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	2^292894-111851	88170	Enzo Doria	05/2014
5002	2^292872-2797349	88164	Enzo Doria	03/2016
5003	2^292860-109685	88160	Enzo Doria	04/2014
5004	9*6^113288-5	88157	Lelio R Paula	10/2014
5005	(2*10^88112-23)/3	88112	Robert Price	09/2017
5006	(73*10^88105+17)/9	88106	Robert Price	10/2015
5007	11^84588+78	88090	Lelio R Paula	11/2015
5008	(265*10^88077+11)/3	88079	Robert Price	03/2017
5009	91^44959-90^44959	88077	Robert Price	07/2015
5010	6^113177-5^113177	88069	Jean-Louis Charton	01/2009
5011	(10^88020+101)/3	88020	Robert Price	04/2016
5012	52^51285-51	88006	Norbert Schneider	09/2018
5013	(10^(243982+1)-610^43982-1)/3	87965	Robert Price	02/2016
5014	(424*10^87930-1)/9	87932	Robert Price	11/2017
5015	p(18225)#/2+128	87929	Robert Price	04/2017
5016	4*6^112977+7	87914	Lelio R Paula	10/2014
5017	14^76677+69	87882	Lelio R Paula	11/2015
5018	(22*10^87863-1)/3	87864	Robert Price	12/2014
5019	2^291822-2797811	87848	Enzo Doria	04/2016
5020	2^291716-111389	87816	Enzo Doria	05/2014
5021	(782*10^87809-71)/9	87811	Robert Price	06/2017
5022	3^184039+1820	87809	Lelio R Paula	12/2015
5023	12^81356+41	87798	Lelio R Paula	11/2015
5024	6^112792-18983	87770	Enzo Doria	03/2013
5025	3*6^112787-5	87766	Lelio R Paula	10/2014
5026	7^103848+82	87762	Lelio R Paula	10/2015
5027	(19*2^291534-1)/178696395	87754	Lelio R Paula	02/2014
5028	(3^183915+5)/128	87748	Lelio R Paula	01/2013
5029	19^68619+24	87747	Lelio R Paula	12/2015
5031	2^291480+1185	87745	Lelio R Paula	10/2013
5030	2^291482+1867369	87745	Enzo Doria	03/2016
5032	2^291467-937	87741	Yves Minet	05/2013
5033	(25*10^87726+161)/3	87727	Robert Price	01/2017
5034	11^84239-2850	87726	Enzo Doria	12/2012
5035	10^87720+215541	87721	Patrick De Geest	01/2011
5036	10^87720-3	87720	Markus Tervooren	07/2010
5037	(5*10^87712-473)/9	87712	Robert Price	12/2017
5038	(2^291357+5)/6847	87704	Lelio R Paula	01/2013
5039	93^44541-2	87679	Lelio R Paula	09/2013
5040	2^291261-109561	87679	Enzo Doria	04/2014
5041	(4*10^87669+149)/9	87669	Robert Price	03/2017
5042	2^291217+4257	87666	Lelio R Paula	10/2013
5043	2*12^81214-5^81214	87645	Mike Oakes	12/2010
5044	(5*10^87622-473)/9	87622	Robert Price	12/2017
5045	12^81188+85	87617	Lelio R Paula	11/2015
5046	(21*2^290980-1)/5	87595	Lelio R Paula	02/2014
5047	2^290958+127	87588	Lelio R Paula	09/2012
5048	2^290923-67	87577	Lelio R Paula	09/2012
5049	3*10^87573-97	87574	Robert Price	08/2017
5050	(13*10^87565+11)/3	87566	Robert Price	05/2015
5051	(2^290857-7)/55	87555	Lelio R Paula	01/2013
5052	2^290802+82875	87541	Lelio R Paula	10/2013
5053	(509203*2^290792-1)/7560987	87536	Lelio R Paula	04/2015
5054	3^183441+236	87524	Lelio R Paula	12/2015
5055	2^290618-33	87485	Lelio R Paula	09/2012
5056	(184*10^87473-1)/3	87475	Robert Price	02/2017
5057	2^290534-115151	87460	Enzo Doria	06/2015
5058	2^290512-109757	87453	Enzo Doria	04/2014
5059	(32*10^87448-41)/9	87449	Robert Price	05/2015
5060	(2^290491+9)/3179	87444	Lelio R Paula	01/2013
5061	(25*2^290489-1)/51809	87443	Lelio R Paula	02/2014
5062	2^290426+82875	87427	Lelio R Paula	11/2013
5063	3*2^290415-7	87425	Lelio R Paula	08/2014
5065	10^87408+57	87409	Robert Price	03/2011
5064	2^290366+74779	87409	Enzo Doria	04/2016
5066	10^87408-123569	87408	Patrick De Geest	07/2013
5067	2^290265+58905	87379	Lelio R Paula	10/2013
5068	7^103391+16	87376	Lelio R Paula	10/2015
5069	(115*10^87368-7)/9	87370	Robert Price	11/2017
5070	(92^44491-1)/91	87369	Paul Bourdelais	08/2017
5071	8*7^103379+3	87367	Lelio R Paula	10/2014
5072	(2^290226+7)/71	87365	Lelio R Paula	01/2013
5073	13^78407-30	87341	Lelio R Paula	11/2015
5074	4*10^87337-99	87338	Robert Price	12/2016
5075	7*10^87319+39	87320	Robert Price	07/2016
5076	3*5^124921+2	87317	Lelio R Paula	10/2014
5077	3^182984+88	87306	Lelio R Paula	12/2015
5078	(10^87323-1)/(9*33909262597306826117)	87303	Alfred Reich	02/2019
5079	4*10^87287-99	87288	Robert Price	12/2016
5080	11^83813-1860	87283	Enzo Doria	12/2012
5081	734^30453+30453^734	87270	Norbert Schneider	04/2017
5082	12^80855+29	87258	Lelio R Paula	11/2015
5083	3*6^112119-5	87247	Lelio R Paula	10/2014
5084	12^80806+79	87205	Lelio R Paula	11/2015
5085	91382^9+9^91382	87201	Andrey Kulsha	11/2004
5086	(21181*2^289657+1)/81	87198	Lelio R Paula	06/2014
5087	6^112054-47	87195	Lelio R Paula	12/2015
5088	(55459*2^289632+1)/55	87191	Lelio R Paula	06/2014
5089	15^74131-68	87185	Lelio R Paula	11/2015
5090	2^289583-741	87174	Lelio R Paula	10/2013
5091	7^103146+12	87169	Lelio R Paula	10/2015
5092	5*2^289556-3	87166	Lelio R Paula	08/2014
5093	2^289543-112735	87162	Enzo Doria	06/2014
5094	8*3^182655-7	87150	Lelio R Paula	08/2014
5095	2*10^87144+81	87145	Robert Price	01/2017
5096	7^103106+2*3^103106	87135	Mike Oakes	08/2010
5097	8*3^182614+7	87130	Lelio R Paula	08/2014
5098	(2^289368-509203)/9	87108	Lelio R Paula	01/2013
5099	3^182566+14	87107	Robert Price	09/2013
5100	(3^182385-5)/2	87020	Lelio R Paula	01/2013
5101	11^83534-8	86992	Lelio R Paula	11/2015
5102	4^144479-14267	86986	Mike Oakes	03/2011
5103	(145*10^86982-1)/9	86984	Serge Batalov	12/2014
5104	(151*10^86963-1)/3	86965	Robert Price	04/2017
5105	15^73940-58	86961	Lelio R Paula	11/2015
5106	2^288761-113143	86926	Enzo Doria	07/2014
5107	2^288747+3083	86922	Yves Minet	03/2011
5108	30^58842+29	86917	Norbert Schneider	03/2017
5109	(10^86906-13)/3	86906	Robert Price	02/2017
5110	2^288692-110027	86905	Enzo Doria	04/2014
5111	(2^288682+7)/259895449	86894	Lelio R Paula	01/2013
5112	(2^288636+47)/1293	86885	Lelio R Paula	01/2013
5113	3^182089-34	86879	Robert Price	11/2013
5114	2^288543-109801	86861	Enzo Doria	04/2014
5115	60^48847-59	86858	Norbert Schneider	10/2014
5116	2^288470-64875	86839	Lelio R Paula	10/2013
5117	10^86816+32997	86817	Patrick De Geest	07/2013
5118	10^86816-99	86816	Robert Price	05/2011
5119	(89*10^86802-539)/9	86803	Robert Price	11/2017
5120	41487!2+256	86786	Robert Price	01/2015
5121	(5*2^288301-1)/999	86785	Lelio R Paula	02/2014
5122	2^288243+76043	86770	Enzo Doria	04/2016
5123	(29*2^288232+1)/15	86767	Lelio R Paula	01/2013
5124	9*6^111495+5	86761	Lelio R Paula	10/2014
5125	(5*2^288202+1)/81	86757	Lelio R Paula	01/2013
5126	9*7^102654-2	86754	Lelio R Paula	10/2014
5127	2^288122-112841	86734	Enzo Doria	06/2014
5128	5^124062-68	86716	Lelio R Paula	10/2015
5129	(2^288007-3)/125	86697	Lelio R Paula	01/2013
5130	379*10^86691+9	86694	Arkadiusz Wesolowski	10/2011
5131	7^102555+48	86670	Lelio R Paula	10/2015
5132	77779!4+2	86660	Robert Price	08/2017
5133	2^287809-111355	86640	Enzo Doria	05/2014
5134	(47*2^287795+1)/7	86636	Lelio R Paula	04/2015
5135	9*7^102504+8	86627	Lelio R Paula	10/2014
5136	3^181551+32	86622	Robert Price	11/2013
5137	2^287735-521347	86617	Paul Bourdelais	05/2013
5138	(1017*2^287600-1)/91	86578	Lelio R Paula	04/2015
5139	2^287540-112967	86559	Enzo Doria	06/2014
5140	3^181407+20	86554	Robert Price	10/2013
5141	(13*10^86546+83)/3	86547	Robert Price	09/2016
5142	3^181378-2^(181378-1)	86540	Robert Price	01/2016
5143	83^45080-2	86513	Lelio R Paula	08/2013
5144	(78557*2^287351+1)/611	86504	Lelio R Paula	06/2014
5145	25*29^59147+20936	86498	Curtis Bright	05/2015
5146	2^287298+1871359	86486	Enzo Doria	05/2016
5147	118^41740-117	86481	Norbert Schneider	08/2018
5148	3*10^86478+89	86479	Robert Price	03/2017
5149	2^287272-79049	86478	Paul Bourdelais	02/2012
5150	9067052((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
5151	8118242((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
5152	7790642((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
5153	7683852((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
5154	7008912((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
5155	6523202((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
5156	3779202((10^86453-1)/9)+1	86458	Danilo Nitsche	01/2016
5157	2550602((10^86453-1)/9)+1	86458	Danilo Nitsche	01/2016
5158	1871112((10^86453-1)/9)+1	86458	Danilo Nitsche	01/2016
5159	(10^86453-1)/9	86453	Lew Baxter	10/2000
5160	87^44563-86^44563	86431	Robert Price	05/2015
5161	6^111057+61	86420	Lelio R Paula	12/2015
5162	2^287057-109909	86413	Enzo Doria	04/2014
5163	5^123608+22	86399	Lelio R Paula	10/2015
5164	(31*10^86364-121)/9	86365	Robert Price	06/2016
5165	2^286859+71663	86354	Enzo Doria	04/2016
5166	2^286740+29835	86318	Lelio R Paula	10/2013
5167	2*10^86310+9^86310	86311	Mike Oakes	05/2011
5168	11^82878-1860	86309	Enzo Doria	12/2012
5169	2^286547+16095	86260	Lelio R Paula	10/2013
5170	(58*10^86242+329)/9	86243	Robert Price	11/2017
5171	2^286455-110427	86232	Enzo Doria	05/2014
5172	(37*10^86230+53)/9	86231	Robert Price	05/2015
5173	8*3^180700+5	86217	Lelio R Paula	08/2014
5174	3^180697-40	86215	Lelio R Paula	12/2015
5175	(13*2^286318-1)/13257	86188	Lelio R Paula	02/2014
5176	2^286165+77	86145	Lelio R Paula	08/2012
5177	9*2^286140+7	86138	Lelio R Paula	08/2014
5178	(29*2^286108-1)/2002367	86123	Lelio R Paula	02/2014
5179	10^86110+161113	86111	Patrick De Geest	07/2013
5180	10^86110-69	86110	Robert Price	05/2011
5181	2^286036-869688105	86106	Lelio R Paula	07/2016
5182	(77*10^86072+31)/9	86073	Robert Price	10/2015
5183	2^285923+345	86072	Lelio R Paula	09/2013
5184	13^77266-90	86070	Lelio R Paula	11/2015
5185	2^285910-458903	86068	Enzo Doria	04/2015
5186	2^285904-125	86066	Lelio R Paula	08/2012
5187	2^285836+65835	86046	Lelio R Paula	09/2013
5188	(2^285766+78557)/3	86024	Lelio R Paula	01/2013
5189	(5*10^86011-107)/3	86012	Robert Price	01/2017
5190	6^110522+163	86003	Lelio R Paula	12/2015
5191	41^53323-40^53323	85999	Robert Price	07/2012
5192	2^285678-109617	85998	Enzo Doria	04/2014
5193	6^110506-16673	85991	Enzo Doria	02/2013
5195	2^285569-741	85965	Lelio R Paula	09/2013
5194	(32*10^85964+31)/9	85965	Robert Price	05/2015
5196	133^40466+132	85944	Norbert Schneider	02/2019
5197	6*10^85910-7	85911	Dmitry Domanov	11/2010
5198	(412*10^85897-7)/9	85899	Robert Price	10/2017
5199	4*10^85881+63	85882	Robert Price	06/2016
5200	(10^85864+53)/9	85864	Robert Price	01/2015
5201	2^285230+345	85863	Lelio R Paula	09/2013
5202	(5*10^85855-473)/9	85855	Robert Price	12/2017
5203	2^285199+75683	85854	Enzo Doria	04/2016
5204	(76*10^85847-211)/9	85848	Robert Price	10/2017
5205	p(17832)#/2+512	85845	Robert Price	05/2017
5206	(16*10^85839+167)/3	85840	Robert Price	10/2017
5207	11^82426-1230	85838	Enzo Doria	11/2012
5208	2^285113-109881	85828	Enzo Doria	04/2014
5209	5^122746-92	85796	Lelio R Paula	10/2015
5210	2^285001-113461	85794	Enzo Doria	08/2014
5211	(11*10^85782-131)/3	85783	Robert Price	02/2017
5212	2^284913-110491	85768	Enzo Doria	05/2014
5213	6^110220+47	85768	Lelio R Paula	12/2015
5214	3*6^110202-5	85755	Lelio R Paula	10/2014
5215	(157^39047-1)/156	85742	Alexander Zhirkov	06/2016
5216	(3^179705+7)/250	85739	Lelio R Paula	12/2012
5217	2^284734-6555	85714	Lelio R Paula	09/2013
5218	(10^85712+53)/9	85712	Robert Price	01/2015
5219	3*10^85703+11	85704	Robert Price	11/2017
5220	(6883*2^284668-1)/3	85697	Lelio R Paula	04/2015
5221	20^65855+83	85680	Lelio R Paula	01/2016
5222	6^110105+53	85679	Lelio R Paula	12/2015
5223	(10^85666-97)/3	85666	Robert Kinser	10/2017
5225	2^284567-7605	85664	Lelio R Paula	09/2013
5224	9*5^122555-2	85664	Lelio R Paula	10/2014
5226	5^122554-14	85662	Lelio R Paula	10/2015
5227	9*5^122543+4	85655	Lelio R Paula	10/2014
5228	3^179489-2^(179489-1)	85639	Robert Price	01/2016
5229	2^284429+177	85622	Lelio R Paula	08/2012
5230	2*3^179452+5	85621	Lelio R Paula	07/2014
5231	(19^66919+3^66919)/22	85572	Robert Price	07/2013
5232	66^47023-65	85561	Norbert Schneider	11/2014
5233	6^109943+13	85553	Lelio R Paula	12/2015
5234	(2^284167-509203)/34564775	85536	Lelio R Paula	01/2013
5235	2^284133-3	85533	M. Frind & P. Underwood	07/2002
5236	2^284113+315	85527	Lelio R Paula	09/2013
5237	(28*10^85500+149)/3	85501	Robert Price	10/2017
5238	(16*10^85495-19)/3	85496	Robert Price	03/2016
5239	2^284004+177	85494	Lelio R Paula	08/2012
5240	(16*10^85473-91)/3	85474	Robert Price	06/2016
5241	3^179120+22	85462	Robert Price	12/2013
5242	2^283872-2792249	85454	Enzo Doria	03/2016
5243	(29*10^85438+259)/9	85439	Robert Price	04/2017
5244	2^283817+82875	85438	Lelio R Paula	09/2013
5245	(2^283815-5)/201	85435	Lelio R Paula	01/2013
5246	2^283796-125	85432	Lelio R Paula	08/2012
5247	(29*2^283784-1)/13	85428	Lelio R Paula	02/2014
5248	15^72592-28	85375	Lelio R Paula	11/2015
5249	2^283604-58695	85374	Lelio R Paula	09/2013
5250	(44*10^85370-503)/9	85371	Robert Price	10/2017

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PRP Records

Probable Primes Top 10000

(252675 PRPs in the top)