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 ?
7751	11^58849-6040	61285	Enzo Doria	02/2013
7752	43694!3-3	61264	Robert Price	10/2014
7753	58(10^(320420)-1)/111-1	61260	Robert Price	10/2014
7754	2^203490+12909	61257	Lelio R Paula	10/2011
7755	(16*10^61251-31)/3	61252	Robert Price	03/2016
7756	20^47077-5703	61249	Enzo Doria	03/2013
7757	2^203434-113081	61240	Enzo Doria	07/2014
7759	5^87606+4	61234	Wojciech Florek	11/2005
7758	2^203412-167	61234	Lelio R Paula	08/2011
7761	2^203402+1089	61231	Lelio R Paula	10/2011
7760	(8*10^61230+67)/3	61231	Robert Price	01/2017
7762	(2^203408+lucasV(1,2,203408)+1)/(2*32993)	61228	Mike Oakes	11/2016
7763	1265^19732+19732^1265	61211	Serge Batalov	05/2014
7764	2^203330+145	61209	Lelio R Paula	08/2011
7765	6^78647-137	61200	Lelio R Paula	04/2013
7766	85^31718+84	61198	Norbert Schneider	10/2015
7767	11^58763-270	61196	Enzo Doria	07/2012
7768	2^203285-112321	61195	Enzo Doria	06/2014
7769	2^203253-995143	61186	Paul Bourdelais	11/2012
7770	15319^9862+9862^15319	61184	Hans Havermann	07/2016
7771	7^72395-44	61181	Lelio R Paula	04/2013
7772	(49*10^61167-67)/9	61168	Robert Price	08/2017
7773	5*2^203176-7	61163	Lelio R Paula	04/2014
7774	(26*10^61156-413)/9	61157	Robert Price	10/2017
7775	7^72358+54	61150	Lelio R Paula	04/2013
7776	2^203133-111775	61150	Enzo Doria	05/2014
7777	(lucasV(1,2,406356)+2)/(3^251119315836979671743)	61145	Mike Oakes	01/2017
7778	2^203112-18009	61143	Enzo Doria	05/2013
7779	43607!3+729	61129	Robert Price	09/2014
7780	2^203065-114853	61129	Enzo Doria	05/2015
7781	3^128111+196	61125	Lelio R Paula	04/2013
7782	128^29007+29007^128	61124	Serge Batalov	05/2014
7783	4*10^61119+49	61120	Robert Price	08/2017
7784	22355*2^203009-3	61117	Donovan Johnson	03/2004
7785	2^203018+33	61115	Lelio R Paula	08/2011
7786	2^203017-1615	61115	Lelio R Paula	10/2011
7787	16697^4570+4570^16697	61110	Hans Havermann	12/2016
7788	2^202998-17241	61109	Enzo Doria	05/2013
7789	20^46964+93	61102	Lelio R Paula	06/2013
7790	(55*10^61097-1)/9	61098	Ray Chandler	02/2012
7791	20^46960-5463	61097	Enzo Doria	03/2013
7792	(11*10^61095+49)/3	61096	Robert Price	05/2016
7793	2^202934-5955	61090	Lelio R Paula	10/2011
7794	19^47772-68	61089	Lelio R Paula	05/2013
7795	2^202877-499423	61073	Paul Bourdelais	03/2013
7796	2^202763-17125	61038	Enzo Doria	05/2013
7797	(23*2^202756+1)/9	61037	Lelio R Paula	03/2012
7798	14788^13355+13355^14788	61011	Hans Havermann	12/2016
7799	16069^6258+6258^16069	61005	Hans Havermann	12/2016
7800	5^87276-14336	61004	Enzo Doria	02/2013
7801	50^35899-49^35899	60992	Robert Price	12/2012
7802	2^202599-3049	60989	Yves Minet	10/2014
7803	2^202535-111571	60970	Enzo Doria	05/2014
7804	(13*10^60966+107)/3	60967	Robert Price	11/2017
7806	10^60959+57	60960	Patrick De Geest	12/2008
7805	6*10^60959-91	60960	Robert Price	11/2017
7808	10^60959-60959	60959	Henri Lifchitz	08/2002
7807	10^60959-29177	60959	Patrick De Geest	08/2008
7809	5^87206+4^(87206+1)	60955	Robert Price	07/2016
7810	2^202476-15909	60952	Enzo Doria	04/2013
7811	2^202472-17513	60951	Enzo Doria	05/2013
7812	14858^12651+12651^14858	60950	Hans Havermann	12/2016
7813	2^202389-58695	60926	Lelio R Paula	09/2011
7814	3^127597-34	60880	Lelio R Paula	04/2013
7815	15088^10831+10831^15088	60876	Hans Havermann	12/2016
7816	2^202198-113261	60868	Enzo Doria	07/2014
7817	2^202182+135	60863	Lelio R Paula	08/2011
7818	2^202176+85	60862	Lelio R Paula	08/2011
7819	5183^16384+5182^16384	60860	Henri Lifchitz	01/2007
7820	(31*2^202163+1)/3	60859	Lelio R Paula	03/2012
7821	14708^13707+13707^14708	60847	Hans Havermann	12/2016
7822	2^202112+202112^2-1	60842	Robert Price	04/2014
7823	(13*2^202142-1)/405984274257	60841	Lelio R Paula	01/2014
7824	64743*10^60832+(6^78175-11)/5	60837	Gilbert Mozzo	05/2012
7825	(19*2^202098-1)/6795	60836	Lelio R Paula	01/2014
7826	(6^78175-11)/5	60832	Paul Bourdelais	11/2011
7827	2^202063+1605	60828	Lelio R Paula	09/2011
7828	2^202058+859	60826	Lelio R Paula	09/2011
7829	1576^19021+19021^1576	60821	Serge Batalov	05/2014
7830	(2^202009+3)/6005	60807	Lelio R Paula	03/2012
7831	10^60776+3	60777	Robert Price	01/2011
7832	10^60776-14819	60776	Patrick De Geest	12/2012
7833	55*10^60772+7	60774	Robert Price	10/2017
7834	(6883*2^201869-1)/35	60771	Lelio R Paula	04/2015
7835	(27*2^201841-1)/43	60760	Lelio R Paula	01/2014
7836	2^201822-177	60755	Lelio R Paula	08/2011
7837	(13*10^60744+17)/3	60745	Robert Price	06/2015
7838	(31*2^201754-1)/99	60734	Lelio R Paula	01/2014
7839	(26*10^60717-71)/9	60718	Robert Price	03/2015
7840	37^38712-2	60709	Lelio R Paula	08/2013
7841	2^201657-112003	60705	Enzo Doria	05/2014
7842	(10^60703+3^60703)/13	60702	Robert Price	01/2013
7843	2^201622-112817	60695	Enzo Doria	06/2014
7844	2^201620-17177	60694	Enzo Doria	05/2013
7845	(2^201615-3)*6-7	60693	Gilbert Mozzo	05/2016
7846	2^201609-49789	60691	Henri Lifchitz	03/2005
7847	2^201582-19061	60683	Enzo Doria	05/2013
7848	43316!3+27	60679	Robert Price	09/2014
7849	(509203*2^201564-1)/5067	60679	Lelio R Paula	04/2015
7850	2^201560+105	60676	Lelio R Paula	08/2011
7851	(27*2^201584-1)/646755486457	60673	Lelio R Paula	01/2014
7852	2^201545-18021	60672	Enzo Doria	05/2013
7853	2^201543+11715	60671	Lelio R Paula	09/2011
7855	2^201512-111755	60662	Enzo Doria	05/2014
7854	p(13013)#/2+64	60662	Robert Price	03/2017
7856	11^58248+16	60660	Lelio R Paula	05/2013
7857	2^201496-27	60657	Lelio R Paula	08/2011
7858	5*10^60655+57	60656	Robert Price	11/2017
7859	(7*10^60643+197)/3	60644	Robert Price	07/2017
7860	2^201426-16097	60636	Enzo Doria	04/2013
7861	(17*10^60631-11)/3	60632	Robert Price	07/2015
7862	6^77916-77	60631	Lelio R Paula	04/2013
7863	(27*2^201410-1)/491	60630	Lelio R Paula	01/2014
7864	5^86727+98	60620	Lelio R Paula	04/2013
7865	17^49266-26	60620	Lelio R Paula	05/2013
7866	20^46589-33	60614	Lelio R Paula	05/2013
7867	6^77889+65	60610	Lelio R Paula	04/2013
7868	139901#+148387	60595	Nicolas PALAU	09/2016
7869	2^201285-111723	60593	Enzo Doria	05/2014
7870	46199*2^201268+129647	60593	Paul Vanderveen	11/2016
7872	3^126991-100	60591	Lelio R Paula	04/2013
7871	2^201278-111623	60591	Enzo Doria	05/2014
7873	5^86682-16004	60589	Enzo Doria	05/2014
7874	(865*10^60583-1)/9	60585	Robert Price	11/2017
7875	(58*10^60579+221)/9	60580	Robert Price	02/2017
7876	9*2^201231-5	60578	Lelio R Paula	04/2014
7877	4*10^60572-89	60573	Robert Price	08/2017
7878	(78557*2^201207+1)/13067	60571	Lelio R Paula	06/2014
7879	2^201186-66945	60564	Lelio R Paula	09/2011
7880	2^201186-94395	60564	Lelio R Paula	09/2011
7881	65^33403+32	60557	Lelio R Paula	01/2016
7882	103^30079+102	60545	Norbert Schneider	10/2016
7883	(1000159^10091+1)/1000160	60541	Faysal YAtim	08/2008
7884	2^201098-17717	60537	Enzo Doria	05/2013
7885	(3^126881+8)/4829	60534	Lelio R Paula	03/2012
7886	2^201074+75049	60530	Enzo Doria	04/2016
7887	11^58111-1290	60517	Enzo Doria	11/2012
7888	(509203*2^201012-1)/9	60516	Lelio R Paula	04/2015
7889	2^200911+5711	60481	Lelio R Paula	10/2011
7890	(2^200912-3)/23	60480	Lelio R Paula	03/2012
7891	18^48179-17^48179	60478	Jean-Louis Charton	12/2010
7893	38^38281-37^38281	60476	Robert Price	09/2012
7892	4*7^71560-3	60476	Lelio R Paula	09/2014
7894	(10^(230232+1)+1510^30232-1)/3	60465	Robert Price	04/2016
7895	lucasV(1,2,401712)+2	60464	Mike Oakes	01/2017
7896	2^200833-18493	60457	Enzo Doria	05/2013
7897	20^46465-5043	60453	Enzo Doria	03/2013
7898	2^200810-18257	60450	Enzo Doria	05/2013
7899	5^86466-14336	60438	Enzo Doria	02/2013
7900	Phi(145558,10)/103928413/161714939/14779231531/36075385837/242411419853	60432	Maksym Voznyy	10/2011
7901	(29*2^200703-1)/231	60417	Lelio R Paula	01/2014
7902	2^200682-1016831	60412	Paul Bourdelais	11/2012
7903	2^200617-17881	60392	Enzo Doria	05/2013
7904	(25^43201+1)/26	60391	Robert Price	06/2013
7906	2^200609-133	60390	Lelio R Paula	08/2011
7905	2^200608-12837	60390	Enzo Doria	10/2012
7907	2^200607-17121	60389	Enzo Doria	05/2013
7908	11^57975-1620	60375	Enzo Doria	11/2012
7909	(9913*2^200538-1)/3801	60369	Lelio R Paula	04/2015
7910	5^86342+64	60351	Lelio R Paula	04/2013
7911	(14*10^60346-23)/9	60347	Robert Price	04/2015
7912	2^200457-8295	60344	Lelio R Paula	09/2011
7913	6^77546+113	60343	Lelio R Paula	04/2013
7915	37^38461-36^38461	60315	Robert Price	06/2012
7914	2^200361-17593	60315	Enzo Doria	05/2013
7916	10103^15059-106	60304	Enzo Doria	07/2012
7917	2^200301-17401	60297	Enzo Doria	05/2013
7918	(37*10^60290+71)/9	60291	Robert Price	04/2015
7919	2^200266-94395	60287	Lelio R Paula	09/2011
7920	2^200261-111613	60285	Enzo Doria	05/2014
7921	46^36238-45	60256	Norbert Schneider	07/2014
7922	13^54091+94	60255	Lelio R Paula	05/2013
7923	311^24171-154	60253	Enzo Doria	07/2012
7924	2^200120-81089	60243	Paul Bourdelais	01/2012
7925	3^126262+8680	60243	Lelio R Paula	04/2013
7926	43031!3-59049	60239	Robert Price	12/2015
7927	2^200100-111269	60237	Enzo Doria	05/2014
7928	(29*2^200069-1)/5373	60225	Lelio R Paula	01/2014
7929	20^46283-1923	60216	Enzo Doria	03/2013
7930	2^200011-112075	60210	Enzo Doria	05/2014
7931	2^200002+74539	60207	Enzo Doria	04/2016
7932	(386027912^200026-1)/(5778492645749*3427009)	60203	Jens K. Andersen	09/2007
7933	(28*10^60180+149)/3	60181	Robert Price	10/2017
7934	2^199872+93	60168	Donovan Johnson	06/2008
7935	6^77321+77	60168	Lelio R Paula	04/2013
7936	(86*10^60165-77)/9	60166	Robert Price	05/2016
7937	(2^199868+78557)/23373	60162	Lelio R Paula	05/2012
7938	7^71180+82	60155	Lelio R Paula	04/2013
7940	2^199814-112295	60151	Enzo Doria	06/2014
7939	(51^35227-1)/50	60151	Paul Bourdelais	08/2017
7941	42964!3-81	60135	Robert Price	09/2014
7942	2^199709-51	60119	Lelio R Paula	05/2011
7943	2^199700-111623	60116	Enzo Doria	05/2014
7944	(15185*2^199681-1)/159	60112	Lelio R Paula	04/2015
7945	2^199672+2533	60108	Henri Lifchitz	09/2004
7946	20^46198-11	60105	Lelio R Paula	04/2013
7947	2^199657+93257	60103	Yves Minet	03/2010
7948	3^125967-110	60102	Lelio R Paula	10/2012
7949	2^199654-18813	60102	Enzo Doria	05/2013
7950	(29*10^60100+19)/3	60101	Robert Price	01/2017
7951	2^199615-2*199615+1	60091	Robert Price	04/2018
7952	129^28468+28468^129	60085	Serge Batalov	05/2014
7953	2^199572-15873	60078	Enzo Doria	04/2013
7954	9*2^199559+7	60075	Lelio R Paula	03/2014
7955	2^199527-111919	60064	Enzo Doria	05/2014
7956	2^199522+82875	60063	Lelio R Paula	10/2012
7957	5^85928-72	60062	Lelio R Paula	10/2012
7958	39^37749+38	60062	Norbert Schneider	05/2014
7959	6^77182-143	60060	Lelio R Paula	10/2012
7960	2^199502-2145	60057	Lelio R Paula	06/2011
7961	2^199493+4257	60054	Lelio R Paula	06/2011
7962	2^199488+40755	60052	Lelio R Paula	06/2011
7963	(2^199451+9)/25619	60037	Lelio R Paula	02/2012
7964	2^199425-61	60033	Lelio R Paula	05/2011
7965	(85*10^60026+23)/9	60027	Robert Price	11/2015
7966	65^33107+62	60021	Lelio R Paula	01/2016
7968	2^199362-1215	60014	Lelio R Paula	06/2011
7967	2^199362-111633	60014	Enzo Doria	05/2014
7969	1537^18832+18832^1537	60012	Serge Batalov	05/2014
7970	2^199324-17433	60003	Enzo Doria	05/2013
7971	10^60000+204331	60001	Milton L. Brown	04/2006
7972	10^60000+87129	60001	Milton L. Brown	04/2006
7973	143^27838-2	60001	Lelio R Paula	10/2017
7987	10^59999+65197	60000	Patrick De Geest	04/2005
7988	10^60000-32529	60000	Patrick De Geest	08/2009
7989	(10^60000+2249)/9	60000	Makoto Morimoto	09/2016
7990	((2^43112609)/10^24296)%10^60000	60000	Michael Vang	10/2016
7991	(2^57885161/10^105090)%10^60000	60000	Michael Vang	10/2016
7992	(2^42643801/10^58945)%10^60000	60000	Michael Vang	10/2016
7974	(2^37156667/10^243655)%10^60000	60000	Michael Vang	10/2016
7975	(2^30402457/10^69028)%10^60000	60000	Michael Vang	11/2016
7976	(2^32582657/10^248088)%10^60000	60000	Michael Vang	11/2016
7977	(2^32582657/10^238942)%10^60000	60000	Michael Vang	11/2016
7978	(2^24036583/10^13547)%10^60000	60000	Michael Vang	11/2016
7979	(2^20996011/10^131008)%10^60000	60000	Michael Vang	11/2016
7980	(2^13466917/10^79774)%10^60000	60000	Michael Vang	11/2016
7981	(2^13466917/10^102581)%10^60000	60000	Michael Vang	11/2016
7982	(2^6972593/10^339640)%10^60000	60000	Michael Vang	11/2016
7983	(2^2976221/10^65464)%10^60000	60000	Michael Vang	12/2016
7984	(2^1398269/10^61138)%10^60000	60000	Michael Vang	12/2016
7985	(2^3021377/10^418881)%10^60000	60000	Michael Vang	12/2016
7986	(2^1257787/10^164080)%10^60000	60000	Michael Vang	12/2016
7996	10^59999-516267	59999	Patrick De Geest	06/2009
7995	20^46116-41	59999	Lelio R Paula	03/2013
7993	(2^74207281/10^184638)%10^60000	59999	Michael Vang	10/2016
7994	(2^25964951/10^135429)%10^60000	59999	Michael Vang	11/2016
7997	6^77100-55	59996	Lelio R Paula	10/2012
7999	(19*2^199274+1)/161	59987	Lelio R Paula	07/2012
7998	(23^44053+1)/24	59987	Robert Price	06/2013
8000	9^62848+6^62848-2^62848	59973	Mike Oakes	08/2010

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PRP Records

Probable Primes Top 10000

(205869 PRPs in the top)