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 ?
5751	17^68747-64	84590	Lelio R Paula	11/2015
5752	5^121018-15596	84588	Enzo Doria	02/2013
5753	6^108702+7	84587	Lelio R Paula	11/2014
5754	10^84582+100677	84583	Patrick De Geest	05/2016
5755	10^84582-8001	84582	Robert Price	03/2016
5756	3*5^121004-8	84579	Lelio R Paula	10/2014
5757	5^120996-84	84573	Lelio R Paula	10/2015
5758	(10223*2^280881+1)/68419	84553	Lelio R Paula	06/2014
5759	2^280852+97681	84545	Yves Minet	08/2004
5760	2^280848-1203	84544	Lelio R Paula	09/2013
5761	5^120946-24	84538	Lelio R Paula	10/2015
5762	2^280810-2111	84533	Yves Minet	08/2013
5763	11^81161-5160	84521	Enzo Doria	01/2013
5764	2^280737-93	84511	Lelio R Paula	08/2012
5765	2^280698+315	84499	Lelio R Paula	09/2013
5766	3^177099-340	84498	Lelio R Paula	12/2015
5767	(5*10^84469-107)/3	84470	Robert Price	01/2017
5768	(3^177002+7)/6696022272161744	84436	Lelio R Paula	12/2012
5769	(2^280500-1017)/823	84436	Lelio R Paula	01/2013
5770	14^73660-5	84424	Lelio R Paula	11/2015
5771	(19*10^84409-61)/3	84410	Robert Price	04/2017
5772	2^280388+117	84406	Lelio R Paula	08/2012
5773	2^280389-566533	84406	Paul Bourdelais	03/2013
5774	(141584^16384+1)/65537	84390	Syoichiro Yamada	06/2008
5775	119^40652+118	84376	Norbert Schneider	09/2018
5776	2^280240-173	84361	Lelio R Paula	08/2012
5777	(184*10^84348-1)/3	84350	Robert Price	02/2017
5778	4*10^84346+93	84347	Robert Price	01/2017
5779	7*2^280156-5	84337	Lelio R Paula	08/2014
5780	8*7^99782-3	84327	Lelio R Paula	10/2014
5781	2^280116+133	84324	Lelio R Paula	08/2012
5782	2^280118+54615	84324	Lelio R Paula	09/2013
5783	(509203*2^280090-1)/3	84321	Lelio R Paula	04/2015
5784	6^108354+47	84316	Lelio R Paula	12/2015
5785	10^84305+141963	84306	Patrick De Geest	07/2013
5786	10^84305-57	84305	Robert Price	05/2011
5787	9^88339+38^88339-24^88339-3*2^88339	84297	Mike Oakes	01/2011
5788	75843!4-32	84295	Robert Price	11/2019
5789	3^176648-112804	84283	Enzo Doria	06/2014
5790	6^108310+115	84282	Lelio R Paula	12/2015
5791	(11*2^279968-1)/5	84280	Lelio R Paula	02/2014
5792	6^108288-16643	84265	Enzo Doria	02/2013
5793	2^279917-58695	84264	Lelio R Paula	08/2013
5794	65^46477+36	84259	Lelio R Paula	01/2016
5795	2^279866-1907	84249	Yves Minet	05/2013
5796	(3^176580-5)/28076	84246	Lelio R Paula	12/2012
5797	(p(17530)#+4)/2	84246	Robert Price	09/2017
5798	(2*10^84239+1)/3	84239	Serge Batalov	07/2009
5799	18^67103-41	84233	Lelio R Paula	11/2015
5800	20^64743-43	84233	Lelio R Paula	01/2016
5801	143^39070+39070^143	84209	Serge Batalov	05/2014
5802	11^80857-5400	84204	Enzo Doria	01/2013
5803	(13*10^84179+161)/3	84180	Robert Price	04/2017
5804	2^279634-110405	84179	Enzo Doria	05/2014
5805	(74*10^84170+313)/9	84171	Robert Price	11/2017
5806	2^279582-1017	84163	Lelio R Paula	08/2013
5807	(22*10^84159-19)/3	84160	Robert Price	02/2017
5808	p(17513)#/2+512	84156	Robert Price	05/2017
5809	(19*10^84144-43)/3	84145	Robert Price	10/2017
5810	(9*2^279507-1)/137	84139	Lelio R Paula	02/2014
5811	11^80792-810	84137	Enzo Doria	11/2012
5812	(97*10^84134-1)/3	84136	Serge Batalov	12/2014
5813	p(17507)#/2+32	84125	Robert Price	12/2016
5814	21485^8224+8224^21485	84116	Hans Havermann	04/2017
5815	3^176294-340	84114	Lelio R Paula	12/2015
5816	(3^176287+4)/2191	84107	Lelio R Paula	12/2012
5817	2^279388-719	84105	Yves Minet	05/2012
5818	(22699*2^279378+1)/221	84104	Lelio R Paula	06/2014
5819	2^279332-110447	84088	Enzo Doria	05/2014
5820	2^279320+7	84084	Lelio R Paula	06/2012
5821	127^39966-2	84081	Lelio R Paula	10/2017
5822	(11*2^279240-1)/95	84059	Lelio R Paula	02/2014
5823	2^279218-111347	84053	Enzo Doria	05/2014
5824	35^54435+2	84052	Lelio R Paula	05/2013
5825	(31*2^279191-1)/12511523	84040	Lelio R Paula	02/2014
5826	20996^10059+10059^20996	84038	Hans Havermann	05/2017
5827	97*10^84033-3	84035	Robert Price	01/2017
5828	21234^9067+9067^21234	84033	Hans Havermann	05/2017
5829	(134569^16384+1)/2	84033	Richard Fischer	06/2018
5830	2^279095-109717	84016	Enzo Doria	04/2014
5831	14^73282-99	83991	Lelio R Paula	11/2015
5832	21457^8200+8200^21457	83979	Hans Havermann	06/2017
5833	89*10^83976-7	83978	Robert Price	03/2017
5834	2^278955+173	83974	Lelio R Paula	06/2012
5835	(7*2^278851+1)/39	83942	Lelio R Paula	12/2012
5836	(9913*2^278844-1)/40803	83940	Lelio R Paula	04/2015
5837	5^120076-14846	83930	Enzo Doria	02/2013
5838	(85*10^83921-1)/3	83923	Robert Price	07/2017
5839	(2^278770-3)/23	83917	Lelio R Paula	12/2012
5840	(10^83916+449)/9	83916	Serge Batalov	12/2014
5842	2^278715+99	83902	Lelio R Paula	06/2012
5841	(132109^16384+1)/2	83902	Richard Fischer	05/2018
5843	40235!2-2^40235	83899	Robert Price	09/2015
5844	2^278698-171	83897	Lelio R Paula	06/2012
5845	(19*10^83894-43)/3	83895	Robert Price	10/2017
5846	6^107802+25	83887	Lelio R Paula	12/2015
5847	8*10^83880+39	83881	Robert Price	01/2017
5848	(58*10^83878+23)/9	83879	Robert Price	09/2015
5849	7^99244-90	83871	Lelio R Paula	10/2015
5850	2^278554+4257	83854	Lelio R Paula	08/2013
5851	2^278504-109619	83839	Enzo Doria	04/2014
5852	2^278499+1870433	83837	Enzo Doria	05/2016
5853	105^41475+104	83829	Norbert Schneider	11/2016
5854	15^71276-68	83828	Lelio R Paula	11/2015
5855	2^278464-216413	83827	Enzo Doria	04/2013
5856	(76*10^83816-211)/9	83817	Robert Price	10/2017
5857	(8*10^83811-101)/3	83812	Robert Price	10/2017
5858	2^278400+40755	83807	Lelio R Paula	08/2013
5859	(9*2^278381-1)/7	83802	Lelio R Paula	02/2014
5860	39^87813+6^87813+24^87813	83796	Mike Oakes	12/2010
5861	19551^19268+19268^19551	83773	Hans Havermann	05/2017
5862	20625^11522+11522^20625	83770	Hans Havermann	05/2017
5863	(44*10^83768-791)/9	83769	Robert Price	10/2017
5864	(87^43189+1)/88	83764	Paul Bourdelais	08/2017
5865	2^278235-49	83758	Lelio R Paula	06/2012
5866	23543^3610+3610^23543	83755	Hans Havermann	05/2017
5868	18^66711-91	83741	Lelio R Paula	11/2015
5867	4*10^83740-89	83741	Robert Price	08/2017
5869	(3*2^278172-1)/11	83738	Lelio R Paula	02/2014
5870	(15*29^57251+2561)/28	83724	Curtis Bright	05/2015
5871	4*7^99059-9	83716	Lelio R Paula	10/2014
5872	(2^278128-3)/126844724149	83714	Lelio R Paula	12/2012
5873	2^278077+1867211	83710	Enzo Doria	03/2016
5874	2^278059-27	83705	Lelio R Paula	06/2012
5875	214^35917+35917^214	83702	Norbert Schneider	12/2014
5876	(23*10^83693+7)/3	83694	Robert Price	10/2015
5877	85^43375-2	83689	Lelio R Paula	09/2013
5878	5*3^175360+4	83669	Lelio R Paula	07/2014
5879	(23^61441-1)/22	83665	Robert Price	01/2012
5880	20091^14596+14596^20091	83664	Hans Havermann	03/2017
5881	2^277907-110629	83659	Enzo Doria	05/2014
5882	19522^19283+19283^19522	83656	Hans Havermann	04/2017
5883	8*5^119664-3	83643	Lelio R Paula	10/2014
5884	8*3^175299-7	83640	Lelio R Paula	07/2014
5885	(26*10^83638-413)/9	83639	Robert Price	10/2017
5886	3^175250+22	83616	Robert Price	12/2013
5888	11^80285+30	83609	Lelio R Paula	10/2015
5887	26870^1293+1293^26870	83609	Hans Havermann	03/2017
5889	2^277691+1874423	83594	Enzo Doria	06/2016
5890	13^75022-60	83571	Lelio R Paula	11/2015
5891	14^72905-51	83559	Lelio R Paula	11/2015
5892	(17*2^277565-1)/543	83554	Lelio R Paula	02/2014
5893	5^119532-12	83550	Lelio R Paula	10/2015
5894	6^107358-16253	83541	Enzo Doria	02/2013
5895	2^277478-460211	83530	Enzo Doria	06/2015
5896	(22*10^83525-7)/3	83526	Erik Branger	09/2014
5897	(30^56543+1)/31	83520	Robert Price	07/2013
5898	2^277417-460783	83511	Paul Bourdelais	04/2013
5899	(22699*2^277387+1)/219	83504	Lelio R Paula	06/2014
5900	(31*2^277383-1)/247	83500	Lelio R Paula	02/2014
5901	21368^8085+8085^21368	83500	Hans Havermann	04/2017
5902	(9*2^277342+1)/13	83489	Lelio R Paula	12/2012
5903	5^119439-66	83485	Lelio R Paula	10/2015
5904	(14*10^83471-101)/3	83472	Robert Price	04/2017
5905	5*6^107263+7	83468	Lelio R Paula	10/2014
5906	(64*10^83461-1)/9	83462	Serge Batalov	11/2010
5907	2^277244-175709	83459	Hans Havermann	10/2018
5908	17^67796-92	83420	Lelio R Paula	11/2015
5909	2^277106-110057	83418	Enzo Doria	04/2014
5910	6^107200-19	83418	Lelio R Paula	12/2015
5911	11^80096-1830	83412	Enzo Doria	12/2012
5912	3^174801+56	83402	Lelio R Paula	12/2015
5913	2^277033-111973	83396	Enzo Doria	05/2014
5914	120^40105-119	83386	Norbert Schneider	09/2018
5915	20519^11572+11572^20519	83378	Hans Havermann	03/2017
5916	20850^9971+9971^20850	83374	Hans Havermann	03/2017
5917	6^107122-18863	83358	Enzo Doria	03/2013
5918	4*10^83354-89	83355	Robert Price	08/2017
5919	3^174697-34	83352	Robert Price	11/2013
5920	(9787*2^276855-1)/2345	83343	Lelio R Paula	04/2015
5921	2^276825+75227	83333	Enzo Doria	04/2016
5922	5^119214+84	83328	Lelio R Paula	10/2015
5923	2^276803-159	83327	Lelio R Paula	06/2012
5924	(3*2^276753-1)/25	83311	Lelio R Paula	02/2014
5925	114^40495+40495^114	83295	Norbert Schneider	12/2014
5926	39967!2+1024	83282	Robert Price	02/2015
5927	2^276641+57	83278	Lelio R Paula	06/2012
5928	35^53934-3414	83278	Enzo Doria	03/2013
5929	(2^276655+78557)/365425	83276	Lelio R Paula	12/2012
5930	2^276615-4035	83270	Lelio R Paula	08/2013
5931	2^276588+1155	83262	Lelio R Paula	08/2013
5932	2^276587-937	83261	Yves Minet	10/2009
5933	2^276584-113183	83261	Enzo Doria	07/2014
5934	(2^276592-1017)/13843739	83256	Lelio R Paula	12/2012
5935	2^276547-109591	83249	Enzo Doria	04/2014
5936	13^74733-32	83249	Lelio R Paula	11/2015
5937	2^276523-2587	83242	Yves Minet	07/2014
5938	18^66311-43	83239	Lelio R Paula	11/2015
5939	11^79919-1530	83228	Enzo Doria	12/2012
5940	2^276468-109745	83226	Enzo Doria	04/2014
5941	2^276462+5385	83224	Lelio R Paula	08/2013
5942	(9787*2^276422-1)/3	83215	Lelio R Paula	04/2015
5944	2^276391-15	83202	Lelio R Paula	06/2012
5943	(4*10^83201+173)/3	83202	Robert Price	01/2017
5945	2^276316-109655	83180	Enzo Doria	04/2014
5946	2^276305-112063	83177	Enzo Doria	06/2014
5947	(10^(241585+1)+5410^41585-1)/9	83171	Robert Price	04/2017
5948	74913!4-2	83161	Robert Price	07/2017
5949	2^276227-1837207	83153	Enzo Doria	05/2015
5950	(2^276227+3)/7	83152	Lelio R Paula	12/2012
5951	2^276184-63389	83140	Paul Bourdelais	02/2012
5952	2^276066-111603	83105	Enzo Doria	05/2014
5953	(2^276028-3)*6-7	83094	Gilbert Mozzo	09/2016
5954	2^275926-4691	83063	Yves Minet	05/2019
5955	(2^275897+9)/1153	83051	Lelio R Paula	12/2012
5956	2^275879-109807	83048	Enzo Doria	04/2014
5958	F(397379)	83047	Henri Lifchitz	08/2003
5957	U(397379)	83047	Serge Batalov	03/2015
5959	3^174040-14	83039	Robert Price	08/2013
5960	(86*10^83038-221)/9	83039	Robert Price	06/2017
5961	2^275841-6883	83037	Lelio R Paula	07/2011
5962	3^174002-140	83021	Lelio R Paula	12/2015
5963	6^106681+77	83014	Lelio R Paula	12/2015
5964	187^36539-2	83011	Lelio R Paula	10/2017
5965	11^79701-3150	83001	Enzo Doria	12/2012
5966	(55459*2^275657+1)/21	82985	Lelio R Paula	06/2014
5967	(7*10^82960-457)/9	82960	Robert Price	09/2017
5968	2^275535-6855	82945	Lelio R Paula	08/2013
5969	3^173828-14	82938	Robert Price	08/2013
5970	2^275512-109677	82938	Enzo Doria	04/2014
5971	2^275446-110045	82918	Enzo Doria	04/2014
5972	(2^275473+47)/29526097447	82916	Lelio R Paula	12/2012
5973	3^173755-14	82903	Robert Price	08/2013
5974	(182*10^82898+43)/9	82900	Robert Price	11/2017
5975	2^275363-112309	82893	Enzo Doria	06/2014
5976	61^46427-60	82888	Norbert Schneider	10/2014
5977	3*10^82880-7^82880	82881	Mike Oakes	02/2010
5978	2^275290+90195	82871	Lelio R Paula	07/2013
5979	(35*10^82870-71)/9	82871	Robert Price	05/2015
5980	2^275270-1859621	82865	Enzo Doria	03/2016
5981	2^275259+81	82862	Henri Lifchitz	01/2007
5982	(113703^16384+1)/2	82834	Richard Fischer	04/2018
5983	7^98003+98003^7+1	82823	Robert Price	05/2014
5984	10^82790+126043	82791	Patrick De Geest	07/2013
5985	10^82790-47	82790	Robert Price	05/2011
5986	2^274985-112663	82779	Enzo Doria	06/2014
5987	2^274935+15015	82764	Lelio R Paula	07/2013
5988	(17*2^274922+1)/3	82761	Lelio R Paula	12/2012
5989	(43*10^82752-61)/9	82753	Robert Price	06/2015
5990	(3*2^274862+1)/1027	82740	Lelio R Paula	12/2012
5991	(31*2^274848-1)/4065	82736	Lelio R Paula	02/2014
5992	(4^137405+23)/3	82726	Robert Price	02/2017
5993	2^274791-110491	82721	Enzo Doria	05/2014
5994	(11*2^274776-1)/95	82715	Lelio R Paula	02/2014
5995	(47*10^82706-119)/9	82707	Robert Price	09/2017
5996	2^274704-111395	82695	Enzo Doria	05/2014
5997	2^274686-3911	82689	Yves Minet	04/2017
5998	(2^274663-1017)/48871318292279	82669	Lelio R Paula	12/2012
5999	(3^173263-5)/14498	82664	Lelio R Paula	12/2012
6000	2^274511-64875	82637	Lelio R Paula	08/2013

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Probable Primes Top 10000

(255244 PRPs in the top)