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 ?
7751	(21*2^214688+1)/293	64627	Lelio R Paula	08/2012
7752	92^32907+32907^92	64623	Serge Batalov	05/2014
7753	(89*10^64608-539)/9	64609	Robert Price	11/2017
7754	6^83013+101	64597	Lelio R Paula	07/2013
7755	p(13775)#/2+8	64594	Robert Price	01/2017
7756	(7*10^64568-43)/9	64568	Robert Price	10/2014
7757	Pell-LucasQ(168677)/2	64566	Eric W. Weisstein	11/2006
7758	(24737*2^214476+1)/2877	64565	Lelio R Paula	06/2014
7759	(47*2^214463+1)/7	64561	Lelio R Paula	04/2015
7760	2^214458+54615	64559	Lelio R Paula	10/2011
7761	(3^135322+7)/122911408	64557	Lelio R Paula	04/2012
7762	2^214389-683113	64538	Paul Bourdelais	03/2013
7763	(76*10^64534+113)/9	64535	Robert Price	11/2017
7764	2^214369-111241	64532	Enzo Doria	05/2014
7765	(19^50461+3^50461)/22	64526	Robert Price	07/2013
7766	11^61954-3660	64519	Enzo Doria	12/2012
7767	(23*2^214319-1)/21	64517	Lelio R Paula	01/2014
7768	(58695*2^214310-1)/571	64516	Lelio R Paula	04/2015
7769	35^41779-34	64510	Norbert Schneider	04/2014
7770	(159^29303+1)/160	64506	Eric Chen	12/2017
7771	(89*10^64504-179)/9	64505	Robert Price	11/2017
7772	11^61939-5220	64503	Enzo Doria	01/2013
7773	(2^214271+78557)/35	64501	Lelio R Paula	05/2012
7774	L(308604)+P(308604)	64495	Robert Price	12/2017
7775	126^30706-125	64494	Norbert Schneider	02/2015
7776	gcd(V(1157265),5F(231453)(F(231453)-1)+1)	64492	Serge Batalov	04/2015
7777	2^214215+12909	64486	Lelio R Paula	10/2011
7778	5^92225+66	64463	Lelio R Paula	06/2013
7779	2^214126-240551	64459	Paul Bourdelais	03/2013
7780	8*6^82827+5	64453	Lelio R Paula	09/2014
7781	(31*2^214120-1)/2170485	64452	Lelio R Paula	01/2014
7782	(31*2^214088-1)/5955	64445	Lelio R Paula	01/2014
7783	14^56227+89	64444	Lelio R Paula	08/2013
7786	2^214055-159	64437	Lelio R Paula	08/2011
7784	10^64436+2667	64437	Patrick De Geest	05/2013
7785	65^35543-64^35543	64437	Robert Price	08/2013
7787	10^64436-53	64436	Robert Price	05/2011
7788	(3^135043-lucasV(1,3,135043)+1)/3	64432	Paul Vanderveen	11/2017
7789	Phi(128878,10)/39503297927	64428	Maksym Voznyy	11/2015
7790	3^135027+100	64425	Lelio R Paula	05/2013
7791	(3^134972-7)/2	64398	Lelio R Paula	04/2012
7792	6*10^64387+7	64388	Dmitry Domanov	11/2010
7793	2^213864-18377	64380	Enzo Doria	05/2013
7794	(2^213821+9)/209	64365	Lelio R Paula	04/2012
7795	2^213788+135	64357	Lelio R Paula	08/2011
7796	(3^134883+2)/48313	64351	Lelio R Paula	04/2012
7797	(49^38069-46^38069)/3	64344	Serge Batalov	12/2016
7798	(11^61781+2^61781)/13	64338	Robert Price	02/2013
7799	6^82670+37	64330	Lelio R Paula	07/2013
7800	(3^134839+4)/32312959	64328	Lelio R Paula	04/2012
7801	(22*10^64326+161)/3	64327	Robert Price	02/2017
7802	11^61767-4050	64324	Enzo Doria	12/2012
7803	2^213645-114853	64314	Enzo Doria	05/2015
7804	13^57733+18	64312	Lelio R Paula	07/2013
7805	2^213621+72707	64307	Enzo Doria	04/2016
7806	10^64305+136791	64306	Patrick De Geest	05/2011
7807	10^64305-9	64305	Alexander Gramolin	01/2011
7808	V(307652)	64295	Serge Batalov	03/2015
7809	4*10^64286-89	64287	Robert Price	08/2017
7810	(2^213546-5)/2221	64281	Lelio R Paula	04/2012
7811	2^213438-58695	64252	Lelio R Paula	10/2011
7812	2^213367-105	64230	Lelio R Paula	08/2011
7813	595^23148+23148^595	64225	Norbert Schneider	07/2016
7814	3^134601+8680	64221	Lelio R Paula	05/2013
7815	(26*10^64220+61)/3	64221	Robert Price	06/2017
7816	500^23793+23793^500	64217	Norbert Schneider	08/2016
7817	179^28504-2	64216	Lelio R Paula	10/2017
7818	2^213314-455	64214	Yves Minet	02/2012
7819	39^40359-38	64214	Norbert Schneider	05/2014
7820	2^213292-16085	64208	Enzo Doria	04/2013
7821	(72524!5+1)/25	64203	Joe McLean	10/2018
7822	2^213274-77	64202	Lelio R Paula	08/2011
7823	19^50203+78	64198	Lelio R Paula	08/2013
7824	(44*10^64192-233)/9	64193	Robert Price	10/2017
7825	2^213240-112865	64192	Enzo Doria	06/2014
7826	2^213190-112391	64177	Enzo Doria	06/2014
7827	(9913*2^213184-1)/9657	64175	Lelio R Paula	04/2015
7828	14^55991+27	64173	Lelio R Paula	07/2013
7829	2^213158-112581	64167	Enzo Doria	06/2014
7830	2^213148+91	64164	Lelio R Paula	08/2011
7831	(96^32369+1)/97	64163	Paul Bourdelais	08/2017
7833	6^82439+125	64151	Lelio R Paula	07/2013
7832	7*2^213102+9	64151	Lelio R Paula	04/2014
7834	L(306854)+F(306855)	64129	Henri Lifchitz	01/2007
7835	610^23017+23017^610	64110	Norbert Schneider	07/2016
7836	2^212950-64875	64105	Lelio R Paula	10/2011
7837	(266*10^64102-17)/3	64104	Robert Price	06/2016
7838	p(13679)#/2+64	64097	Robert Price	03/2017
7839	19^50119+94	64090	Lelio R Paula	08/2013
7840	2^212880-147	64084	Lelio R Paula	08/2011
7841	11^61523-4590	64070	Enzo Doria	01/2013
7842	5^91663+38	64070	Lelio R Paula	05/2013
7843	5^91650+52	64061	Lelio R Paula	05/2013
7844	2^212770+69	64051	Lelio R Paula	08/2011
7845	(3^134227+1)/4	64042	Paul Bourdelais	11/2007
7846	(2*10^64041-17)/3	64041	Robert Price	08/2014
7847	(15^54449+1)/16	64036	Paul Bourdelais	03/2010
7848	(29*10^64027+91)/3	64028	Robert Price	03/2016
7849	(lucasV(1,2,425405)+2)/(17*89)	64027	Mike Oakes	03/2017
7850	16878!+16878#-1	64022	D. Gazzoni Filho & Lucas Teixeira	05/2005
7851	2^212663+53	64018	Lelio R Paula	08/2011
7852	(4*10^64014+197)/3	64015	Robert Price	03/2017
7853	85402!6-3	64014	Robert Price	08/2018
7854	(140^29819+1)/141	63994	Richard Fischer	05/2018
7855	10^63986+63	63987	Robert Price	01/2011
7856	10^63986-31557	63986	Patrick De Geest	05/2013
7857	31487!2-2^31487	63982	Robert Price	09/2015
7858	(21*2^212522-1)/1416323	63971	Lelio R Paula	01/2014
7859	5^91517+98	63968	Lelio R Paula	04/2013
7860	(19*10^63960-43)/3	63961	Robert Price	10/2017
7861	(62*10^63954-17)/9	63955	Robert Price	09/2015
7863	5^91493-4^91493	63951	Predrag Minovic	04/2004
7862	V(364793)	63951	Serge Batalov	03/2015
7865	19^50004+58	63943	Lelio R Paula	05/2013
7864	5*6^82172-7	63943	Lelio R Paula	09/2014
7866	(56*10^63942+223)/9	63943	Robert Price	07/2016
7867	19^50000-24	63938	Lelio R Paula	05/2013
7868	(23*2^212374-1)/27019	63928	Lelio R Paula	01/2014
7869	(9*2^212355-1)/761	63924	Lelio R Paula	01/2014
7871	2^212344-183	63922	Lelio R Paula	08/2011
7870	(58695*2^212336-1)/379	63922	Lelio R Paula	04/2015
7872	10^63916+79	63917	Robert Price	01/2011
7873	10^63916-76823	63916	Patrick De Geest	05/2013
7874	2^212295-25	63908	Lelio R Paula	08/2011
7876	2^212285-2383	63905	Yves Minet	10/2013
7875	267^26336+26336^267	63905	Norbert Schneider	09/2014
7877	(-lucasV(1,2,424552)-2)/1601	63899	Mike Oakes	03/2017
7878	19^49962+60	63890	Lelio R Paula	05/2013
7879	3^133906-113056	63890	Enzo Doria	07/2014
7880	(lucasV(1,2,424451)+2)/3	63886	Mike Oakes	03/2017
7881	3*6^82092+5	63881	Lelio R Paula	09/2014
7882	15441^13706+13706^15441	63879	Hans Havermann	02/2017
7883	2^212154-776351	63865	Paul Bourdelais	03/2013
7884	35^41359+2	63862	Lelio R Paula	05/2013
7885	(61*10^63857-43)/9	63858	Robert Price	09/2015
7886	(2^212131-3)/485	63856	Lelio R Paula	04/2012
7887	2^212112-459995	63853	Enzo Doria	06/2015
7888	15^54290+58	63850	Lelio R Paula	05/2013
7889	3*2^212097-7	63849	Lelio R Paula	04/2014
7890	55^36683-54	63842	Norbert Schneider	08/2014
7891	(509203*2^212056-1)/3	63841	Lelio R Paula	04/2015
7892	(3^133805-7)/172	63839	Lelio R Paula	04/2012
7893	2^212049+149	63834	Lelio R Paula	08/2011
7894	5^91318-18	63829	Lelio R Paula	04/2013
7895	18468^2857+2857^18468	63824	Hans Havermann	03/2017
7896	(2^212024-5)/1111	63823	Lelio R Paula	04/2012
7897	2^211961+12915	63807	Lelio R Paula	02/2013
7899	(3^133707-7)/5780	63791	Lelio R Paula	04/2012
7898	(44*10^63790-161)/9	63791	Robert Price	11/2017
7900	747^22198+22198^747	63782	Norbert Schneider	07/2016
7901	2^211800-17169	63759	Enzo Doria	05/2013
7902	(85*10^63757-1)/3	63759	Robert Price	07/2017
7903	85089!6-8	63757	Robert Price	08/2018
7904	(14*10^63747-11)/3	63748	Erik Branger	09/2014
7905	91*19^49848+6	63746	Curtis Bright	05/2015
7906	18855^2402+2402^18855	63741	Hans Havermann	03/2017
7907	(142*10^63734-7)/9	63736	Robert Price	02/2017
7908	2^211699-111	63728	Lelio R Paula	08/2011
7909	11^61192-5550	63725	Enzo Doria	01/2013
7910	(11*10^63718+7)/9	63719	Serge Batalov	06/2011
7911	6^81872-13	63709	Lelio R Paula	04/2013
7912	3^133522+98	63707	Lelio R Paula	05/2013
7914	2^211607-61	63701	Lelio R Paula	08/2011
7913	5^91135+8	63701	Lelio R Paula	04/2013
7915	11^61157-270	63689	Enzo Doria	07/2012
7917	10^63685+1145141919	63686	Marisa Kirisame	03/2015
7916	10^63685+103837	63686	Patrick De Geest	03/2016
7918	10^63685-130797	63685	Patrick De Geest	03/2016
7919	2^211547+1155*211547	63682	Henri Lifchitz	02/2005
7920	2^211543+45	63681	Lelio R Paula	08/2011
7921	2^211534+43	63679	Lelio R Paula	08/2011
7922	11^61140-60	63671	Enzo Doria	07/2012
7923	2^211491-112321	63666	Enzo Doria	06/2014
7924	19085^2164+2164^19085	63654	Hans Havermann	03/2017
7925	(2^211430-5)/859	63644	Lelio R Paula	04/2012
7926	2^211401-91	63639	Lelio R Paula	08/2011
7927	(6883*2^211378-1)/69	63634	Lelio R Paula	04/2015
7928	(F(152232)^3-F(152231)^3)/F(152230)	63629	Wayne Halsdorf	03/2012
7929	(29*2^211384-1)/50122621	63627	Lelio R Paula	01/2014
7930	2^211333+15015	63618	Lelio R Paula	01/2013
7931	33^41889-32	63610	Norbert Schneider	03/2014
7932	13^57093+18	63599	Lelio R Paula	05/2013
7933	(5*2^211219-1)/9	63583	Lelio R Paula	01/2014
7934	(107*10^63576-17)/9	63578	Robert Price	02/2017
7935	23^46687-1020	63575	Enzo Doria	08/2012
7936	(67607*2^211188+1)/5234319	63573	Lelio R Paula	06/2014
7937	(3^133243+7)/10726	63570	Lelio R Paula	04/2012
7938	(7*2^211181+1)/2745	63570	Lelio R Paula	06/2012
7940	(20^48859-1)/19	63566	Paul Bourdelais	03/2010
7939	2*3^133227+5	63566	Lelio R Paula	04/2014
7941	2^211155+113	63564	Lelio R Paula	08/2011
7942	2^211134+345	63558	Lelio R Paula	09/2011
7943	2^211121+16385	63554	Lelio R Paula	09/2011
7944	16996^5483+5483^16996	63549	Hans Havermann	02/2017
7945	(2^211079+9)/364283	63536	Lelio R Paula	03/2012
7946	3*10^63522+13	63523	Robert Price	08/2017
7947	15852^10157+10157^15852	63516	Hans Havermann	02/2017
7948	2^210948-15873	63502	Enzo Doria	04/2013
7949	7^75136+6	63498	Lelio R Paula	04/2013
7950	2^210928+12915	63496	Lelio R Paula	02/2013
7951	7*10^63493+39	63494	Robert Price	07/2016
7952	2^210909+135	63490	Lelio R Paula	08/2011
7953	(3*2^210832+1)/7	63467	Lelio R Paula	07/2012
7954	8*7^75098-3	63467	Lelio R Paula	09/2014
7955	17683^3882+3882^17683	63466	Hans Havermann	03/2017
7957	Pell-LucasQ(165799)/2	63464	Eric W. Weisstein	11/2006
7956	2^210820-16905	63464	Enzo Doria	05/2013
7958	5^90795-36	63463	Lelio R Paula	04/2013
7959	84731!6-48	63463	Robert Price	08/2018
7960	2^210816-13197	63462	Enzo Doria	10/2012
7961	2^210750+133	63443	Lelio R Paula	08/2011
7962	291^25742+25742^291	63426	Norbert Schneider	09/2014
7963	(3^132908+8)/279859	63408	Lelio R Paula	04/2012
7964	6^81480-139	63404	Lelio R Paula	04/2013
7965	2^210576-173	63390	Lelio R Paula	08/2011
7966	18^50497+55	63388	Lelio R Paula	05/2013
7967	2^210545+11	63381	Lelio R Paula	08/2011
7968	2^210543+63	63380	Lelio R Paula	08/2011
7969	155^28929-154	63365	Norbert Schneider	12/2018
7970	83^33016+82	63361	Norbert Schneider	04/2015
7971	2^210464+98765331	63356	Jason Earls	12/2008
7972	7*10^63351+9	63352	Dmitry Domanov	11/2010
7973	p(13534)#/2+512	63348	Robert Price	05/2017
7974	1741^19546+19546^1741	63345	Serge Batalov	05/2014
7975	10^63336+19819	63337	Patrick De Geest	12/2013
7976	10^63336-122883	63336	Patrick De Geest	12/2013
7977	(19^49523-2^49523)/17	63327	Robert Price	09/2013
7978	(2^210378+47)/95516931	63323	Lelio R Paula	03/2012
7979	31191!2+256	63316	Robert Price	01/2015
7980	16458^7031+7031^16458	63315	Hans Havermann	01/2017
7981	(lucasV(1,2,420636)-2)/(731^2210319)	63303	Mike Oakes	03/2017
7982	156^28864+155	63303	Norbert Schneider	12/2018
7983	(2^210283+7)/1691145	63296	Lelio R Paula	03/2012
7984	2^210217+1299	63282	Lelio R Paula	09/2011
7985	(2^210221-3)/269	63281	Lelio R Paula	04/2012
7986	Phi(193404,10)/386809/8122969	63268	Maksym Voznyy	10/2011
7987	96^31913-95	63261	Norbert Schneider	04/2016
7988	3^132572+280	63253	Lelio R Paula	04/2013
7989	3^132570-2^(132570-1)	63252	Robert Price	01/2016
7990	11^60734-4920	63248	Enzo Doria	01/2013
7992	2^210061+21	63235	Donovan Johnson	06/2006
7991	18^50375+95	63235	Lelio R Paula	05/2013
7993	85^32773-2	63233	Lelio R Paula	08/2013
7994	(-lucasV(1,2,420115)-2)/(3*5^3)	63232	Mike Oakes	02/2017
7995	(2^210054-1017)/671	63230	Lelio R Paula	04/2012
7996	3*2^210022+5	63224	Lelio R Paula	04/2014
7997	15^53756+32	63222	Lelio R Paula	05/2013
7999	17^51380+22	63221	Lelio R Paula	05/2013
7998	(lucasV(1,2,420045)+2)/257	63221	Mike Oakes	02/2017
8000	43^38700+42	63216	Norbert Schneider	06/2014

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Probable Primes Top 10000

(252538 PRPs in the top)