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 (> 30000)	Who ?	When ?
5751	6^97366+95	75766	Lelio R Paula	01/2015
5752	s(23010)	75760	Hans Havermann	11/2017
5753	8*6^97337-7	75744	Lelio R Paula	10/2014
5754	2^251588-111677	75736	Enzo Doria	05/2014
5755	5^108346-13256	75731	Enzo Doria	02/2013
5756	(31^50777+1)/32	75726	Robert Price	07/2013
5757	(10^75707+77)/3	75707	Robert Price	01/2017
5758	(174907#+1673)/(723915467899)	75700	Makoto Morimoto	10/2017
5759	2^251466+193	75699	Lelio R Paula	03/2012
5760	(5*2^251464+1)/9423	75695	Lelio R Paula	07/2012
5761	2^251422-109991	75686	Enzo Doria	04/2014
5762	4*5^108245-3	75661	Lelio R Paula	10/2014
5763	12^70067-11^70067	75615	Jean-Louis Charton	11/2006
5764	12^70066+95	75614	Lelio R Paula	02/2015
5765	-E20534/2063	75607	Thomas Ritschel	02/2017
5766	19^59120-50	75600	Lelio R Paula	01/2015
5767	18^60222-4697	75596	Enzo Doria	03/2013
5768	18^60211-4355	75582	Enzo Doria	03/2013
5769	7*2^251014-9	75564	Lelio R Paula	06/2014
5770	6^97101-25	75560	Lelio R Paula	01/2015
5771	8^83663-7^83663	75556	Jean-Louis Charton	01/2004
5772	3^158331-140	75544	Lelio R Paula	01/2015
5773	(37^48157-1)/36	75519	Robert Price	03/2012
5774	(19*10^75518-43)/3	75519	Robert Price	10/2017
5775	10^75516+31467	75517	Patrick De Geest	03/2016
5777	10^75516-10^2256-1	75516	Serge Batalov	01/2011
5776	10^75516-66591	75516	Patrick De Geest	03/2016
5778	2^250851-187	75514	Lelio R Paula	03/2012
5779	(43*10^75498-7)/9	75499	Robert Price	12/2014
5780	(3^158244-5)/247916	75497	Lelio R Paula	06/2012
5781	4*5^107971-3	75470	Lelio R Paula	10/2014
5782	(25*10^75465+71)/3	75466	Robert Price	01/2017
5783	(5*2^250681-1)/999	75461	Lelio R Paula	01/2014
5784	(182*10^75456+1)/3	75458	Robert Price	02/2017
5785	(2^250669-9)/98897729	75451	Lelio R Paula	07/2012
5786	10^75441+13	75442	Robert Price	01/2011
5787	10^75441-9923	75441	Patrick De Geest	05/2013
5788	(27*2^250546-1)/6457	75420	Lelio R Paula	01/2014
5789	5*7^89231-6	75410	Lelio R Paula	10/2014
5791	2^250503-16995	75409	Lelio R Paula	05/2013
5790	11^72411-28	75409	Lelio R Paula	02/2015
5792	3*5^107860-8	75392	Lelio R Paula	10/2014
5793	(34*10^75387-403)/9	75388	Robert Price	10/2017
5795	2^250426+29835	75386	Lelio R Paula	05/2013
5794	8*3^157999-7	75386	Lelio R Paula	05/2014
5796	(88*10^75381-43)/9	75382	Robert Price	11/2015
5797	2^250382-111755	75373	Enzo Doria	05/2014
5798	2^250374-2798051	75371	Eric Chen	03/2016
5799	(22*10^75368-1)/3	75369	Robert Price	12/2014
5800	(19*10^75338+119)/3	75339	Robert Price	02/2017
5801	2^250223-1859167	75325	Enzo Doria	03/2016
5802	(3^157854-7)/66025282	75308	Lelio R Paula	06/2012
5803	3^157831-98	75305	Lelio R Paula	01/2015
5804	(46^45281+11^45281)/57	75290	Serge Batalov	12/2016
5805	92^38335-91	75282	Norbert Schneider	01/2016
5806	2^250020+18915	75264	Lelio R Paula	05/2013
5807	2^250002+8193	75259	Lelio R Paula	05/2013
5808	(11*2^249977-7)/15	75251	Renaud Lifchitz	02/2011
5809	(2^249968+78557)/63	75247	Lelio R Paula	07/2012
5810	(5*10^75244+91)/3	75245	Robert Price	11/2016
5811	(10489!)^2+Prime(10489)	75242	Robert Price	08/2014
5812	14^65644+67	75237	Lelio R Paula	01/2015
5813	(2^249928-5)/11859059	75229	Lelio R Paula	06/2012
5814	129^35638+2	75218	Lelio R Paula	05/2013
5815	2^249853-110475	75214	Enzo Doria	05/2014
5816	2^249762+75409	75186	Enzo Doria	04/2016
5817	565^27318+27318^565	75181	Norbert Schneider	12/2016
5818	(2^249741-7)/685	75177	Lelio R Paula	06/2012
5819	2^249726-112181	75176	Enzo Doria	06/2014
5820	2^249721+11715	75174	Lelio R Paula	05/2013
5821	(38661^16384+1)/2	75158	Lelio R Paula	11/2011
5822	2^249658-47355	75155	Lelio R Paula	05/2013
5823	155^34311+2	75153	Lelio R Paula	05/2013
5824	(10^87682+1)/(10^12526+1)/990099009901	75145	Maksym Voznyy	06/2015
5825	(23*2^249602+1)/93	75138	Lelio R Paula	08/2012
5826	2^249522+8415	75114	Lelio R Paula	05/2013
5827	2^249489-110911	75104	Enzo Doria	05/2014
5828	(28*10^75078+131)/3	75079	Robert Price	02/2017
5829	(206*10^75073-17)/9	75075	Robert Price	03/2017
5830	2^249368-110573	75068	Enzo Doria	05/2014
5831	NaturalLogarithmOf10(75067)	75067	Eric W. Weisstein	10/2015
5832	(2^249375+78557)/45056125	75062	Lelio R Paula	07/2012
5833	(26*10^75055-173)/3	75056	Robert Price	10/2017
5834	2^249272+193	75039	Lelio R Paula	03/2012
5835	14^65468+43	75035	Lelio R Paula	01/2015
5836	37^47844+36	75030	Norbert Schneider	05/2014
5837	(52*10^75027-7)/9	75028	Robert Price	12/2014
5838	20^57653+89	75009	Lelio R Paula	01/2015
5839	2^249061-1868353	74975	Enzo Doria	04/2016
5840	7^88713+2*3^88713	74972	Mike Oakes	07/2010
5841	2*6^96313+5	74947	Lelio R Paula	10/2014
5842	(8*10^74944+49)/3	74945	Robert Price	03/2016
5843	300^30247+30247^300	74926	Norbert Schneider	11/2014
5844	2^248866-171	74917	Lelio R Paula	03/2012
5845	6*5^107168-7	74908	Lelio R Paula	10/2014
5846	11^71926+78	74904	Lelio R Paula	02/2015
5847	2^248824+1869391	74904	Enzo Doria	05/2016
5848	2^248816+1111	74902	Lelio R Paula	01/2011
5849	V(388219)	74890	Serge Batalov	03/2015
5850	2*F(358297)-1	74880	Henri Lifchitz	12/2009
5851	(22*10^74874-31)/9	74875	Robert Price	04/2015
5852	11^71892-76800000	74868	Enzo Doria	01/2013
5853	9*5^107107-4	74866	Lelio R Paula	10/2014
5854	2^248678-710111	74860	Paul Bourdelais	03/2013
5855	(14*10^74858+211)/9	74859	Robert Price	11/2017
5856	13^67194+12	74851	Lelio R Paula	01/2015
5857	(7*2^248634+1)/71	74846	Lelio R Paula	08/2012
5858	11^71867-3090	74842	Enzo Doria	12/2012
5859	2^248609+262145	74839	Lelio R Paula	05/2013
5860	3^156852+50	74838	Lelio R Paula	01/2015
5861	18^59607-11	74824	Lelio R Paula	01/2015
5862	2^248556-110507	74823	Enzo Doria	05/2014
5863	7^88531-36	74818	Lelio R Paula	01/2015
5864	p(15738)#/2+1024	74814	Robert Price	07/2017
5865	4*3^156740-5	74785	Lelio R Paula	05/2014
5866	(32*10^74773-41)/9	74774	Robert Price	05/2015
5867	(29*2^248384-1)/13	74772	Lelio R Paula	01/2014
5868	19401!+19401#+1	74765	D. Gazzoni Filho & Lucas Teixeira	06/2005
5869	2^248357-12797413	74763	Enzo Doria	03/2016
5870	42^46057+41	74762	Lelio R Paula	07/2012
5871	11^71784-3000	74756	Enzo Doria	12/2012
5872	19^58458+18	74754	Lelio R Paula	01/2015
5873	12^69265-35	74750	Lelio R Paula	02/2015
5874	11^71771-48000	74742	Enzo Doria	12/2012
5875	(7*10^74741+197)/3	74742	Robert Price	07/2017
5876	(2^248282-5)/50129	74736	Lelio R Paula	06/2012
5877	2^248252-110105	74732	Enzo Doria	04/2014
5878	(7*10^74729+71)/3	74730	Robert Price	03/2016
5879	3^156614-50	74724	Lelio R Paula	01/2015
5880	(7*2^248213+1)/135	74719	Lelio R Paula	07/2012
5881	(2^248173+78557)/767	74705	Lelio R Paula	07/2012
5882	125^35622+124	74697	Norbert Schneider	02/2015
5883	(19*2^248099-1)/29	74686	Lelio R Paula	01/2014
5884	(86*10^74676-41)/9	74677	Robert Price	11/2015
5885	(p(15711)#-4)/2	74672	Robert Price	09/2017
5886	10^74670+31	74671	Robert Price	01/2011
5887	10^74670-122463	74670	Patrick De Geest	05/2013
5888	2^248036-69	74667	Lelio R Paula	03/2012
5889	11^71698-6000	74666	Enzo Doria	12/2012
5890	58(10^(324887)-1)/111-1	74661	Robert Price	10/2014
5891	14^65139-45	74658	Lelio R Paula	01/2015
5892	6^95921-133	74642	Lelio R Paula	01/2015
5893	11^71675+78	74642	Lelio R Paula	02/2015
5894	18^59449-91	74625	Lelio R Paula	01/2015
5895	6^95864-16043	74597	Enzo Doria	02/2013
5896	5*7^88261+6	74590	Lelio R Paula	10/2014
5897	9*5^106710+4	74589	Lelio R Paula	10/2014
5898	(7772^247788+1)/(11754121)	74588	Jens K. Andersen	09/2007
5899	(265*10^74579+17)/3	74581	Robert Price	05/2016
5900	(2^247759-1017)/3318311717	74574	Lelio R Paula	07/2012
5901	5^106682-24	74568	Lelio R Paula	08/2014
5902	474^27863+27863^474	74556	Norbert Schneider	01/2017
5903	(14*10^74540+79)/3	74541	Robert Price	11/2017
5904	(35365^16384+1)/2	74524	Lelio R Paula	11/2011
5905	3^156161+2660	74508	Lelio R Paula	01/2015
5906	2^247474-58695	74498	Lelio R Paula	05/2013
5907	11^71519-90	74480	Enzo Doria	07/2012
5908	(19*2^247419-1)/23202983	74475	Lelio R Paula	01/2014
5910	(2^247394-7)/3	74473	Lelio R Paula	06/2012
5909	18^59328+17	74473	Lelio R Paula	01/2015
5911	2^247379-181	74469	Lelio R Paula	03/2012
5912	(15*2^247370-1)/479	74465	Lelio R Paula	01/2014
5913	2^247344+2047	74458	Lelio R Paula	05/2013
5914	2^247311-1017	74449	Lelio R Paula	05/2013
5915	2^247280+7	74439	Lelio R Paula	03/2012
5916	(68*10^74434+13)/9	74435	Ray Chandler	11/2010
5917	3^156004-62	74433	Lelio R Paula	01/2015
5918	36095!2-64	74416	Robert Price	06/2015
5919	2^247165-3	74405	M. Frind & P. Underwood	07/2002
5920	2^247150+32769	74400	Lelio R Paula	05/2013
5921	12^68911+73	74368	Lelio R Paula	01/2015
5922	2^246999+74903	74355	Enzo Doria	04/2016
5923	2^246989-110643	74352	Enzo Doria	05/2014
5924	10^74350+279439	74351	Patrick De Geest	07/2017
5927	(10^74350+11)/3	74350	Robert Price	11/2014
5925	10^74350-400000001	74350	Robert Price	07/2017
5926	10^74350-716241	74350	Patrick De Geest	07/2017
5928	10^74335+13659	74336	Patrick De Geest	05/2013
5929	10^74335-53	74335	Robert Price	05/2011
5930	2^246906-1215	74327	Lelio R Paula	05/2013
5931	2^246848+111	74309	Lelio R Paula	03/2012
5932	6^95490-18443	74306	Enzo Doria	03/2013
5933	18^59188-2369	74298	Enzo Doria	03/2013
5934	(13632^246767+1)/(35713^2*743)	74281	Jens K. Andersen	09/2007
5935	2^246744+40755	74278	Lelio R Paula	05/2013
5936	(29*10^74276+91)/3	74277	Robert Price	03/2016
5937	6^95441+163	74268	Lelio R Paula	01/2015
5938	V(390863)	74258	Serge Batalov	03/2015
5939	10^74254+91	74255	Robert Price	03/2011
5940	(19*10^74253-1)/9	74254	Ray Chandler	02/2012
5941	10^74254-130569	74254	Patrick De Geest	05/2013
5942	771^25718+25718^771	74250	Norbert Schneider	10/2016
5943	2^246618+427	74240	Henri Lifchitz	02/2005
5944	88*10^74234+3	74236	Robert Price	11/2016
5945	8*10^74234-49	74235	Robert Price	04/2016
5946	2^246578+12285	74228	Lelio R Paula	05/2013
5947	(3^155569-5)/2	74225	Lelio R Paula	06/2012
5948	13^66628+46	74220	Lelio R Paula	01/2015
5949	2^246476-17295	74197	Lelio R Paula	05/2013
5950	(61*10^74189-1)/3	74191	Robert Price	11/2017
5951	(15185*2^246432-1)/13	74187	Lelio R Paula	04/2015
5952	5*2^246413-3	74179	Lelio R Paula	05/2014
5953	2^246386-28635	74170	Lelio R Paula	05/2013
5954	2^246334-111245	74154	Enzo Doria	05/2014
5955	39^77708+7^77708-24^77708-3	74153	Mike Oakes	12/2010
5956	15^63045+82	74147	Lelio R Paula	01/2015
5957	19255!+19255#+1	74140	D. Gazzoni Filho & Lucas Teixeira	06/2005
5958	2^246268-110507	74135	Enzo Doria	05/2014
5959	3^155328+2660	74111	Lelio R Paula	01/2015
5960	2^246148-2786249	74098	Enzo Doria	03/2016
5961	(16*10^74092-19)/3	74093	Robert Price	03/2016
5962	2^246115-110767	74088	Enzo Doria	05/2014
5963	7^87666-68	74087	Lelio R Paula	08/2014
5964	10^74079+1145141919	74080	Marisa Kirisame	03/2015
5965	10^74079+6219	74080	Patrick De Geest	03/2016
5966	10^74079-282707	74079	Patrick De Geest	03/2016
5967	129^35098+2	74078	Lelio R Paula	05/2013
5968	2^246025-112123	74061	Enzo Doria	06/2014
5969	(67*10^74045+17)/3	74047	Robert Price	02/2017
5970	2^245823+66831	74001	Marek Hubal	02/2017
5971	5^105869+42	74000	Lelio R Paula	08/2014
5972	(21*2^245806+1)/634555	73991	Lelio R Paula	08/2012
5973	(22699*2^245762+1)/119	73985	Lelio R Paula	06/2014
5974	(3^155048-7)/262	73975	Lelio R Paula	06/2012
5975	9998*2^245696+3	73966	Donovan Johnson	10/2004
5976	13^66400-80	73966	Lelio R Paula	01/2015
5977	(2^245704+9)/25	73963	Lelio R Paula	07/2012
5979	11^71023-7170	73963	Enzo Doria	01/2013
5978	3*10^73962+13	73963	Robert Price	08/2017
5980	(31*2^245660-1)/114195	73948	Lelio R Paula	01/2014
5981	2^245629-2797813	73942	Eric Chen	03/2016
5982	2^245557-153	73921	Lelio R Paula	03/2012
5983	(77*10^73917-59)/9	73918	Robert Price	11/2017
5984	2^245525+1869881	73911	Enzo Doria	06/2016
5985	2^245522+159	73910	Lelio R Paula	03/2012
5986	(13*10^73891-43)/3	73892	Robert Price	08/2017
5987	19^57783-56	73891	Lelio R Paula	01/2015
5988	7*10^73888+79	73889	Robert Price	02/2017
5989	6^94948+174281	73884	Mike Oakes	02/2011
5990	11^70939-4860	73876	Enzo Doria	01/2013
5991	2^245372+54615	73865	Lelio R Paula	05/2013
5992	2^245362-143	73862	Lelio R Paula	03/2012
5993	7^87396+6^(87396-1)	73859	Robert Price	03/2016
5994	(22*10^73853-37)/3	73854	Robert Price	05/2017
5995	5^105646-14246	73844	Enzo Doria	02/2013
5997	2^245290-41	73840	Lelio R Paula	03/2012
5996	2^245290-94395	73840	Lelio R Paula	05/2013
5998	8*5^105600-7	73813	Lelio R Paula	10/2014
5999	7*5^105573-4	73794	Lelio R Paula	10/2014
6000	18^58742-4805	73738	Enzo Doria	03/2013

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PRP Records

Probable Primes Top 10000

(205869 PRPs in the top)