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 ?
6751	2^215623+183	64909	Lelio R Paula	08/2011
6752	(46*10^64904+521)/9	64905	Robert Price	08/2017
6753	(3^136043-2^136043)/(19862279*33466579)	64895	Mike Oakes	12/2016
6754	5*2^215554+3	64889	Lelio R Paula	04/2014
6755	2^215541-112075	64885	Enzo Doria	06/2014
6756	2*10^64882-3	64883	Dmitry Domanov	11/2010
6757	10^64862+342339	64863	Patrick De Geest	05/2013
6758	10^64862-47	64862	Robert Price	05/2011
6759	19^50718-84	64856	Lelio R Paula	08/2013
6760	(30452^215471-1)/(17115127067173473)	64853	Jens K. Andersen	09/2007
6762	10^64843+4278697839	64844	Robert Price	05/2015
6761	10^64843+21967	64844	Patrick De Geest	03/2016
6763	10^64843-340073	64843	Patrick De Geest	03/2016
6764	11^62254+70	64831	Lelio R Paula	07/2013
6765	2^215351-111925	64828	Enzo Doria	05/2014
6766	2^215310-117	64815	Lelio R Paula	08/2011
6767	124^30958-123	64809	Norbert Schneider	02/2015
6768	(7*10^64807+17)/3	64808	Erik Branger	03/2014
6769	(710^(232400+1)-27*10^32400-7)/9	64801	Robert Price	11/2015
6770	2^215243-15949	64795	Enzo Doria	04/2013
6771	23^47581-22^47581	64793	Robert Price	08/2012
6772	(62*10^64783-17)/9	64784	Robert Price	09/2015
6773	5*3^135747-4	64769	Lelio R Paula	04/2014
6774	(59*10^64767-41)/9	64768	Robert Price	09/2015
6775	(2^215140+3)/19	64763	Lelio R Paula	04/2012
6776	2^215135-17169	64763	Enzo Doria	05/2013
6777	2^215115-111277	64757	Enzo Doria	05/2014
6778	9*5^92641+2	64755	Lelio R Paula	09/2014
6779	(lucasV(1,2,430086)-2)/(7*1033)	64731	Mike Oakes	03/2017
6780	(5*10^64715-23)/9	64715	Robert Price	11/2014
6781	2^214938-1781	64703	Yves Minet	03/2013
6782	11^62111-420	64682	Enzo Doria	08/2012
6783	5^92525+42	64673	Lelio R Paula	06/2013
6784	2^214824+71893	64669	Enzo Doria	04/2016
6785	2^214799-2221	64661	Yves Minet	08/2013
6786	(21*2^214688+1)/293	64627	Lelio R Paula	08/2012
6787	92^32907+32907^92	64623	Serge Batalov	05/2014
6788	6^83013+101	64597	Lelio R Paula	07/2013
6789	p(13775)#/2+8	64594	Robert Price	01/2017
6790	(7*10^64568-43)/9	64568	Robert Price	10/2014
6791	Pell-LucasQ(168677)/2	64566	Eric W. Weisstein	11/2006
6792	(24737*2^214476+1)/2877	64565	Lelio R Paula	06/2014
6793	(47*2^214463+1)/7	64561	Lelio R Paula	04/2015
6794	2^214458+54615	64559	Lelio R Paula	10/2011
6795	(3^135322+7)/122911408	64557	Lelio R Paula	04/2012
6796	2^214389-683113	64538	Paul Bourdelais	03/2013
6797	2^214369-111241	64532	Enzo Doria	05/2014
6798	(19^50461+3^50461)/22	64526	Robert Price	07/2013
6799	11^61954-3660	64519	Enzo Doria	12/2012
6800	(23*2^214319-1)/21	64517	Lelio R Paula	01/2014
6801	(58695*2^214310-1)/571	64516	Lelio R Paula	04/2015
6802	35^41779-34	64510	Norbert Schneider	04/2014
6803	11^61939-5220	64503	Enzo Doria	01/2013
6804	(2^214271+78557)/35	64501	Lelio R Paula	05/2012
6805	126^30706-125	64494	Norbert Schneider	02/2015
6806	gcd(V(1157265),5F(231453)(F(231453)-1)+1)	64492	Serge Batalov	04/2015
6807	2^214215+12909	64486	Lelio R Paula	10/2011
6808	5^92225+66	64463	Lelio R Paula	06/2013
6809	2^214126-240551	64459	Paul Bourdelais	03/2013
6810	8*6^82827+5	64453	Lelio R Paula	09/2014
6811	(31*2^214120-1)/2170485	64452	Lelio R Paula	01/2014
6812	(31*2^214088-1)/5955	64445	Lelio R Paula	01/2014
6813	14^56227+89	64444	Lelio R Paula	08/2013
6816	2^214055-159	64437	Lelio R Paula	08/2011
6814	10^64436+2667	64437	Patrick De Geest	05/2013
6815	65^35543-64^35543	64437	Robert Price	08/2013
6817	10^64436-53	64436	Robert Price	05/2011
6818	Phi(128878,10)/39503297927	64428	Maksym Voznyy	11/2015
6819	3^135027+100	64425	Lelio R Paula	05/2013
6820	(3^134972-7)/2	64398	Lelio R Paula	04/2012
6821	6*10^64387+7	64388	Dmitry Domanov	11/2010
6822	2^213864-18377	64380	Enzo Doria	05/2013
6823	(2^213821+9)/209	64365	Lelio R Paula	04/2012
6824	2^213788+135	64357	Lelio R Paula	08/2011
6825	(3^134883+2)/48313	64351	Lelio R Paula	04/2012
6826	(49^38069-46^38069)/3	64344	Serge Batalov	12/2016
6827	(11^61781+2^61781)/13	64338	Robert Price	02/2013
6828	6^82670+37	64330	Lelio R Paula	07/2013
6829	(3^134839+4)/32312959	64328	Lelio R Paula	04/2012
6830	(22*10^64326+161)/3	64327	Robert Price	02/2017
6831	11^61767-4050	64324	Enzo Doria	12/2012
6832	2^213645-114853	64314	Enzo Doria	05/2015
6833	13^57733+18	64312	Lelio R Paula	07/2013
6834	2^213621+72707	64307	Enzo Doria	04/2016
6835	10^64305+136791	64306	Patrick De Geest	05/2011
6836	10^64305-9	64305	Alexander Gramolin	01/2011
6837	V(307652)	64295	Serge Batalov	03/2015
6838	4*10^64286-89	64287	Robert Price	08/2017
6839	(2^213546-5)/2221	64281	Lelio R Paula	04/2012
6840	2^213438-58695	64252	Lelio R Paula	10/2011
6841	2^213367-105	64230	Lelio R Paula	08/2011
6842	595^23148+23148^595	64225	Norbert Schneider	07/2016
6844	3^134601+8680	64221	Lelio R Paula	05/2013
6843	(26*10^64220+61)/3	64221	Robert Price	06/2017
6845	500^23793+23793^500	64217	Norbert Schneider	08/2016
6846	2^213314-455	64214	Yves Minet	02/2012
6847	39^40359-38	64214	Norbert Schneider	05/2014
6848	2^213292-16085	64208	Enzo Doria	04/2013
6849	2^213274-77	64202	Lelio R Paula	08/2011
6850	19^50203+78	64198	Lelio R Paula	08/2013
6851	2^213240-112865	64192	Enzo Doria	06/2014
6852	2^213190-112391	64177	Enzo Doria	06/2014
6853	(9913*2^213184-1)/9657	64175	Lelio R Paula	04/2015
6854	14^55991+27	64173	Lelio R Paula	07/2013
6855	2^213158-112581	64167	Enzo Doria	06/2014
6856	2^213148+91	64164	Lelio R Paula	08/2011
6857	(96^32369+1)/97	64163	Paul Bourdelais	08/2017
6859	6^82439+125	64151	Lelio R Paula	07/2013
6858	7*2^213102+9	64151	Lelio R Paula	04/2014
6860	L(306854)+F(306855)	64129	Henri Lifchitz	01/2007
6861	610^23017+23017^610	64110	Norbert Schneider	07/2016
6862	2^212950-64875	64105	Lelio R Paula	10/2011
6863	(266*10^64102-17)/3	64104	Robert Price	06/2016
6864	p(13679)#/2+64	64097	Robert Price	03/2017
6865	19^50119+94	64090	Lelio R Paula	08/2013
6866	2^212880-147	64084	Lelio R Paula	08/2011
6867	11^61523-4590	64070	Enzo Doria	01/2013
6868	5^91663+38	64070	Lelio R Paula	05/2013
6869	5^91650+52	64061	Lelio R Paula	05/2013
6870	2^212770+69	64051	Lelio R Paula	08/2011
6871	(3^134227+1)/4	64042	Paul Bourdelais	11/2007
6872	(2*10^64041-17)/3	64041	Robert Price	08/2014
6873	(15^54449+1)/16	64036	Paul Bourdelais	03/2010
6874	(29*10^64027+91)/3	64028	Robert Price	03/2016
6875	(lucasV(1,2,425405)+2)/(17*89)	64027	Mike Oakes	03/2017
6876	16878!+16878#-1	64022	D. Gazzoni Filho & Lucas Teixeira	05/2005
6877	2^212663+53	64018	Lelio R Paula	08/2011
6878	(4*10^64014+197)/3	64015	Robert Price	03/2017
6879	10^63986+63	63987	Robert Price	01/2011
6880	10^63986-31557	63986	Patrick De Geest	05/2013
6881	31487!2-2^31487	63982	Robert Price	09/2015
6882	(21*2^212522-1)/1416323	63971	Lelio R Paula	01/2014
6883	5^91517+98	63968	Lelio R Paula	04/2013
6884	(62*10^63954-17)/9	63955	Robert Price	09/2015
6886	5^91493-4^91493	63951	Predrag Minovic	04/2004
6885	V(364793)	63951	Serge Batalov	03/2015
6888	19^50004+58	63943	Lelio R Paula	05/2013
6887	5*6^82172-7	63943	Lelio R Paula	09/2014
6889	(56*10^63942+223)/9	63943	Robert Price	07/2016
6890	19^50000-24	63938	Lelio R Paula	05/2013
6891	(23*2^212374-1)/27019	63928	Lelio R Paula	01/2014
6892	(9*2^212355-1)/761	63924	Lelio R Paula	01/2014
6894	2^212344-183	63922	Lelio R Paula	08/2011
6893	(58695*2^212336-1)/379	63922	Lelio R Paula	04/2015
6895	10^63916+79	63917	Robert Price	01/2011
6896	10^63916-76823	63916	Patrick De Geest	05/2013
6897	2^212295-25	63908	Lelio R Paula	08/2011
6899	2^212285-2383	63905	Yves Minet	10/2013
6898	267^26336+26336^267	63905	Norbert Schneider	09/2014
6900	(-lucasV(1,2,424552)-2)/1601	63899	Mike Oakes	03/2017
6901	19^49962+60	63890	Lelio R Paula	05/2013
6902	3^133906-113056	63890	Enzo Doria	07/2014
6903	(lucasV(1,2,424451)+2)/3	63886	Mike Oakes	03/2017
6904	3*6^82092+5	63881	Lelio R Paula	09/2014
6905	15441^13706+13706^15441	63879	Hans Havermann	02/2017
6906	2^212154-776351	63865	Paul Bourdelais	03/2013
6907	35^41359+2	63862	Lelio R Paula	05/2013
6908	(61*10^63857-43)/9	63858	Robert Price	09/2015
6909	(2^212131-3)/485	63856	Lelio R Paula	04/2012
6910	2^212112-459995	63853	Enzo Doria	06/2015
6911	15^54290+58	63850	Lelio R Paula	05/2013
6912	3*2^212097-7	63849	Lelio R Paula	04/2014
6913	55^36683-54	63842	Norbert Schneider	08/2014
6914	(509203*2^212056-1)/3	63841	Lelio R Paula	04/2015
6915	(3^133805-7)/172	63839	Lelio R Paula	04/2012
6916	2^212049+149	63834	Lelio R Paula	08/2011
6917	5^91318-18	63829	Lelio R Paula	04/2013
6918	18468^2857+2857^18468	63824	Hans Havermann	03/2017
6919	(2^212024-5)/1111	63823	Lelio R Paula	04/2012
6920	2^211961+12915	63807	Lelio R Paula	02/2013
6921	(3^133707-7)/5780	63791	Lelio R Paula	04/2012
6922	747^22198+22198^747	63782	Norbert Schneider	07/2016
6923	2^211800-17169	63759	Enzo Doria	05/2013
6924	(85*10^63757-1)/3	63759	Robert Price	07/2017
6925	(14*10^63747-11)/3	63748	Erik Branger	09/2014
6926	91*19^49848+6	63746	Curtis Bright	05/2015
6927	18855^2402+2402^18855	63741	Hans Havermann	03/2017
6928	(142*10^63734-7)/9	63736	Robert Price	02/2017
6929	2^211699-111	63728	Lelio R Paula	08/2011
6930	11^61192-5550	63725	Enzo Doria	01/2013
6931	(11*10^63718+7)/9	63719	Serge Batalov	06/2011
6932	6^81872-13	63709	Lelio R Paula	04/2013
6933	3^133522+98	63707	Lelio R Paula	05/2013
6935	2^211607-61	63701	Lelio R Paula	08/2011
6934	5^91135+8	63701	Lelio R Paula	04/2013
6936	11^61157-270	63689	Enzo Doria	07/2012
6938	10^63685+1145141919	63686	Marisa Kirisame	03/2015
6937	10^63685+103837	63686	Patrick De Geest	03/2016
6939	10^63685-130797	63685	Patrick De Geest	03/2016
6940	2^211547+1155*211547	63682	Henri Lifchitz	02/2005
6941	2^211543+45	63681	Lelio R Paula	08/2011
6942	2^211534+43	63679	Lelio R Paula	08/2011
6943	11^61140-60	63671	Enzo Doria	07/2012
6944	2^211491-112321	63666	Enzo Doria	06/2014
6945	19085^2164+2164^19085	63654	Hans Havermann	03/2017
6946	(2^211430-5)/859	63644	Lelio R Paula	04/2012
6947	2^211401-91	63639	Lelio R Paula	08/2011
6948	(6883*2^211378-1)/69	63634	Lelio R Paula	04/2015
6949	(F(152232)^3-F(152231)^3)/F(152230)	63629	Wayne Halsdorf	03/2012
6950	(29*2^211384-1)/50122621	63627	Lelio R Paula	01/2014
6951	2^211333+15015	63618	Lelio R Paula	01/2013
6952	33^41889-32	63610	Norbert Schneider	03/2014
6953	13^57093+18	63599	Lelio R Paula	05/2013
6954	(5*2^211219-1)/9	63583	Lelio R Paula	01/2014
6955	(107*10^63576-17)/9	63578	Robert Price	02/2017
6956	23^46687-1020	63575	Enzo Doria	08/2012
6957	(67607*2^211188+1)/5234319	63573	Lelio R Paula	06/2014
6958	(3^133243+7)/10726	63570	Lelio R Paula	04/2012
6959	(7*2^211181+1)/2745	63570	Lelio R Paula	06/2012
6961	(20^48859-1)/19	63566	Paul Bourdelais	03/2010
6960	2*3^133227+5	63566	Lelio R Paula	04/2014
6962	2^211155+113	63564	Lelio R Paula	08/2011
6963	2^211134+345	63558	Lelio R Paula	09/2011
6964	2^211121+16385	63554	Lelio R Paula	09/2011
6965	16996^5483+5483^16996	63549	Hans Havermann	02/2017
6966	(2^211079+9)/364283	63536	Lelio R Paula	03/2012
6967	3*10^63522+13	63523	Robert Price	08/2017
6968	15852^10157+10157^15852	63516	Hans Havermann	02/2017
6969	2^210948-15873	63502	Enzo Doria	04/2013
6970	7^75136+6	63498	Lelio R Paula	04/2013
6971	2^210928+12915	63496	Lelio R Paula	02/2013
6972	7*10^63493+39	63494	Robert Price	07/2016
6973	2^210909+135	63490	Lelio R Paula	08/2011
6974	(3*2^210832+1)/7	63467	Lelio R Paula	07/2012
6975	8*7^75098-3	63467	Lelio R Paula	09/2014
6976	17683^3882+3882^17683	63466	Hans Havermann	03/2017
6977	Pell-LucasQ(165799)/2	63464	Eric W. Weisstein	11/2006
6978	2^210820-16905	63464	Enzo Doria	05/2013
6979	5^90795-36	63463	Lelio R Paula	04/2013
6980	2^210816-13197	63462	Enzo Doria	10/2012
6981	2^210750+133	63443	Lelio R Paula	08/2011
6982	291^25742+25742^291	63426	Norbert Schneider	09/2014
6983	(3^132908+8)/279859	63408	Lelio R Paula	04/2012
6984	6^81480-139	63404	Lelio R Paula	04/2013
6985	2^210576-173	63390	Lelio R Paula	08/2011
6986	18^50497+55	63388	Lelio R Paula	05/2013
6987	2^210545+11	63381	Lelio R Paula	08/2011
6988	2^210543+63	63380	Lelio R Paula	08/2011
6989	83^33016+82	63361	Norbert Schneider	04/2015
6990	2^210464+98765331	63356	Jason Earls	12/2008
6991	7*10^63351+9	63352	Dmitry Domanov	11/2010
6992	p(13534)#/2+512	63348	Robert Price	05/2017
6993	1741^19546+19546^1741	63345	Serge Batalov	05/2014
6994	10^63336+19819	63337	Patrick De Geest	12/2013
6995	10^63336-122883	63336	Patrick De Geest	12/2013
6996	(19^49523-2^49523)/17	63327	Robert Price	09/2013
6997	(2^210378+47)/95516931	63323	Lelio R Paula	03/2012
6998	31191!2+256	63316	Robert Price	01/2015
6999	16458^7031+7031^16458	63315	Hans Havermann	01/2017
7000	(lucasV(1,2,420636)-2)/(731^2210319)	63303	Mike Oakes	03/2017

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PRP Records

Probable Primes Top 10000

(181746 PRPs in the top)