Paula	04/2015
5134	20^65855+83	85680	Lelio R Paula	01/2016
5135	6^110105+53	85679	Lelio R Paula	12/2015
5136	(10^85666-97)/3	85666	Robert Kinser	10/2017
5138	2^284567-7605	85664	Lelio R Paula	09/2013
5137	9*5^122555-2	85664	Lelio R Paula	10/2014
5139	5^122554-14	85662	Lelio R Paula	10/2015
5140	9*5^122543+4	85655	Lelio R Paula	10/2014
5141	3^179489-2^(179489-1)	85639	Robert Price	01/2016
5142	2^284429+177	85622	Lelio R Paula	08/2012
5143	2*3^179452+5	85621	Lelio R Paula	07/2014
5144	(19^66919+3^66919)/22	85572	Robert Price	07/2013
5145	66^47023-65	85561	Norbert Schneider	11/2014
5146	6^109943+13	85553	Lelio R Paula	12/2015
5147	(2^284167-509203)/34564775	85536	Lelio R Paula	01/2013
5148	2^284133-3	85533	M. Frind & P. Underwood	07/2002
5149	2^284113+315	85527	Lelio R Paula	09/2013
5150	(28*10^85500+149)/3	85501	Robert Price	10/2017
5151	(16*10^85495-19)/3	85496	Robert Price	03/2016
5152	2^284004+177	85494	Lelio R Paula	08/2012
5153	(16*10^85473-91)/3	85474	Robert Price	06/2016
5154	3^179120+22	85462	Robert Price	12/2013
5155	2^283872-2792249	85454	Enzo Doria	03/2016
5156	(29*10^85438+259)/9	85439	Robert Price	04/2017
5157	2^283817+82875	85438	Lelio R Paula	09/2013
5158	(2^283815-5)/201	85435	Lelio R Paula	01/2013
5159	2^283796-125	85432	Lelio R Paula	08/2012
5160	(29*2^283784-1)/13	85428	Lelio R Paula	02/2014
5161	15^72592-28	85375	Lelio R Paula	11/2015
5162	2^283604-58695	85374	Lelio R Paula	09/2013
5163	(44*10^85370-503)/9	85371	Robert Price	10/2017
5164	496^31671+31671^496	85369	Norbert Schneider	07/2017
5165	(15*2^283583-1)/103051	85364	Lelio R Paula	02/2014
5166	15^72572+92	85352	Lelio R Paula	11/2015
5167	2^283473-1615	85334	Lelio R Paula	09/2013
5168	2^283466-15	85332	Lelio R Paula	08/2012
5169	11^81916-7020	85307	Enzo Doria	02/2013
5170	6^109626-7	85306	Lelio R Paula	11/2014
5171	2^283374-110327	85305	Enzo Doria	05/2014
5172	33*10^85297+7	85299	Robert Price	07/2016
5173	18^67933+41	85275	Lelio R Paula	11/2015
5174	2^283271-109341	85274	Enzo Doria	04/2014
5175	(25*10^85249-73)/3	85250	Robert Price	09/2016
5176	2*5^121959+3	85246	Lelio R Paula	10/2014
5177	19834^19834+8947	85235	Henri Lifchitz	11/2004
5178	2^283140+1915	85234	Lelio R Paula	09/2013
5179	3*10^85227-97	85228	Robert Price	08/2017
5180	(16*10^85221-31)/3	85222	Robert Price	03/2016
5181	2^283083+1869383	85217	Enzo Doria	05/2016
5182	(24737*2^283051+1)/17	85211	Lelio R Paula	06/2014
5183	(2^283032+78557)/3	85201	Lelio R Paula	01/2013
5184	2^283026-109893	85200	Enzo Doria	04/2014
5185	(2^283012+78557)/129	85193	Lelio R Paula	01/2013
5186	(10^(242589+1)+7210^42589-1)/9	85179	Robert Price	09/2017
5187	2^282860-109727	85150	Enzo Doria	04/2014
5188	2^282819+1869413	85138	Enzo Doria	05/2016
5189	3^178428+2	85132	Ray Chandler	07/2011
5190	(22699*2^282742+1)/73	85117	Lelio R Paula	06/2014
5191	(16^70687+5^70687)/21	85115	Robert Price	07/2013
5192	(3^178352-2)/7	85095	Lelio R Paula	12/2012
5193	11^81699-2790	85081	Enzo Doria	12/2012
5194	2^282612-95	85075	Lelio R Paula	08/2012
5195	2^282609-4069	85074	Yves Minet	02/2018
5196	75^45366-2	85065	Lelio R Paula	08/2013
5197	2^282511+69	85045	Lelio R Paula	08/2012
5198	69^46249+2	85045	Lelio R Paula	06/2013
5199	3^178226+10	85036	Robert Price	10/2013
5200	(182*10^85017+43)/9	85019	Robert Price	11/2017
5201	(14*10^85010+73)/3	85011	Robert Price	04/2016
5202	9*2^282338-7	84994	Lelio R Paula	08/2014
5203	(9913*2^282330-1)/1578003	84988	Lelio R Paula	04/2015
5204	2^282203+5	84952	Lelio R Paula	08/2012
5205	2^282184+13	84946	Lelio R Paula	08/2012
5206	11^81568-2400	84945	Enzo Doria	12/2012
5207	11^81562-2340	84939	Enzo Doria	12/2012
5208	(41*10^84927+31)/9	84928	Robert Price	05/2015
5209	(2*10^84904-17)/3	84904	Robert Price	08/2014
5210	(4^141017+23)/3	84901	Robert Price	02/2017
5211	6^109100-18653	84897	Enzo Doria	03/2013
5212	2^281973+1025	84883	Lelio R Paula	09/2013
5213	2^281951-109651	84876	Enzo Doria	04/2014
5214	11^81491-5430	84865	Enzo Doria	01/2013
5215	((1+sqrt(3)+sqrt(2))^79357-1)((1+sqrt(3)-sqrt(2))^79357-1)((1-sqrt(3)+sqrt(2))^79357-1)*((1-sqrt(3	84849	Mike Oakes	04/2009
5216	2^281825-1861483	84838	Enzo Doria	03/2016
5217	2^281809-97305	84833	Lelio R Paula	09/2013
5218	2^281780-114893	84825	Enzo Doria	05/2015
5219	3^177719+64	84794	Lelio R Paula	12/2015
5221	2^281675-199	84793	Lelio R Paula	08/2012
5220	2^281673-111223	84793	Enzo Doria	05/2014
5222	(4*10^84779+149)/9	84779	Robert Price	03/2017
5223	129^40167-128	84777	Norbert Schneider	01/2019
5224	(72*10^84772-27)/9	84773	Ray Chandler	01/2011
5225	11^81398-630	84768	Enzo Doria	11/2012
5226	(25*2^281577-1)/23	84764	Lelio R Paula	02/2014
5227	2^281500-455	84740	Yves Minet	03/2012
5228	10^84725+1145141919	84726	Marisa Kirisame	03/2015
5229	10^84725+142041	84726	Patrick De Geest	10/2015
5230	10^84725-138677	84725	Patrick De Geest	02/2016
5231	76^45044+75	84720	Norbert Schneider	02/2015
5232	54^48897-53	84709	Norbert Schneider	08/2014
5233	(9913*2^281377-1)/65	84706	Lelio R Paula	04/2015
5234	Phi(171124,10)/29946701/7761329021/58560344041	84700	Maksym Voznyy	11/2015
5235	2^281337-111223	84691	Enzo Doria	05/2014
5236	2^281308+54615	84683	Lelio R Paula	09/2013
5237	7*5^121144-6	84677	Lelio R Paula	10/2014
5238	(2^281252+47)/3	84665	Lelio R Paula	01/2013
5239	11^81297-3150	84663	Enzo Doria	12/2012
5240	2^281208-303	84653	Yves Minet	02/2012
5241	197^36892-2	84648	Lelio R Paula	10/2017
5242	(21*2^281187+1)/2483	84644	Lelio R Paula	01/2013
5243	11^81247-84	84611	Lelio R Paula	10/2015
5244	17^68747-64	84590	Lelio R Paula	11/2015
5245	5^121018-15596	84588	Enzo Doria	02/2013
5246	6^108702+7	84587	Lelio R Paula	11/2014
5247	10^84582+100677	84583	Patrick De Geest	05/2016
5248	10^84582-8001	84582	Robert Price	03/2016
5249	3*5^121004-8	84579	Lelio R Paula	10/2014
5250	5^120996-84	84573	Lelio R Paula	10/2015

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PRP Records

Probable Primes Top 10000

(252538 PRPs in the top)