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 ?
6751	2^249726-112181	75176	Enzo Doria	06/2014
6752	2^249721+11715	75174	Lelio R Paula	05/2013
6753	(38661^16384+1)/2	75158	Lelio R Paula	11/2011
6754	2^249658-47355	75155	Lelio R Paula	05/2013
6755	155^34311+2	75153	Lelio R Paula	05/2013
6756	(10^87682+1)/(10^12526+1)/990099009901	75145	Maksym Voznyy	06/2015
6757	(23*2^249602+1)/93	75138	Lelio R Paula	08/2012
6758	2^249522+8415	75114	Lelio R Paula	05/2013
6759	2^249489-110911	75104	Enzo Doria	05/2014
6760	(28*10^75078+131)/3	75079	Robert Price	02/2017
6761	(206*10^75073-17)/9	75075	Robert Price	03/2017
6762	2^249368-110573	75068	Enzo Doria	05/2014
6763	NaturalLogarithmOf10(75067)	75067	Eric W. Weisstein	10/2015
6764	(2^249375+78557)/45056125	75062	Lelio R Paula	07/2012
6765	(26*10^75055-173)/3	75056	Robert Price	10/2017
6766	2^249272+193	75039	Lelio R Paula	03/2012
6767	14^65468+43	75035	Lelio R Paula	01/2015
6768	37^47844+36	75030	Norbert Schneider	05/2014
6769	(52*10^75027-7)/9	75028	Robert Price	12/2014
6770	20^57653+89	75009	Lelio R Paula	01/2015
6771	2^249061-1868353	74975	Enzo Doria	04/2016
6772	7^88713+2*3^88713	74972	Mike Oakes	07/2010
6773	2*6^96313+5	74947	Lelio R Paula	10/2014
6774	(8*10^74944+49)/3	74945	Robert Price	03/2016
6775	300^30247+30247^300	74926	Norbert Schneider	11/2014
6776	2^248866-171	74917	Lelio R Paula	03/2012
6777	6*5^107168-7	74908	Lelio R Paula	10/2014
6778	11^71926+78	74904	Lelio R Paula	02/2015
6779	2^248824+1869391	74904	Enzo Doria	05/2016
6780	2^248816+1111	74902	Lelio R Paula	01/2011
6781	V(388219)	74890	Serge Batalov	03/2015
6782	159^34017+158	74885	Norbert Schneider	12/2018
6783	2*F(358297)-1	74880	Henri Lifchitz	12/2009
6784	(22*10^74874-31)/9	74875	Robert Price	04/2015
6785	11^71892-76800000	74868	Enzo Doria	01/2013
6786	9*5^107107-4	74866	Lelio R Paula	10/2014
6787	2^248678-710111	74860	Paul Bourdelais	03/2013
6788	(14*10^74858+211)/9	74859	Robert Price	11/2017
6789	13^67194+12	74851	Lelio R Paula	01/2015
6790	(7*2^248634+1)/71	74846	Lelio R Paula	08/2012
6791	11^71867-3090	74842	Enzo Doria	12/2012
6792	2^248609+262145	74839	Lelio R Paula	05/2013
6793	3^156852+50	74838	Lelio R Paula	01/2015
6794	18^59607-11	74824	Lelio R Paula	01/2015
6795	2^248556-110507	74823	Enzo Doria	05/2014
6796	7^88531-36	74818	Lelio R Paula	01/2015
6797	p(15738)#/2+1024	74814	Robert Price	07/2017
6798	4*3^156740-5	74785	Lelio R Paula	05/2014
6799	(32*10^74773-41)/9	74774	Robert Price	05/2015
6800	(29*2^248384-1)/13	74772	Lelio R Paula	01/2014
6801	19401!+19401#+1	74765	D. Gazzoni Filho & Lucas Teixeira	06/2005
6802	2^248357-12797413	74763	Enzo Doria	03/2016
6803	42^46057+41	74762	Lelio R Paula	07/2012
6804	11^71784-3000	74756	Enzo Doria	12/2012
6805	19^58458+18	74754	Lelio R Paula	01/2015
6806	12^69265-35	74750	Lelio R Paula	02/2015
6807	11^71771-48000	74742	Enzo Doria	12/2012
6808	(7*10^74741+197)/3	74742	Robert Price	07/2017
6809	(2^248282-5)/50129	74736	Lelio R Paula	06/2012
6810	2^248252-110105	74732	Enzo Doria	04/2014
6811	(7*10^74729+71)/3	74730	Robert Price	03/2016
6812	3^156614-50	74724	Lelio R Paula	01/2015
6813	(7*2^248213+1)/135	74719	Lelio R Paula	07/2012
6814	(2^248173+78557)/767	74705	Lelio R Paula	07/2012
6815	125^35622+124	74697	Norbert Schneider	02/2015
6816	(19*2^248099-1)/29	74686	Lelio R Paula	01/2014
6817	(86*10^74676-41)/9	74677	Robert Price	11/2015
6818	(p(15711)#-4)/2	74672	Robert Price	09/2017
6819	10^74670+31	74671	Robert Price	01/2011
6820	10^74670-122463	74670	Patrick De Geest	05/2013
6821	2^248036-69	74667	Lelio R Paula	03/2012
6822	11^71698-6000	74666	Enzo Doria	12/2012
6823	58(10^(324887)-1)/111-1	74661	Robert Price	10/2014
6824	14^65139-45	74658	Lelio R Paula	01/2015
6825	6^95921-133	74642	Lelio R Paula	01/2015
6826	11^71675+78	74642	Lelio R Paula	02/2015
6827	18^59449-91	74625	Lelio R Paula	01/2015
6828	6^95864-16043	74597	Enzo Doria	02/2013
6829	5*7^88261+6	74590	Lelio R Paula	10/2014
6830	9*5^106710+4	74589	Lelio R Paula	10/2014
6831	(7772^247788+1)/(11754121)	74588	Jens K. Andersen	09/2007
6832	(265*10^74579+17)/3	74581	Robert Price	05/2016
6833	(2^247759-1017)/3318311717	74574	Lelio R Paula	07/2012
6834	5^106682-24	74568	Lelio R Paula	08/2014
6835	474^27863+27863^474	74556	Norbert Schneider	01/2017
6836	(14*10^74540+79)/3	74541	Robert Price	11/2017
6837	(35365^16384+1)/2	74524	Lelio R Paula	11/2011
6838	3^156161+2660	74508	Lelio R Paula	01/2015
6839	2^247474-58695	74498	Lelio R Paula	05/2013
6840	11^71519-90	74480	Enzo Doria	07/2012
6841	(19*2^247419-1)/23202983	74475	Lelio R Paula	01/2014
6843	(2^247394-7)/3	74473	Lelio R Paula	06/2012
6842	18^59328+17	74473	Lelio R Paula	01/2015
6844	2^247379-181	74469	Lelio R Paula	03/2012
6845	(15*2^247370-1)/479	74465	Lelio R Paula	01/2014
6846	2^247344+2047	74458	Lelio R Paula	05/2013
6847	2^247311-1017	74449	Lelio R Paula	05/2013
6848	2^247280+7	74439	Lelio R Paula	03/2012
6849	(68*10^74434+13)/9	74435	Ray Chandler	11/2010
6850	3^156004-62	74433	Lelio R Paula	01/2015
6851	36095!2-64	74416	Robert Price	06/2015
6852	2^247165-3	74405	M. Frind & P. Underwood	07/2002
6853	2^247150+32769	74400	Lelio R Paula	05/2013
6854	12^68911+73	74368	Lelio R Paula	01/2015
6855	2^246999+74903	74355	Enzo Doria	04/2016
6856	2^246989-110643	74352	Enzo Doria	05/2014
6857	10^74350+279439	74351	Patrick De Geest	07/2017
6860	(10^74350+11)/3	74350	Robert Price	11/2014
6858	10^74350-400000001	74350	Robert Price	07/2017
6859	10^74350-716241	74350	Patrick De Geest	07/2017
6861	10^74335+13659	74336	Patrick De Geest	05/2013
6862	10^74335-53	74335	Robert Price	05/2011
6863	2^246906-1215	74327	Lelio R Paula	05/2013
6864	2^246848+111	74309	Lelio R Paula	03/2012
6865	6^95490-18443	74306	Enzo Doria	03/2013
6866	18^59188-2369	74298	Enzo Doria	03/2013
6867	(13632^246767+1)/(35713^2*743)	74281	Jens K. Andersen	09/2007
6868	2^246744+40755	74278	Lelio R Paula	05/2013
6869	(29*10^74276+91)/3	74277	Robert Price	03/2016
6870	6^95441+163	74268	Lelio R Paula	01/2015
6871	V(390863)	74258	Serge Batalov	03/2015
6872	10^74254+91	74255	Robert Price	03/2011
6874	(19*10^74253-1)/9	74254	Ray Chandler	02/2012
6873	10^74254-130569	74254	Patrick De Geest	05/2013
6875	771^25718+25718^771	74250	Norbert Schneider	10/2016
6876	2^246618+427	74240	Henri Lifchitz	02/2005
6877	88*10^74234+3	74236	Robert Price	11/2016
6878	8*10^74234-49	74235	Robert Price	04/2016
6879	2^246578+12285	74228	Lelio R Paula	05/2013
6880	(3^155569-5)/2	74225	Lelio R Paula	06/2012
6881	13^66628+46	74220	Lelio R Paula	01/2015
6882	2^246476-17295	74197	Lelio R Paula	05/2013
6883	(61*10^74189-1)/3	74191	Robert Price	11/2017
6884	(15185*2^246432-1)/13	74187	Lelio R Paula	04/2015
6885	5*2^246413-3	74179	Lelio R Paula	05/2014
6886	2^246386-28635	74170	Lelio R Paula	05/2013
6887	2^246334-111245	74154	Enzo Doria	05/2014
6888	39^77708+7^77708-24^77708-3	74153	Mike Oakes	12/2010
6889	15^63045+82	74147	Lelio R Paula	01/2015
6890	19255!+19255#+1	74140	D. Gazzoni Filho & Lucas Teixeira	06/2005
6891	2^246268-110507	74135	Enzo Doria	05/2014
6892	3^155328+2660	74111	Lelio R Paula	01/2015
6893	2^246148-2786249	74098	Enzo Doria	03/2016
6894	(16*10^74092-19)/3	74093	Robert Price	03/2016
6895	2^246115-110767	74088	Enzo Doria	05/2014
6896	7^87666-68	74087	Lelio R Paula	08/2014
6897	10^74079+1145141919	74080	Marisa Kirisame	03/2015
6898	10^74079+6219	74080	Patrick De Geest	03/2016
6899	10^74079-282707	74079	Patrick De Geest	03/2016
6900	129^35098+2	74078	Lelio R Paula	05/2013
6901	2^246025-112123	74061	Enzo Doria	06/2014
6902	(67*10^74045+17)/3	74047	Robert Price	02/2017
6903	2^245823+66831	74001	Marek Hubal	02/2017
6904	5^105869+42	74000	Lelio R Paula	08/2014
6905	(21*2^245806+1)/634555	73991	Lelio R Paula	08/2012
6906	(22699*2^245762+1)/119	73985	Lelio R Paula	06/2014
6907	(3^155048-7)/262	73975	Lelio R Paula	06/2012
6908	9998*2^245696+3	73966	Donovan Johnson	10/2004
6909	13^66400-80	73966	Lelio R Paula	01/2015
6910	(2^245704+9)/25	73963	Lelio R Paula	07/2012
6912	11^71023-7170	73963	Enzo Doria	01/2013
6911	3*10^73962+13	73963	Robert Price	08/2017
6913	(31*2^245660-1)/114195	73948	Lelio R Paula	01/2014
6914	2^245629-2797813	73942	Eric Chen	03/2016
6915	2^245557-153	73921	Lelio R Paula	03/2012
6916	(77*10^73917-59)/9	73918	Robert Price	11/2017
6917	2^245525+1869881	73911	Enzo Doria	06/2016
6918	2^245522+159	73910	Lelio R Paula	03/2012
6919	(13*10^73891-43)/3	73892	Robert Price	08/2017
6920	19^57783-56	73891	Lelio R Paula	01/2015
6921	7*10^73888+79	73889	Robert Price	02/2017
6922	6^94948+174281	73884	Mike Oakes	02/2011
6923	11^70939-4860	73876	Enzo Doria	01/2013
6924	2^245372+54615	73865	Lelio R Paula	05/2013
6925	2^245362-143	73862	Lelio R Paula	03/2012
6926	7^87396+6^(87396-1)	73859	Robert Price	03/2016
6927	(22*10^73853-37)/3	73854	Robert Price	05/2017
6928	5^105646-14246	73844	Enzo Doria	02/2013
6930	2^245290-41	73840	Lelio R Paula	03/2012
6929	2^245290-94395	73840	Lelio R Paula	05/2013
6931	8*5^105600-7	73813	Lelio R Paula	10/2014
6932	7*5^105573-4	73794	Lelio R Paula	10/2014
6933	18^58742-4805	73738	Enzo Doria	03/2013
6934	13^66179+66	73720	Lelio R Paula	01/2015
6935	(82*10^73714-1)/9	73715	Robert Price	12/2014
6936	(29*2^244856-1)/186121	73706	Lelio R Paula	01/2014
6937	(13*2^244840-1)/2799	73702	Lelio R Paula	01/2014
6938	(13*10^73701+17)/3	73702	Robert Price	06/2015
6939	(2^244787-1017)/28411	73684	Lelio R Paula	07/2012
6940	(3^154421-4)/23	73677	Lelio R Paula	06/2012
6941	8*7^87170+5	73669	Lelio R Paula	10/2014
6942	(29*10^73659-113)/3	73660	Robert Price	11/2017
6943	Phi(40100,-40100)	73651	Henri Lifchitz	06/2013
6944	(4*10^73647-19)/3	73648	Robert Price	06/2017
6945	2^244618-2297	73638	Yves Minet	10/2009
6946	3*5^105344+8	73633	Lelio R Paula	10/2014
6947	5^105334-14096	73626	Enzo Doria	02/2013
6948	(2^244584-7)/13237074243033	73614	Lelio R Paula	07/2012
6949	2^244465-110185	73592	Enzo Doria	05/2014
6950	2^244443+40755	73585	Lelio R Paula	05/2013
6951	2^244404+3841	73573	Yves Minet	03/2011
6952	2^244372-110627	73564	Enzo Doria	05/2014
6953	(3*2^244255+1)/245	73527	Lelio R Paula	08/2012
6954	(11*2^244245+1)/23	73525	Lelio R Paula	08/2012
6955	(15185*2^244187-1)/6111	73509	Lelio R Paula	04/2015
6956	17063^17362+17362^17063	73477	Norbert Schneider	04/2019
6957	(91^37507+1)/92	73476	Paul Bourdelais	08/2017
6958	18^58521+65	73460	Lelio R Paula	01/2015
6959	13^65940+36	73454	Lelio R Paula	01/2015
6960	(625^26267+1)/626	73437	Richard Fischer	12/2017
6961	5^105050-14	73427	Lelio R Paula	08/2014
6962	(((((((((((((30201^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2	73401	Serge Batalov	07/2016
6963	15^62410-46	73400	Lelio R Paula	01/2015
6964	2^243733+1869707	73371	Enzo Doria	05/2016
6965	11^70439-5430	73355	Enzo Doria	01/2013
6966	2^243676-87	73354	Lelio R Paula	03/2012
6967	(101*10^73346-17)/3	73348	Robert Price	08/2016
6968	2^243621-113185	73338	Enzo Doria	07/2014
6969	(5*2^243610-1)/1669	73332	Lelio R Paula	01/2014
6970	2*5^104888-7	73314	Lelio R Paula	10/2014
6971	(58695*2^243516-1)/983	73308	Lelio R Paula	04/2015
6972	(3^153648-2)/33423138097	73299	Lelio R Paula	06/2012
6973	18^58376-5255	73278	Enzo Doria	03/2013
6974	11^70363+32	73276	Lelio R Paula	02/2015
6975	2^243413+4257	73275	Lelio R Paula	05/2013
6976	104824^5+5^104824	73269	Andrey Kulsha	07/2010
6977	7^86689-6^86689	73261	Predrag Minovic	09/2004
6978	2^243296+90195	73240	Lelio R Paula	05/2013
6979	2^243281-4843	73235	Yves Minet	05/2019
6981	p(15433)#/2-4	73218	Robert Price	12/2016
6980	(59*10^73217-77)/9	73218	Robert Price	11/2017
6982	2^243127+71355	73189	Lelio R Paula	05/2013
6983	2^243116-249419	73186	Paul Bourdelais	03/2013
6984	(58695*2^243085-1)/11	73180	Lelio R Paula	04/2015
6985	11^70262-98	73171	Lelio R Paula	02/2015
6986	(2^243034+47)/722703303	73152	Lelio R Paula	07/2012
6987	(2^242966+47)/46887	73136	Lelio R Paula	07/2012
6988	(43^44773-1)/42	73134	Robert Price	04/2014
6989	6^93980-158359	73131	Mike Oakes	02/2011
6990	6^93915+53	73081	Lelio R Paula	01/2015
6991	(5*10^73079+211)/9	73079	Robert Price	12/2017
6992	(74*10^73076+43)/9	73077	Robert Price	10/2015
6993	(3^153125+2)/1144955	73054	Lelio R Paula	06/2012
6994	2^242632-112199	73040	Enzo Doria	06/2014
6995	V(351646)	73029	Serge Batalov	03/2015
6996	18^58175-85	73026	Lelio R Paula	01/2015
6997	p(15395)#/2-4	73019	Robert Price	12/2016
6998	(4^121271+3^121271)/7	73012	Jean-Louis Charton	03/2011
6999	8*6^93825-5	73011	Lelio R Paula	10/2014
7000	(73^39181+1)/74	73005	Paul Bourdelais	08/2017

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Probable Primes Top 10000

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