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) !!!

Submit your PRPs

See the Top discoverers
See the Latest PRPs
Search by form


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	734^30453+30453^734	87270	Norbert Schneider	04/2017
4752	12^80855+29	87258	Lelio R Paula	11/2015
4753	3*6^112119-5	87247	Lelio R Paula	10/2014
4754	12^80806+79	87205	Lelio R Paula	11/2015
4755	91382^9+9^91382	87201	Andrey Kulsha	11/2004
4756	(21181*2^289657+1)/81	87198	Lelio R Paula	06/2014
4757	6^112054-47	87195	Lelio R Paula	12/2015
4758	(55459*2^289632+1)/55	87191	Lelio R Paula	06/2014
4759	15^74131-68	87185	Lelio R Paula	11/2015
4760	2^289583-741	87174	Lelio R Paula	10/2013
4761	7^103146+12	87169	Lelio R Paula	10/2015
4762	5*2^289556-3	87166	Lelio R Paula	08/2014
4763	2^289543-112735	87162	Enzo Doria	06/2014
4764	8*3^182655-7	87150	Lelio R Paula	08/2014
4765	2*10^87144+81	87145	Robert Price	01/2017
4766	7^103106+2*3^103106	87135	Mike Oakes	08/2010
4767	8*3^182614+7	87130	Lelio R Paula	08/2014
4768	(2^289368-509203)/9	87108	Lelio R Paula	01/2013
4769	3^182566+14	87107	Robert Price	09/2013
4770	(3^182385-5)/2	87020	Lelio R Paula	01/2013
4771	11^83534-8	86992	Lelio R Paula	11/2015
4772	4^144479-14267	86986	Mike Oakes	03/2011
4773	(145*10^86982-1)/9	86984	Serge Batalov	12/2014
4774	(151*10^86963-1)/3	86965	Robert Price	04/2017
4775	15^73940-58	86961	Lelio R Paula	11/2015
4776	2^288761-113143	86926	Enzo Doria	07/2014
4777	2^288747+3083	86922	Yves Minet	03/2011
4778	30^58842+29	86917	Norbert Schneider	03/2017
4779	(10^86906-13)/3	86906	Robert Price	02/2017
4780	2^288692-110027	86905	Enzo Doria	04/2014
4781	(2^288682+7)/259895449	86894	Lelio R Paula	01/2013
4782	(2^288636+47)/1293	86885	Lelio R Paula	01/2013
4783	3^182089-34	86879	Robert Price	11/2013
4784	2^288543-109801	86861	Enzo Doria	04/2014
4785	60^48847-59	86858	Norbert Schneider	10/2014
4786	2^288470-64875	86839	Lelio R Paula	10/2013
4787	10^86816+32997	86817	Patrick De Geest	07/2013
4788	10^86816-99	86816	Robert Price	05/2011
4789	(89*10^86802-539)/9	86803	Robert Price	11/2017
4790	41487!2+256	86786	Robert Price	01/2015
4791	(5*2^288301-1)/999	86785	Lelio R Paula	02/2014
4792	2^288243+76043	86770	Enzo Doria	04/2016
4793	(29*2^288232+1)/15	86767	Lelio R Paula	01/2013
4794	9*6^111495+5	86761	Lelio R Paula	10/2014
4795	(5*2^288202+1)/81	86757	Lelio R Paula	01/2013
4796	9*7^102654-2	86754	Lelio R Paula	10/2014
4797	2^288122-112841	86734	Enzo Doria	06/2014
4798	5^124062-68	86716	Lelio R Paula	10/2015
4799	(2^288007-3)/125	86697	Lelio R Paula	01/2013
4800	379*10^86691+9	86694	Arkadiusz Wesolowski	10/2011
4801	7^102555+48	86670	Lelio R Paula	10/2015
4802	77779!4+2	86660	Robert Price	08/2017
4803	2^287809-111355	86640	Enzo Doria	05/2014
4804	(47*2^287795+1)/7	86636	Lelio R Paula	04/2015
4805	9*7^102504+8	86627	Lelio R Paula	10/2014
4806	3^181551+32	86622	Robert Price	11/2013
4807	2^287735-521347	86617	Paul Bourdelais	05/2013
4808	(1017*2^287600-1)/91	86578	Lelio R Paula	04/2015
4809	2^287540-112967	86559	Enzo Doria	06/2014
4810	3^181407+20	86554	Robert Price	10/2013
4811	(13*10^86546+83)/3	86547	Robert Price	09/2016
4812	3^181378-2^(181378-1)	86540	Robert Price	01/2016
4813	83^45080-2	86513	Lelio R Paula	08/2013
4814	(78557*2^287351+1)/611	86504	Lelio R Paula	06/2014
4815	25*29^59147+20936	86498	Curtis Bright	05/2015
4816	2^287298+1871359	86486	Enzo Doria	05/2016
4817	118^41740-117	86481	Norbert Schneider	08/2018
4818	3*10^86478+89	86479	Robert Price	03/2017
4819	2^287272-79049	86478	Paul Bourdelais	02/2012
4820	9067052((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
4821	8118242((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
4822	7790642((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
4823	7683852((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
4824	7008912((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
4825	6523202((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
4826	3779202((10^86453-1)/9)+1	86458	Danilo Nitsche	01/2016
4827	2550602((10^86453-1)/9)+1	86458	Danilo Nitsche	01/2016
4828	1871112((10^86453-1)/9)+1	86458	Danilo Nitsche	01/2016
4829	(10^86453-1)/9	86453	Lew Baxter	10/2000
4830	87^44563-86^44563	86431	Robert Price	05/2015
4831	6^111057+61	86420	Lelio R Paula	12/2015
4832	2^287057-109909	86413	Enzo Doria	04/2014
4833	5^123608+22	86399	Lelio R Paula	10/2015
4834	(31*10^86364-121)/9	86365	Robert Price	06/2016
4835	2^286859+71663	86354	Enzo Doria	04/2016
4836	2^286740+29835	86318	Lelio R Paula	10/2013
4837	2*10^86310+9^86310	86311	Mike Oakes	05/2011
4838	11^82878-1860	86309	Enzo Doria	12/2012
4839	2^286547+16095	86260	Lelio R Paula	10/2013
4840	(58*10^86242+329)/9	86243	Robert Price	11/2017
4841	2^286455-110427	86232	Enzo Doria	05/2014
4842	(37*10^86230+53)/9	86231	Robert Price	05/2015
4843	8*3^180700+5	86217	Lelio R Paula	08/2014
4844	3^180697-40	86215	Lelio R Paula	12/2015
4845	(13*2^286318-1)/13257	86188	Lelio R Paula	02/2014
4846	2^286165+77	86145	Lelio R Paula	08/2012
4847	9*2^286140+7	86138	Lelio R Paula	08/2014
4848	(29*2^286108-1)/2002367	86123	Lelio R Paula	02/2014
4849	10^86110+161113	86111	Patrick De Geest	07/2013
4850	10^86110-69	86110	Robert Price	05/2011
4851	2^286036-869688105	86106	Lelio R Paula	07/2016
4852	(77*10^86072+31)/9	86073	Robert Price	10/2015
4853	2^285923+345	86072	Lelio R Paula	09/2013
4854	13^77266-90	86070	Lelio R Paula	11/2015
4855	2^285910-458903	86068	Enzo Doria	04/2015
4856	2^285904-125	86066	Lelio R Paula	08/2012
4857	2^285836+65835	86046	Lelio R Paula	09/2013
4858	(2^285766+78557)/3	86024	Lelio R Paula	01/2013
4859	(5*10^86011-107)/3	86012	Robert Price	01/2017
4860	6^110522+163	86003	Lelio R Paula	12/2015
4861	41^53323-40^53323	85999	Robert Price	07/2012
4862	2^285678-109617	85998	Enzo Doria	04/2014
4863	6^110506-16673	85991	Enzo Doria	02/2013
4865	2^285569-741	85965	Lelio R Paula	09/2013
4864	(32*10^85964+31)/9	85965	Robert Price	05/2015
4866	6*10^85910-7	85911	Dmitry Domanov	11/2010
4867	(412*10^85897-7)/9	85899	Robert Price	10/2017
4868	4*10^85881+63	85882	Robert Price	06/2016
4869	(10^85864+53)/9	85864	Robert Price	01/2015
4870	2^285230+345	85863	Lelio R Paula	09/2013
4871	(5*10^85855-473)/9	85855	Robert Price	12/2017
4872	2^285199+75683	85854	Enzo Doria	04/2016
4873	(76*10^85847-211)/9	85848	Robert Price	10/2017
4874	p(17832)#/2+512	85845	Robert Price	05/2017
4875	(16*10^85839+167)/3	85840	Robert Price	10/2017
4876	11^82426-1230	85838	Enzo Doria	11/2012
4877	2^285113-109881	85828	Enzo Doria	04/2014
4878	5^122746-92	85796	Lelio R Paula	10/2015
4879	2^285001-113461	85794	Enzo Doria	08/2014
4880	(11*10^85782-131)/3	85783	Robert Price	02/2017
4881	2^284913-110491	85768	Enzo Doria	05/2014
4882	6^110220+47	85768	Lelio R Paula	12/2015
4883	3*6^110202-5	85755	Lelio R Paula	10/2014
4884	(157^39047-1)/156	85742	Alexander Zhirkov	06/2016
4885	(3^179705+7)/250	85739	Lelio R Paula	12/2012
4886	2^284734-6555	85714	Lelio R Paula	09/2013
4887	(10^85712+53)/9	85712	Robert Price	01/2015
4888	3*10^85703+11	85704	Robert Price	11/2017
4889	(6883*2^284668-1)/3	85697	Lelio R Paula	04/2015
4890	20^65855+83	85680	Lelio R Paula	01/2016
4891	6^110105+53	85679	Lelio R Paula	12/2015
4892	(10^85666-97)/3	85666	Robert Kinser	10/2017
4894	2^284567-7605	85664	Lelio R Paula	09/2013
4893	9*5^122555-2	85664	Lelio R Paula	10/2014
4895	5^122554-14	85662	Lelio R Paula	10/2015
4896	9*5^122543+4	85655	Lelio R Paula	10/2014
4897	3^179489-2^(179489-1)	85639	Robert Price	01/2016
4898	2^284429+177	85622	Lelio R Paula	08/2012
4899	2*3^179452+5	85621	Lelio R Paula	07/2014
4900	(19^66919+3^66919)/22	85572	Robert Price	07/2013
4901	66^47023-65	85561	Norbert Schneider	11/2014
4902	6^109943+13	85553	Lelio R Paula	12/2015
4903	(2^284167-509203)/34564775	85536	Lelio R Paula	01/2013
4904	2^284133-3	85533	M. Frind & P. Underwood	07/2002
4905	2^284113+315	85527	Lelio R Paula	09/2013
4906	(28*10^85500+149)/3	85501	Robert Price	10/2017
4907	(16*10^85495-19)/3	85496	Robert Price	03/2016
4908	2^284004+177	85494	Lelio R Paula	08/2012
4909	(16*10^85473-91)/3	85474	Robert Price	06/2016
4910	3^179120+22	85462	Robert Price	12/2013
4911	2^283872-2792249	85454	Enzo Doria	03/2016
4912	(29*10^85438+259)/9	85439	Robert Price	04/2017
4913	2^283817+82875	85438	Lelio R Paula	09/2013
4914	(2^283815-5)/201	85435	Lelio R Paula	01/2013
4915	2^283796-125	85432	Lelio R Paula	08/2012
4916	(29*2^283784-1)/13	85428	Lelio R Paula	02/2014
4917	15^72592-28	85375	Lelio R Paula	11/2015
4918	2^283604-58695	85374	Lelio R Paula	09/2013
4919	(44*10^85370-503)/9	85371	Robert Price	10/2017
4920	496^31671+31671^496	85369	Norbert Schneider	07/2017
4921	(15*2^283583-1)/103051	85364	Lelio R Paula	02/2014
4922	15^72572+92	85352	Lelio R Paula	11/2015
4923	2^283473-1615	85334	Lelio R Paula	09/2013
4924	2^283466-15	85332	Lelio R Paula	08/2012
4925	11^81916-7020	85307	Enzo Doria	02/2013
4926	6^109626-7	85306	Lelio R Paula	11/2014
4927	2^283374-110327	85305	Enzo Doria	05/2014
4928	33*10^85297+7	85299	Robert Price	07/2016
4929	18^67933+41	85275	Lelio R Paula	11/2015
4930	2^283271-109341	85274	Enzo Doria	04/2014
4931	(25*10^85249-73)/3	85250	Robert Price	09/2016
4932	2*5^121959+3	85246	Lelio R Paula	10/2014
4933	19834^19834+8947	85235	Henri Lifchitz	11/2004
4934	2^283140+1915	85234	Lelio R Paula	09/2013
4935	3*10^85227-97	85228	Robert Price	08/2017
4936	(16*10^85221-31)/3	85222	Robert Price	03/2016
4937	2^283083+1869383	85217	Enzo Doria	05/2016
4938	(24737*2^283051+1)/17	85211	Lelio R Paula	06/2014
4939	(2^283032+78557)/3	85201	Lelio R Paula	01/2013
4940	2^283026-109893	85200	Enzo Doria	04/2014
4941	(2^283012+78557)/129	85193	Lelio R Paula	01/2013
4942	(10^(242589+1)+7210^42589-1)/9	85179	Robert Price	09/2017
4943	2^282860-109727	85150	Enzo Doria	04/2014
4944	2^282819+1869413	85138	Enzo Doria	05/2016
4945	3^178428+2	85132	Ray Chandler	07/2011
4946	(22699*2^282742+1)/73	85117	Lelio R Paula	06/2014
4947	(16^70687+5^70687)/21	85115	Robert Price	07/2013
4948	(3^178352-2)/7	85095	Lelio R Paula	12/2012
4949	11^81699-2790	85081	Enzo Doria	12/2012
4950	2^282612-95	85075	Lelio R Paula	08/2012
4951	2^282609-4069	85074	Yves Minet	02/2018
4952	75^45366-2	85065	Lelio R Paula	08/2013
4953	2^282511+69	85045	Lelio R Paula	08/2012
4954	69^46249+2	85045	Lelio R Paula	06/2013
4955	3^178226+10	85036	Robert Price	10/2013
4956	(182*10^85017+43)/9	85019	Robert Price	11/2017
4957	(14*10^85010+73)/3	85011	Robert Price	04/2016
4958	9*2^282338-7	84994	Lelio R Paula	08/2014
4959	(9913*2^282330-1)/1578003	84988	Lelio R Paula	04/2015
4960	2^282203+5	84952	Lelio R Paula	08/2012
4961	2^282184+13	84946	Lelio R Paula	08/2012
4962	11^81568-2400	84945	Enzo Doria	12/2012
4963	11^81562-2340	84939	Enzo Doria	12/2012
4964	(41*10^84927+31)/9	84928	Robert Price	05/2015
4965	(2*10^84904-17)/3	84904	Robert Price	08/2014
4966	(4^141017+23)/3	84901	Robert Price	02/2017
4967	6^109100-18653	84897	Enzo Doria	03/2013
4968	2^281973+1025	84883	Lelio R Paula	09/2013
4969	2^281951-109651	84876	Enzo Doria	04/2014
4970	11^81491-5430	84865	Enzo Doria	01/2013
4971	((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
4972	2^281825-1861483	84838	Enzo Doria	03/2016
4973	2^281809-97305	84833	Lelio R Paula	09/2013
4974	2^281780-114893	84825	Enzo Doria	05/2015
4975	3^177719+64	84794	Lelio R Paula	12/2015
4977	2^281675-199	84793	Lelio R Paula	08/2012
4976	2^281673-111223	84793	Enzo Doria	05/2014
4978	(4*10^84779+149)/9	84779	Robert Price	03/2017
4979	(72*10^84772-27)/9	84773	Ray Chandler	01/2011
4980	11^81398-630	84768	Enzo Doria	11/2012
4981	(25*2^281577-1)/23	84764	Lelio R Paula	02/2014
4982	2^281500-455	84740	Yves Minet	03/2012
4983	10^84725+1145141919	84726	Marisa Kirisame	03/2015
4984	10^84725+142041	84726	Patrick De Geest	10/2015
4985	10^84725-138677	84725	Patrick De Geest	02/2016
4986	76^45044+75	84720	Norbert Schneider	02/2015
4987	54^48897-53	84709	Norbert Schneider	08/2014
4988	(9913*2^281377-1)/65	84706	Lelio R Paula	04/2015
4989	Phi(171124,10)/29946701/7761329021/58560344041	84700	Maksym Voznyy	11/2015
4990	2^281337-111223	84691	Enzo Doria	05/2014
4991	2^281308+54615	84683	Lelio R Paula	09/2013
4992	7*5^121144-6	84677	Lelio R Paula	10/2014
4993	(2^281252+47)/3	84665	Lelio R Paula	01/2013
4994	11^81297-3150	84663	Enzo Doria	12/2012
4995	2^281208-303	84653	Yves Minet	02/2012
4996	197^36892-2	84648	Lelio R Paula	10/2017
4997	(21*2^281187+1)/2483	84644	Lelio R Paula	01/2013
4998	11^81247-84	84611	Lelio R Paula	10/2015
4999	17^68747-64	84590	Lelio R Paula	11/2015
5000	5^121018-15596	84588	Enzo Doria	02/2013

Find by discoverer :

PRP Records

Probable Primes Top 10000

(225451 PRPs in the top)