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	2^280388+117	84406	Lelio R Paula	08/2012
4752	2^280389-566533	84406	Paul Bourdelais	03/2013
4753	(141584^16384+1)/65537	84390	Syoichiro Yamada	06/2008
4754	2^280240-173	84361	Lelio R Paula	08/2012
4755	(184*10^84348-1)/3	84350	Robert Price	02/2017
4756	4*10^84346+93	84347	Robert Price	01/2017
4757	7*2^280156-5	84337	Lelio R Paula	08/2014
4758	8*7^99782-3	84327	Lelio R Paula	10/2014
4760	2^280116+133	84324	Lelio R Paula	08/2012
4759	2^280118+54615	84324	Lelio R Paula	09/2013
4761	(509203*2^280090-1)/3	84321	Lelio R Paula	04/2015
4762	6^108354+47	84316	Lelio R Paula	12/2015
4763	10^84305+141963	84306	Patrick De Geest	07/2013
4764	10^84305-57	84305	Robert Price	05/2011
4765	9^88339+38^88339-24^88339-3*2^88339	84297	Mike Oakes	01/2011
4766	3^176648-112804	84283	Enzo Doria	06/2014
4767	6^108310+115	84282	Lelio R Paula	12/2015
4768	(11*2^279968-1)/5	84280	Lelio R Paula	02/2014
4769	6^108288-16643	84265	Enzo Doria	02/2013
4770	2^279917-58695	84264	Lelio R Paula	08/2013
4771	65^46477+36	84259	Lelio R Paula	01/2016
4772	2^279866-1907	84249	Yves Minet	05/2013
4773	(3^176580-5)/28076	84246	Lelio R Paula	12/2012
4774	(p(17530)#+4)/2	84246	Robert Price	09/2017
4775	(2*10^84239+1)/3	84239	Serge Batalov	07/2009
4777	18^67103-41	84233	Lelio R Paula	11/2015
4776	20^64743-43	84233	Lelio R Paula	01/2016
4778	143^39070+39070^143	84209	Serge Batalov	05/2014
4779	11^80857-5400	84204	Enzo Doria	01/2013
4780	(13*10^84179+161)/3	84180	Robert Price	04/2017
4781	2^279634-110405	84179	Enzo Doria	05/2014
4782	(74*10^84170+313)/9	84171	Robert Price	11/2017
4783	2^279582-1017	84163	Lelio R Paula	08/2013
4784	(22*10^84159-19)/3	84160	Robert Price	02/2017
4785	p(17513)#/2+512	84156	Robert Price	05/2017
4786	(19*10^84144-43)/3	84145	Robert Price	10/2017
4787	(9*2^279507-1)/137	84139	Lelio R Paula	02/2014
4788	11^80792-810	84137	Enzo Doria	11/2012
4789	(97*10^84134-1)/3	84136	Serge Batalov	12/2014
4790	p(17507)#/2+32	84125	Robert Price	12/2016
4791	21485^8224+8224^21485	84116	Hans Havermann	04/2017
4792	3^176294-340	84114	Lelio R Paula	12/2015
4793	(3^176287+4)/2191	84107	Lelio R Paula	12/2012
4794	2^279388-719	84105	Yves Minet	05/2012
4795	(22699*2^279378+1)/221	84104	Lelio R Paula	06/2014
4796	2^279332-110447	84088	Enzo Doria	05/2014
4797	2^279320+7	84084	Lelio R Paula	06/2012
4798	127^39966-2	84081	Lelio R Paula	10/2017
4799	(11*2^279240-1)/95	84059	Lelio R Paula	02/2014
4800	2^279218-111347	84053	Enzo Doria	05/2014
4801	35^54435+2	84052	Lelio R Paula	05/2013
4802	(31*2^279191-1)/12511523	84040	Lelio R Paula	02/2014
4803	20996^10059+10059^20996	84038	Hans Havermann	05/2017
4804	97*10^84033-3	84035	Robert Price	01/2017
4805	21234^9067+9067^21234	84033	Hans Havermann	05/2017
4806	2^279095-109717	84016	Enzo Doria	04/2014
4807	14^73282-99	83991	Lelio R Paula	11/2015
4808	21457^8200+8200^21457	83979	Hans Havermann	06/2017
4809	89*10^83976-7	83978	Robert Price	03/2017
4810	2^278955+173	83974	Lelio R Paula	06/2012
4811	(7*2^278851+1)/39	83942	Lelio R Paula	12/2012
4812	(9913*2^278844-1)/40803	83940	Lelio R Paula	04/2015
4813	5^120076-14846	83930	Enzo Doria	02/2013
4814	(85*10^83921-1)/3	83923	Robert Price	07/2017
4815	(2^278770-3)/23	83917	Lelio R Paula	12/2012
4816	(10^83916+449)/9	83916	Serge Batalov	12/2014
4817	2^278715+99	83902	Lelio R Paula	06/2012
4818	40235!2-2^40235	83899	Robert Price	09/2015
4819	2^278698-171	83897	Lelio R Paula	06/2012
4820	(19*10^83894-43)/3	83895	Robert Price	10/2017
4821	6^107802+25	83887	Lelio R Paula	12/2015
4822	8*10^83880+39	83881	Robert Price	01/2017
4823	(58*10^83878+23)/9	83879	Robert Price	09/2015
4824	7^99244-90	83871	Lelio R Paula	10/2015
4825	2^278554+4257	83854	Lelio R Paula	08/2013
4826	2^278504-109619	83839	Enzo Doria	04/2014
4827	2^278499+1870433	83837	Enzo Doria	05/2016
4828	105^41475+104	83829	Norbert Schneider	11/2016
4829	15^71276-68	83828	Lelio R Paula	11/2015
4830	2^278464-216413	83827	Enzo Doria	04/2013
4831	(76*10^83816-211)/9	83817	Robert Price	10/2017
4832	(8*10^83811-101)/3	83812	Robert Price	10/2017
4833	2^278400+40755	83807	Lelio R Paula	08/2013
4834	(9*2^278381-1)/7	83802	Lelio R Paula	02/2014
4835	39^87813+6^87813+24^87813	83796	Mike Oakes	12/2010
4836	19551^19268+19268^19551	83773	Hans Havermann	05/2017
4837	20625^11522+11522^20625	83770	Hans Havermann	05/2017
4838	(44*10^83768-791)/9	83769	Robert Price	10/2017
4839	(87^43189+1)/88	83764	Paul Bourdelais	08/2017
4840	2^278235-49	83758	Lelio R Paula	06/2012
4841	23543^3610+3610^23543	83755	Hans Havermann	05/2017
4843	18^66711-91	83741	Lelio R Paula	11/2015
4842	4*10^83740-89	83741	Robert Price	08/2017
4844	(3*2^278172-1)/11	83738	Lelio R Paula	02/2014
4845	(15*29^57251+2561)/28	83724	Curtis Bright	05/2015
4846	4*7^99059-9	83716	Lelio R Paula	10/2014
4847	(2^278128-3)/126844724149	83714	Lelio R Paula	12/2012
4848	2^278077+1867211	83710	Enzo Doria	03/2016
4849	2^278059-27	83705	Lelio R Paula	06/2012
4850	214^35917+35917^214	83702	Norbert Schneider	12/2014
4851	(23*10^83693+7)/3	83694	Robert Price	10/2015
4852	85^43375-2	83689	Lelio R Paula	09/2013
4853	5*3^175360+4	83669	Lelio R Paula	07/2014
4854	(23^61441-1)/22	83665	Robert Price	01/2012
4855	20091^14596+14596^20091	83664	Hans Havermann	03/2017
4856	2^277907-110629	83659	Enzo Doria	05/2014
4857	19522^19283+19283^19522	83656	Hans Havermann	04/2017
4858	8*5^119664-3	83643	Lelio R Paula	10/2014
4859	8*3^175299-7	83640	Lelio R Paula	07/2014
4860	(26*10^83638-413)/9	83639	Robert Price	10/2017
4861	3^175250+22	83616	Robert Price	12/2013
4862	11^80285+30	83609	Lelio R Paula	10/2015
4863	26870^1293+1293^26870	83609	Hans Havermann	03/2017
4864	2^277691+1874423	83594	Enzo Doria	06/2016
4865	13^75022-60	83571	Lelio R Paula	11/2015
4866	14^72905-51	83559	Lelio R Paula	11/2015
4867	(17*2^277565-1)/543	83554	Lelio R Paula	02/2014
4868	5^119532-12	83550	Lelio R Paula	10/2015
4869	6^107358-16253	83541	Enzo Doria	02/2013
4870	2^277478-460211	83530	Enzo Doria	06/2015
4871	(22*10^83525-7)/3	83526	Erik Branger	09/2014
4872	(30^56543+1)/31	83520	Robert Price	07/2013
4873	2^277417-460783	83511	Paul Bourdelais	04/2013
4874	(22699*2^277387+1)/219	83504	Lelio R Paula	06/2014
4875	(31*2^277383-1)/247	83500	Lelio R Paula	02/2014
4876	21368^8085+8085^21368	83500	Hans Havermann	04/2017
4877	(9*2^277342+1)/13	83489	Lelio R Paula	12/2012
4878	5^119439-66	83485	Lelio R Paula	10/2015
4879	(14*10^83471-101)/3	83472	Robert Price	04/2017
4880	5*6^107263+7	83468	Lelio R Paula	10/2014
4881	(64*10^83461-1)/9	83462	Serge Batalov	11/2010
4882	17^67796-92	83420	Lelio R Paula	11/2015
4883	2^277106-110057	83418	Enzo Doria	04/2014
4884	6^107200-19	83418	Lelio R Paula	12/2015
4885	11^80096-1830	83412	Enzo Doria	12/2012
4886	3^174801+56	83402	Lelio R Paula	12/2015
4887	2^277033-111973	83396	Enzo Doria	05/2014
4888	20519^11572+11572^20519	83378	Hans Havermann	03/2017
4889	20850^9971+9971^20850	83374	Hans Havermann	03/2017
4890	6^107122-18863	83358	Enzo Doria	03/2013
4891	4*10^83354-89	83355	Robert Price	08/2017
4892	3^174697-34	83352	Robert Price	11/2013
4893	(9787*2^276855-1)/2345	83343	Lelio R Paula	04/2015
4894	2^276825+75227	83333	Enzo Doria	04/2016
4895	5^119214+84	83328	Lelio R Paula	10/2015
4896	2^276803-159	83327	Lelio R Paula	06/2012
4897	(3*2^276753-1)/25	83311	Lelio R Paula	02/2014
4898	114^40495+40495^114	83295	Norbert Schneider	12/2014
4899	39967!2+1024	83282	Robert Price	02/2015
4901	2^276641+57	83278	Lelio R Paula	06/2012
4900	35^53934-3414	83278	Enzo Doria	03/2013
4902	(2^276655+78557)/365425	83276	Lelio R Paula	12/2012
4903	2^276615-4035	83270	Lelio R Paula	08/2013
4904	2^276588+1155	83262	Lelio R Paula	08/2013
4906	2^276587-937	83261	Yves Minet	10/2009
4905	2^276584-113183	83261	Enzo Doria	07/2014
4907	(2^276592-1017)/13843739	83256	Lelio R Paula	12/2012
4908	2^276547-109591	83249	Enzo Doria	04/2014
4909	13^74733-32	83249	Lelio R Paula	11/2015
4910	2^276523-2587	83242	Yves Minet	07/2014
4911	18^66311-43	83239	Lelio R Paula	11/2015
4912	11^79919-1530	83228	Enzo Doria	12/2012
4913	2^276468-109745	83226	Enzo Doria	04/2014
4914	2^276462+5385	83224	Lelio R Paula	08/2013
4915	(9787*2^276422-1)/3	83215	Lelio R Paula	04/2015
4917	2^276391-15	83202	Lelio R Paula	06/2012
4916	(4*10^83201+173)/3	83202	Robert Price	01/2017
4918	2^276316-109655	83180	Enzo Doria	04/2014
4919	2^276305-112063	83177	Enzo Doria	06/2014
4920	(10^(241585+1)+5410^41585-1)/9	83171	Robert Price	04/2017
4921	74913!4-2	83161	Robert Price	07/2017
4922	2^276227-1837207	83153	Enzo Doria	05/2015
4923	(2^276227+3)/7	83152	Lelio R Paula	12/2012
4924	2^276184-63389	83140	Paul Bourdelais	02/2012
4925	2^276066-111603	83105	Enzo Doria	05/2014
4926	(2^276028-3)*6-7	83094	Gilbert Mozzo	09/2016
4927	(2^275897+9)/1153	83051	Lelio R Paula	12/2012
4928	2^275879-109807	83048	Enzo Doria	04/2014
4930	F(397379)	83047	Henri Lifchitz	08/2003
4929	U(397379)	83047	Serge Batalov	03/2015
4932	3^174040-14	83039	Robert Price	08/2013
4931	(86*10^83038-221)/9	83039	Robert Price	06/2017
4933	2^275841-6883	83037	Lelio R Paula	07/2011
4934	3^174002-140	83021	Lelio R Paula	12/2015
4935	6^106681+77	83014	Lelio R Paula	12/2015
4936	187^36539-2	83011	Lelio R Paula	10/2017
4937	11^79701-3150	83001	Enzo Doria	12/2012
4938	(55459*2^275657+1)/21	82985	Lelio R Paula	06/2014
4939	(7*10^82960-457)/9	82960	Robert Price	09/2017
4940	2^275535-6855	82945	Lelio R Paula	08/2013
4941	3^173828-14	82938	Robert Price	08/2013
4942	2^275512-109677	82938	Enzo Doria	04/2014
4943	2^275446-110045	82918	Enzo Doria	04/2014
4944	(2^275473+47)/29526097447	82916	Lelio R Paula	12/2012
4945	3^173755-14	82903	Robert Price	08/2013
4946	(182*10^82898+43)/9	82900	Robert Price	11/2017
4947	2^275363-112309	82893	Enzo Doria	06/2014
4948	61^46427-60	82888	Norbert Schneider	10/2014
4949	3*10^82880-7^82880	82881	Mike Oakes	02/2010
4951	2^275290+90195	82871	Lelio R Paula	07/2013
4950	(35*10^82870-71)/9	82871	Robert Price	05/2015
4952	2^275270-1859621	82865	Enzo Doria	03/2016
4953	2^275259+81	82862	Henri Lifchitz	01/2007
4954	(113703^16384+1)/2	82834	Richard Fischer	04/2018
4955	7^98003+98003^7+1	82823	Robert Price	05/2014
4956	10^82790+126043	82791	Patrick De Geest	07/2013
4957	10^82790-47	82790	Robert Price	05/2011
4958	2^274985-112663	82779	Enzo Doria	06/2014
4959	2^274935+15015	82764	Lelio R Paula	07/2013
4960	(17*2^274922+1)/3	82761	Lelio R Paula	12/2012
4961	(43*10^82752-61)/9	82753	Robert Price	06/2015
4962	(3*2^274862+1)/1027	82740	Lelio R Paula	12/2012
4963	(31*2^274848-1)/4065	82736	Lelio R Paula	02/2014
4964	(4^137405+23)/3	82726	Robert Price	02/2017
4965	2^274791-110491	82721	Enzo Doria	05/2014
4966	(11*2^274776-1)/95	82715	Lelio R Paula	02/2014
4967	(47*10^82706-119)/9	82707	Robert Price	09/2017
4968	2^274704-111395	82695	Enzo Doria	05/2014
4969	2^274686-3911	82689	Yves Minet	04/2017
4970	(2^274663-1017)/48871318292279	82669	Lelio R Paula	12/2012
4971	(3^173263-5)/14498	82664	Lelio R Paula	12/2012
4972	2^274511-64875	82637	Lelio R Paula	08/2013
4973	12^76572-83	82636	Lelio R Paula	11/2015
4974	3^173191-2^173191	82634	Mike Oakes	02/2004
4975	14^72072-15	82604	Lelio R Paula	11/2015
4976	(55459*2^274339+1)/3	82589	Lelio R Paula	06/2014
4977	2^274351+123	82588	Lelio R Paula	06/2012
4978	(1017*2^274339-1)/3515	82584	Lelio R Paula	04/2015
4979	6^106086+113	82551	Lelio R Paula	12/2015
4980	(17*10^82540-377)/9	82541	Robert Price	11/2017
4981	2^274093-58695	82511	Lelio R Paula	07/2013
4982	7*10^82509-47	82510	Robert Price	02/2017
4983	2^274081-6555	82507	Lelio R Paula	07/2013
4985	2^274074-274074+1	82505	Robert Price	10/2014
4986	14^71985+47	82505	Lelio R Paula	11/2015
4984	5*10^82504+21	82505	Robert Price	01/2017
4987	6^106014-139	82495	Lelio R Paula	12/2015
4988	(2^274046+47)/753	82494	Lelio R Paula	12/2012
4989	2^274008-1838099	82485	Enzo Doria	05/2015
4990	2^273981-110029	82477	Enzo Doria	04/2014
4991	19^64490-30	82467	Lelio R Paula	12/2015
4992	2^273785+11715	82418	Lelio R Paula	07/2013
4993	8*10^82417+51	82418	Robert Price	05/2017
4994	11^79133-10	82409	Theodore Burton	11/2005
4995	91^42063+90	82404	Norbert Schneider	01/2016
4996	2^273662-63	82381	Lelio R Paula	06/2012
4997	2^273661+255	82381	Lelio R Paula	07/2013
4998	(62*10^82377-17)/9	82378	Robert Price	09/2015
4999	8*10^82360-51	82361	Robert Price	10/2017
5000	(79*10^82347-1)/3	82349	Robert Price	11/2017

Find by discoverer :

PRP Records

Probable Primes Top 10000

(205869 PRPs in the top)