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	2^216752+21	65249	Lelio R Paula	08/2011
7752	3*10^65247+11	65248	Robert Price	11/2017
7753	11^62651-2700	65245	Enzo Doria	12/2012
7754	15130^15609-15609^15130	65244	Norbert Schneider	07/2018
7755	Pell-LucasQ(170413)/2	65230	Eric W. Weisstein	12/2006
7756	gcd(V(790525),5F(158105)(F(158105)+1)+1)	65230	Serge Batalov	04/2015
7757	(2^216676-1017)/637	65224	Lelio R Paula	04/2012
7758	2^216652-2327	65219	Yves Minet	10/2013
7759	(9179*2^216648-1)/4667	65218	Lelio R Paula	04/2015
7760	(5*10^65203-119)/3	65204	Robert Price	04/2016
7761	2^216555-113269	65190	Enzo Doria	07/2014
7762	(9513^16384+1)/2	65181	Henri Lifchitz	02/2007
7763	2^216474+12915	65166	Lelio R Paula	02/2013
7764	19^50958-32	65163	Lelio R Paula	08/2013
7765	2^216442-112133	65156	Enzo Doria	06/2014
7766	2^216437-112213	65155	Enzo Doria	06/2014
7767	2^216435-112767	65154	Enzo Doria	06/2014
7768	2^216420+12705	65149	Lelio R Paula	02/2013
7769	8*3^136507-7	65132	Lelio R Paula	04/2014
7770	(-lucasV(1,2,432719)-2)/(5*461)	65128	Mike Oakes	03/2017
7771	15132^15575-15575^15132	65102	Norbert Schneider	07/2018
7772	5*10^65086-51	65087	Robert Price	10/2017
7773	2^216197-111769	65082	Enzo Doria	05/2014
7774	6^83631-79	65078	Lelio R Paula	07/2013
7775	572^23601+23601^572	65078	Norbert Schneider	08/2016
7776	(3^136399-7)/544220	65074	Lelio R Paula	04/2012
7777	2^216154-1421	65069	Yves Minet	01/2013
7778	2^216145-112663	65067	Enzo Doria	06/2014
7779	(7*10^65064+53)/3	65065	Robert Price	10/2017
7780	132013*10^65050+2^216091-1	65056	Gilbert Mozzo	01/2014
7781	132019*10^65050+2^216091-1	65056	Gilbert Mozzo	01/2014
7782	148918*10^65050+2^216091-1	65056	Gilbert Mozzo	02/2014
7783	194014*10^65050+2^216091-1	65056	Gilbert Mozzo	02/2014
7784	223864*10^65050+2^216091-1	65056	Gilbert Mozzo	04/2014
7786	82090*10^65050+2^216091-1	65055	Gilbert Mozzo	07/2012
7787	95133*10^65050+2^216091-1	65055	Gilbert Mozzo	12/2013
7785	98142*10^65050+2^216091-1	65055	Gilbert Mozzo	12/2013
7788	((2^216091-1)*34009-48)/25	65054	Serge Batalov	01/2012
7789	5977*10^65050+2^216091-1	65054	Gilbert Mozzo	03/2012
7790	7*2^216091+2^298-13	65051	Peter Lesala	03/2007
7791	2^216091+2*29208-1	65050	Makoto Morimoto	10/2013
7792	(10^(232521+1)-610^32521-1)/3	65043	Robert Price	02/2016
7793	p(13861)#/2+256	65039	Robert Price	05/2017
7794	(2^216091-2096)/(2^432918437*5220283)	65036	Makoto Morimoto	10/2017
7795	11^62439-4380	65024	Enzo Doria	01/2013
7796	3^136244+2	65005	Mike Oakes	11/2009
7797	13^58343-50	64991	Lelio R Paula	07/2013
7798	331^25791-10002	64989	Enzo Doria	07/2012
7799	2^215877+131	64986	Lelio R Paula	08/2011
7800	4*5^92959+9	64977	Lelio R Paula	09/2014
7801	2^215789-18825	64959	Lelio R Paula	09/2011
7802	(2^215801-509203)/41327	64958	Lelio R Paula	05/2012
7803	U(315311)	64954	Serge Batalov	03/2015
7804	46072!3-59049	64951	Robert Price	12/2015
7805	2^215750-5955	64948	Lelio R Paula	09/2011
7806	13^58281+46	64922	Lelio R Paula	07/2013
7807	2^215623+183	64909	Lelio R Paula	08/2011
7808	(46*10^64904+521)/9	64905	Robert Price	08/2017
7809	(3^136043-2^136043)/(19862279*33466579)	64895	Mike Oakes	12/2016
7810	5*2^215554+3	64889	Lelio R Paula	04/2014
7811	2^215541-112075	64885	Enzo Doria	06/2014
7812	2*10^64882-3	64883	Dmitry Domanov	11/2010
7813	10^64862+342339	64863	Patrick De Geest	05/2013
7814	10^64862-47	64862	Robert Price	05/2011
7815	19^50718-84	64856	Lelio R Paula	08/2013
7816	(30452^215471-1)/(17115127067173473)	64853	Jens K. Andersen	09/2007
7817	86413!6-12	64846	Robert Price	08/2018
7818	10^64843+4278697839	64844	Robert Price	05/2015
7819	10^64843+21967	64844	Patrick De Geest	03/2016
7820	10^64843-340073	64843	Patrick De Geest	03/2016
7821	11^62254+70	64831	Lelio R Paula	07/2013
7822	2^215351-111925	64828	Enzo Doria	05/2014
7823	2^215310-117	64815	Lelio R Paula	08/2011
7824	124^30958-123	64809	Norbert Schneider	02/2015
7825	(7*10^64807+17)/3	64808	Erik Branger	03/2014
7826	(710^(232400+1)-27*10^32400-7)/9	64801	Robert Price	11/2015
7827	2^215243-15949	64795	Enzo Doria	04/2013
7828	23^47581-22^47581	64793	Robert Price	08/2012
7829	(62*10^64783-17)/9	64784	Robert Price	09/2015
7830	5*3^135747-4	64769	Lelio R Paula	04/2014
7831	(59*10^64767-41)/9	64768	Robert Price	09/2015
7833	(2^215140+3)/19	64763	Lelio R Paula	04/2012
7832	2^215135-17169	64763	Enzo Doria	05/2013
7834	2^215115-111277	64757	Enzo Doria	05/2014
7835	9*5^92641+2	64755	Lelio R Paula	09/2014
7836	(lucasV(1,2,430086)-2)/(7*1033)	64731	Mike Oakes	03/2017
7837	5791^17200+17200^5791	64720	Norbert Schneider	12/2018
7838	(5*10^64715-23)/9	64715	Robert Price	11/2014
7839	2^214938-1781	64703	Yves Minet	03/2013
7840	11^62111-420	64682	Enzo Doria	08/2012
7841	5^92525+42	64673	Lelio R Paula	06/2013
7842	2^214824+71893	64669	Enzo Doria	04/2016
7843	2^214799-2221	64661	Yves Minet	08/2013
7844	5939^17128+17128^5939	64637	Norbert Schneider	10/2018
7845	(21*2^214688+1)/293	64627	Lelio R Paula	08/2012
7846	92^32907+32907^92	64623	Serge Batalov	05/2014
7847	(89*10^64608-539)/9	64609	Robert Price	11/2017
7848	6^83013+101	64597	Lelio R Paula	07/2013
7849	p(13775)#/2+8	64594	Robert Price	01/2017
7850	(7*10^64568-43)/9	64568	Robert Price	10/2014
7851	Pell-LucasQ(168677)/2	64566	Eric W. Weisstein	11/2006
7852	(24737*2^214476+1)/2877	64565	Lelio R Paula	06/2014
7853	(47*2^214463+1)/7	64561	Lelio R Paula	04/2015
7854	2^214458+54615	64559	Lelio R Paula	10/2011
7855	(3^135322+7)/122911408	64557	Lelio R Paula	04/2012
7856	2^214389-683113	64538	Paul Bourdelais	03/2013
7857	(76*10^64534+113)/9	64535	Robert Price	11/2017
7858	2^214369-111241	64532	Enzo Doria	05/2014
7859	(19^50461+3^50461)/22	64526	Robert Price	07/2013
7860	11^61954-3660	64519	Enzo Doria	12/2012
7861	(23*2^214319-1)/21	64517	Lelio R Paula	01/2014
7862	(58695*2^214310-1)/571	64516	Lelio R Paula	04/2015
7863	2^214300-4547	64511	Yves Minet	03/2019
7864	35^41779-34	64510	Norbert Schneider	04/2014
7865	(159^29303+1)/160	64506	Eric Chen	12/2017
7866	(89*10^64504-179)/9	64505	Robert Price	11/2017
7867	11^61939-5220	64503	Enzo Doria	01/2013
7868	(2^214271+78557)/35	64501	Lelio R Paula	05/2012
7869	L(308604)+P(308604)	64495	Robert Price	12/2017
7870	126^30706-125	64494	Norbert Schneider	02/2015
7871	gcd(V(1157265),5F(231453)(F(231453)-1)+1)	64492	Serge Batalov	04/2015
7872	2^214215+12909	64486	Lelio R Paula	10/2011
7873	5^92225+66	64463	Lelio R Paula	06/2013
7874	2^214126-240551	64459	Paul Bourdelais	03/2013
7875	8*6^82827+5	64453	Lelio R Paula	09/2014
7876	(31*2^214120-1)/2170485	64452	Lelio R Paula	01/2014
7877	(31*2^214088-1)/5955	64445	Lelio R Paula	01/2014
7878	14^56227+89	64444	Lelio R Paula	08/2013
7881	2^214055-159	64437	Lelio R Paula	08/2011
7879	10^64436+2667	64437	Patrick De Geest	05/2013
7880	65^35543-64^35543	64437	Robert Price	08/2013
7882	10^64436-53	64436	Robert Price	05/2011
7883	(3^135043-lucasV(1,3,135043)+1)/3	64432	Paul Vanderveen	11/2017
7884	Phi(128878,10)/39503297927	64428	Maksym Voznyy	11/2015
7885	3^135027+100	64425	Lelio R Paula	05/2013
7886	(3^134972-7)/2	64398	Lelio R Paula	04/2012
7887	6*10^64387+7	64388	Dmitry Domanov	11/2010
7888	2^213864-18377	64380	Enzo Doria	05/2013
7889	(2^213821+9)/209	64365	Lelio R Paula	04/2012
7890	2^213788+135	64357	Lelio R Paula	08/2011
7891	(3^134883+2)/48313	64351	Lelio R Paula	04/2012
7892	(49^38069-46^38069)/3	64344	Serge Batalov	12/2016
7893	(11^61781+2^61781)/13	64338	Robert Price	02/2013
7894	6^82670+37	64330	Lelio R Paula	07/2013
7895	(3^134839+4)/32312959	64328	Lelio R Paula	04/2012
7896	(22*10^64326+161)/3	64327	Robert Price	02/2017
7897	11^61767-4050	64324	Enzo Doria	12/2012
7898	2^213645-114853	64314	Enzo Doria	05/2015
7899	13^57733+18	64312	Lelio R Paula	07/2013
7900	2^213621+72707	64307	Enzo Doria	04/2016
7901	10^64305+136791	64306	Patrick De Geest	05/2011
7902	10^64305-9	64305	Alexander Gramolin	01/2011
7903	V(307652)	64295	Serge Batalov	03/2015
7904	4*10^64286-89	64287	Robert Price	08/2017
7905	(2^213546-5)/2221	64281	Lelio R Paula	04/2012
7906	2^213438-58695	64252	Lelio R Paula	10/2011
7907	2^213367-105	64230	Lelio R Paula	08/2011
7908	595^23148+23148^595	64225	Norbert Schneider	07/2016
7909	3^134601+8680	64221	Lelio R Paula	05/2013
7910	(26*10^64220+61)/3	64221	Robert Price	06/2017
7911	500^23793+23793^500	64217	Norbert Schneider	08/2016
7912	179^28504-2	64216	Lelio R Paula	10/2017
7913	2^213314-455	64214	Yves Minet	02/2012
7914	39^40359-38	64214	Norbert Schneider	05/2014
7915	2^213292-16085	64208	Enzo Doria	04/2013
7916	(72524!5+1)/25	64203	Joe McLean	10/2018
7917	2^213274-77	64202	Lelio R Paula	08/2011
7918	19^50203+78	64198	Lelio R Paula	08/2013
7919	(44*10^64192-233)/9	64193	Robert Price	10/2017
7920	2^213240-112865	64192	Enzo Doria	06/2014
7921	2^213190-112391	64177	Enzo Doria	06/2014
7922	(9913*2^213184-1)/9657	64175	Lelio R Paula	04/2015
7923	14^55991+27	64173	Lelio R Paula	07/2013
7924	2^213158-112581	64167	Enzo Doria	06/2014
7925	2^213148+91	64164	Lelio R Paula	08/2011
7926	(96^32369+1)/97	64163	Paul Bourdelais	08/2017
7928	6^82439+125	64151	Lelio R Paula	07/2013
7927	7*2^213102+9	64151	Lelio R Paula	04/2014
7929	L(306854)+F(306855)	64129	Henri Lifchitz	01/2007
7930	610^23017+23017^610	64110	Norbert Schneider	07/2016
7931	2^212950-64875	64105	Lelio R Paula	10/2011
7932	(266*10^64102-17)/3	64104	Robert Price	06/2016
7933	p(13679)#/2+64	64097	Robert Price	03/2017
7934	19^50119+94	64090	Lelio R Paula	08/2013
7935	2^212880-147	64084	Lelio R Paula	08/2011
7936	11^61523-4590	64070	Enzo Doria	01/2013
7937	5^91663+38	64070	Lelio R Paula	05/2013
7938	5^91650+52	64061	Lelio R Paula	05/2013
7939	2^212770+69	64051	Lelio R Paula	08/2011
7940	(3^134227+1)/4	64042	Paul Bourdelais	11/2007
7941	(2*10^64041-17)/3	64041	Robert Price	08/2014
7942	(15^54449+1)/16	64036	Paul Bourdelais	03/2010
7943	(29*10^64027+91)/3	64028	Robert Price	03/2016
7944	(lucasV(1,2,425405)+2)/(17*89)	64027	Mike Oakes	03/2017
7945	16878!+16878#-1	64022	D. Gazzoni Filho & Lucas Teixeira	05/2005
7946	2^212663+53	64018	Lelio R Paula	08/2011
7947	(4*10^64014+197)/3	64015	Robert Price	03/2017
7948	85402!6-3	64014	Robert Price	08/2018
7949	(140^29819+1)/141	63994	Richard Fischer	05/2018
7950	10^63986+63	63987	Robert Price	01/2011
7951	10^63986-31557	63986	Patrick De Geest	05/2013
7952	31487!2-2^31487	63982	Robert Price	09/2015
7953	(21*2^212522-1)/1416323	63971	Lelio R Paula	01/2014
7954	5^91517+98	63968	Lelio R Paula	04/2013
7955	(19*10^63960-43)/3	63961	Robert Price	10/2017
7956	(62*10^63954-17)/9	63955	Robert Price	09/2015
7958	5^91493-4^91493	63951	Predrag Minovic	04/2004
7957	V(364793)	63951	Serge Batalov	03/2015
7959	19^50004+58	63943	Lelio R Paula	05/2013
7961	5*6^82172-7	63943	Lelio R Paula	09/2014
7960	(56*10^63942+223)/9	63943	Robert Price	07/2016
7962	19^50000-24	63938	Lelio R Paula	05/2013
7963	(23*2^212374-1)/27019	63928	Lelio R Paula	01/2014
7964	(9*2^212355-1)/761	63924	Lelio R Paula	01/2014
7966	2^212344-183	63922	Lelio R Paula	08/2011
7965	(58695*2^212336-1)/379	63922	Lelio R Paula	04/2015
7967	10^63916+79	63917	Robert Price	01/2011
7968	10^63916-76823	63916	Patrick De Geest	05/2013
7969	2^212295-25	63908	Lelio R Paula	08/2011
7970	2^212285-2383	63905	Yves Minet	10/2013
7971	267^26336+26336^267	63905	Norbert Schneider	09/2014
7972	(-lucasV(1,2,424552)-2)/1601	63899	Mike Oakes	03/2017
7973	19^49962+60	63890	Lelio R Paula	05/2013
7974	3^133906-113056	63890	Enzo Doria	07/2014
7975	(lucasV(1,2,424451)+2)/3	63886	Mike Oakes	03/2017
7976	3*6^82092+5	63881	Lelio R Paula	09/2014
7977	15441^13706+13706^15441	63879	Hans Havermann	02/2017
7978	2^212154-776351	63865	Paul Bourdelais	03/2013
7979	35^41359+2	63862	Lelio R Paula	05/2013
7980	(61*10^63857-43)/9	63858	Robert Price	09/2015
7981	(2^212131-3)/485	63856	Lelio R Paula	04/2012
7982	2^212112-459995	63853	Enzo Doria	06/2015
7983	15^54290+58	63850	Lelio R Paula	05/2013
7984	3*2^212097-7	63849	Lelio R Paula	04/2014
7985	55^36683-54	63842	Norbert Schneider	08/2014
7986	(509203*2^212056-1)/3	63841	Lelio R Paula	04/2015
7987	(3^133805-7)/172	63839	Lelio R Paula	04/2012
7988	2^212049+149	63834	Lelio R Paula	08/2011
7989	5^91318-18	63829	Lelio R Paula	04/2013
7990	18468^2857+2857^18468	63824	Hans Havermann	03/2017
7991	(2^212024-5)/1111	63823	Lelio R Paula	04/2012
7992	2^211961+12915	63807	Lelio R Paula	02/2013
7993	(3^133707-7)/5780	63791	Lelio R Paula	04/2012
7994	(44*10^63790-161)/9	63791	Robert Price	11/2017
7995	747^22198+22198^747	63782	Norbert Schneider	07/2016
7997	2^211800-17169	63759	Enzo Doria	05/2013
7996	(85*10^63757-1)/3	63759	Robert Price	07/2017
7998	85089!6-8	63757	Robert Price	08/2018
7999	(14*10^63747-11)/3	63748	Erik Branger	09/2014
8000	91*19^49848+6	63746	Curtis Bright	05/2015

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PRP Records

Probable Primes Top 10000

(252675 PRPs in the top)