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*5^104888-7	73314	Lelio R Paula	10/2014
6752	(58695*2^243516-1)/983	73308	Lelio R Paula	04/2015
6753	(3^153648-2)/33423138097	73299	Lelio R Paula	06/2012
6754	18^58376-5255	73278	Enzo Doria	03/2013
6755	11^70363+32	73276	Lelio R Paula	02/2015
6756	2^243413+4257	73275	Lelio R Paula	05/2013
6757	104824^5+5^104824	73269	Andrey Kulsha	07/2010
6758	7^86689-6^86689	73261	Predrag Minovic	09/2004
6759	2^243296+90195	73240	Lelio R Paula	05/2013
6760	2^243281-4843	73235	Yves Minet	05/2019
6762	p(15433)#/2-4	73218	Robert Price	12/2016
6761	(59*10^73217-77)/9	73218	Robert Price	11/2017
6763	2^243127+71355	73189	Lelio R Paula	05/2013
6764	2^243116-249419	73186	Paul Bourdelais	03/2013
6765	(58695*2^243085-1)/11	73180	Lelio R Paula	04/2015
6766	11^70262-98	73171	Lelio R Paula	02/2015
6767	(2^243034+47)/722703303	73152	Lelio R Paula	07/2012
6768	(2^242966+47)/46887	73136	Lelio R Paula	07/2012
6769	(43^44773-1)/42	73134	Robert Price	04/2014
6770	6^93980-158359	73131	Mike Oakes	02/2011
6771	6^93915+53	73081	Lelio R Paula	01/2015
6772	(5*10^73079+211)/9	73079	Robert Price	12/2017
6773	(74*10^73076+43)/9	73077	Robert Price	10/2015
6774	(3^153125+2)/1144955	73054	Lelio R Paula	06/2012
6775	2^242632-112199	73040	Enzo Doria	06/2014
6776	V(351646)	73029	Serge Batalov	03/2015
6777	18^58175-85	73026	Lelio R Paula	01/2015
6778	p(15395)#/2-4	73019	Robert Price	12/2016
6779	(4^121271+3^121271)/7	73012	Jean-Louis Charton	03/2011
6780	8*6^93825-5	73011	Lelio R Paula	10/2014
6781	(F(220)^1601-F(219)^1601)/F(218)	73005	Wayne Halsdorf	08/2013
6782	(73^39181+1)/74	73005	Paul Bourdelais	08/2017
6783	6^93815+143	73003	Lelio R Paula	01/2015
6784	6^93812+5	73000	Wojciech Florek	03/2006
6785	19^57078-62	72989	Lelio R Paula	01/2015
6786	(29*10^72985+91)/3	72986	Robert Price	03/2016
6787	11^70082-2520	72983	Enzo Doria	12/2012
6788	6^93773+133	72970	Lelio R Paula	01/2015
6789	2^242328-59	72948	Lelio R Paula	03/2012
6790	5^104358-13016	72944	Enzo Doria	02/2013
6791	(75*10^72941-57)/99	72941	Ray Chandler	03/2011
6792	12^67585-95	72937	Lelio R Paula	02/2015
6793	2^242230-113285	72919	Enzo Doria	07/2014
6794	(5*10^72916-11)/3	72917	Erik Branger	12/2013
6795	2^242220-110399	72916	Enzo Doria	05/2014
6796	2^242205-113413	72911	Enzo Doria	07/2014
6797	(3^152809+3^76405+1)/7	72908	Serge Batalov	03/2014
6798	2^242175+74243	72902	Yves Minet	03/2011
6799	2^242150+17659	72895	Lelio R Paula	11/2009
6800	11^69982-2340	72879	Enzo Doria	12/2012
6801	(23*2^242093+1)/10117	72875	Lelio R Paula	08/2012
6802	(67607*2^242043+1)/33263	72863	Lelio R Paula	06/2014
6803	2^242032+87	72859	Lelio R Paula	03/2012
6804	2^241968-110595	72840	Enzo Doria	05/2014
6805	(10^72821+71)/9	72821	Robert Price	11/2014
6806	2^241852-64875	72805	Lelio R Paula	05/2013
6807	F(348307)/20562890865908093	72776	Donovan Johnson	07/2007
6808	(67*10^72772+23)/9	72773	Ray Chandler	11/2010
6809	(8*10^72759+67)/3	72760	Robert Price	01/2017
6810	2^241670+145	72750	Lelio R Paula	03/2012
6811	5^104074+52	72745	Lelio R Paula	08/2014
6812	(3^152466-5)/724	72742	Lelio R Paula	06/2012
6813	20^55908-41	72738	Lelio R Paula	01/2015
6814	(73*10^72735+53)/9	72736	Robert Price	10/2015
6815	10^72730+224011	72731	Patrick De Geest	05/2013
6816	10^72730-99	72730	Robert Price	05/2011
6817	3*10^72723+67	72724	Robert Price	11/2017
6818	(11^69833+3^69833)/14	72723	Robert Price	03/2013
6819	(10^72723-79)/3	72723	Robert Price	10/2017
6820	(88*10^72711-43)/9	72712	Robert Price	11/2015
6821	3^152379+280	72704	Lelio R Paula	01/2015
6822	(25*10^72703-241)/9	72704	Robert Price	01/2017
6823	(47*10^72696+133)/9	72697	Robert Price	04/2017
6824	17^59077-90	72692	Lelio R Paula	01/2015
6825	65^40096+58	72691	Lelio R Paula	01/2016
6826	(29*2^241446-1)/245	72682	Lelio R Paula	01/2014
6828	11^69783-38400000	72672	Enzo Doria	01/2013
6827	2^241409-112903	72672	Enzo Doria	06/2014
6829	(3^152287+1)/4	72659	Paul Bourdelais	04/2008
6830	3^152249-56	72642	Lelio R Paula	01/2015
6831	10^72631+37	72632	Robert Price	01/2011
6832	10^72631-8813	72631	Patrick De Geest	05/2013
6833	(19*2^241254+1)/101	72624	Lelio R Paula	08/2012
6834	(9^76103+8^76103)/17	72620	Robert Price	12/2012
6835	2^241220-112337	72615	Enzo Doria	06/2014
6836	(82*10^72612+449)/9	72613	Robert Price	02/2017
6837	2^241169-15793	72600	Enzo Doria	04/2013
6838	9*10^72595+11	72596	Robert Kinser	01/2017
6839	(25*2^241048+1)/89	72563	Lelio R Paula	08/2012
6840	(22*10^72560+17)/3	72561	Robert Price	09/2015
6841	2^241032-23	72558	Lelio R Paula	02/2012
6842	34485*10^72550+2^241004-3	72555	Gilbert Mozzo	12/2012
6843	2^241004-3	72550	M. Frind & P. Underwood	07/2002
6844	97*10^72522-3	72524	Robert Price	01/2017
6845	(68*10^72516+7)/3	72518	Robert Price	03/2016
6846	(78557*2^240844+1)/63	72505	Lelio R Paula	06/2014
6847	67^39701-66	72497	Norbert Schneider	11/2014
6848	(185*10^72484+7)/3	72486	Robert Price	02/2017
6850	(293*27^50631-1736)/13	72473	Curtis Bright	05/2015
6849	103^36005-102	72473	Norbert Schneider	10/2016
6851	15^61616+88	72467	Lelio R Paula	01/2015
6852	45^43831+2	72462	Lelio R Paula	05/2013
6853	2^240692-492389	72456	Paul Bourdelais	03/2013
6854	(646*10^72446-7)/9	72448	Robert Price	07/2016
6855	9*6^93083+7	72434	Lelio R Paula	10/2014
6856	2^240617-3645	72433	Lelio R Paula	05/2013
6857	11^69531-24000	72410	Enzo Doria	12/2012
6858	(22699*2^240396+1)/55	72370	Lelio R Paula	06/2014
6859	6^92995+13	72365	Lelio R Paula	01/2015
6860	(11*10^72362-149)/3	72363	Robert Price	01/2017
6861	(2^240381+3)/51655	72358	Lelio R Paula	05/2012
6862	6^92974-55	72348	Lelio R Paula	01/2015
6863	2^240295+11	72337	Lelio R Paula	02/2012
6864	(14*10^72326-53)/3	72327	Robert Price	12/2016
6865	15^61493-46	72322	Lelio R Paula	01/2015
6866	lucasU(46,1,43497)-lucasU(46,1,43496)	72315	Mike Oakes	04/2009
6867	5*10^72302+9	72303	Dmitry Domanov	11/2010
6868	(9787*2^240179-1)/265	72303	Lelio R Paula	04/2015
6869	11^69419-3120	72293	Enzo Doria	12/2012
6870	4*10^72274-83	72275	Robert Price	10/2017
6871	10^72267+33	72268	Robert Price	01/2011
6872	10^72267-553947	72267	Patrick De Geest	05/2013
6873	11^69389-1380	72262	Enzo Doria	12/2012
6874	(16^60013-5^60013)/11	72262	Robert Price	07/2013
6875	7^85507-30	72262	Lelio R Paula	08/2014
6876	(19*2^240026-1)/15	72256	Lelio R Paula	02/2014
6877	(3^151426-2)/661337	72243	Lelio R Paula	06/2012
6878	gcd(V(1296375),5F(259275)(F(259275)-1)+1)	72227	Serge Batalov	04/2015
6879	2^239863-112267	72206	Enzo Doria	06/2014
6880	2^239853-114853	72203	Enzo Doria	05/2015
6881	(4*10^72174+149)/9	72174	Robert Price	03/2017
6882	(2^239671+9)/296131	72143	Lelio R Paula	05/2012
6883	2^239651-110665	72143	Enzo Doria	05/2014
6884	(29*2^239650-1)/3305	72140	Lelio R Paula	01/2014
6885	241^30280+30280^241	72128	Norbert Schneider	11/2014
6886	(68*10^72120-23)/9	72121	Robert Price	10/2015
6887	(9^75571+8^75571)/17	72112	Robert Price	12/2012
6888	(15*2^239530-1)/173	72105	Lelio R Paula	01/2014
6889	2^239513-112519	72101	Enzo Doria	06/2014
6890	(10^72097+149)/3	72097	Serge Batalov	12/2014
6891	2^239442-6555	72080	Lelio R Paula	05/2012
6892	2*5^103106+3	72069	Lelio R Paula	10/2014
6893	2^239402-197	72068	Lelio R Paula	02/2012
6894	2^239356-111875	72054	Enzo Doria	05/2014
6895	(38*10^72050-119)/9	72051	Robert Price	11/2016
6896	2^239339+15015	72049	Lelio R Paula	01/2013
6897	159^32728+2	72048	Lelio R Paula	05/2013
6898	15^61259-38	72047	Lelio R Paula	01/2015
6899	92^36683-91^36683	72038	Robert Price	08/2015
6900	2^239280+54615	72031	Lelio R Paula	05/2012
6902	(47*2^239267+1)/77	72027	Lelio R Paula	04/2015
6901	(85*10^72025-1)/3	72027	Robert Price	07/2017
6903	2^239236-97305	72018	Lelio R Paula	05/2012
6904	144^33361-143	72006	Norbert Schneider	11/2018
6905	2^239169+59	71998	Lelio R Paula	02/2012
6907	lucasU(2010,1,21796)-lucasU(2010,1,21795)	71994	Mike Oakes	05/2009
6906	(15*2^239171-1)/106301	71994	Lelio R Paula	01/2014
6908	(29^49211-1)/28	71965	Robert Price	04/2012
6909	(299*10^71963+1)/3	71965	Robert Price	11/2017
6911	L(344293)	71953	Renaud Lifchitz	09/2003
6910	V(344293)	71953	Serge Batalov	03/2015
6912	6*10^71951+7	71952	Dmitry Domanov	11/2010
6913	3^150798+40	71949	Lelio R Paula	01/2015
6914	2^238961+95	71935	Lelio R Paula	02/2012
6915	2^238936-407	71927	Yves Minet	02/2012
6916	2^238923-28635	71923	Lelio R Paula	05/2012
6917	10^71910+25119	71911	Patrick De Geest	05/2016
6918	10^71910-801	71910	Robert Price	04/2016
6919	2^238845-112651	71900	Enzo Doria	06/2014
6920	2^238792-111245	71884	Enzo Doria	05/2014
6921	6*7^85059+5	71884	Lelio R Paula	10/2014
6922	2^238752-110589	71872	Enzo Doria	05/2014
6923	12^66581+7	71853	Lelio R Paula	07/2014
6924	(7*2^238691+1)/41229	71850	Lelio R Paula	06/2012
6925	4*3^150568-5	71840	Lelio R Paula	04/2014
6926	6^92301+67	71825	Lelio R Paula	01/2015
6927	2^238568+98765331	71817	Jason Earls	01/2009
6928	2^238541-112723	71808	Enzo Doria	06/2014
6929	2^238529-15949	71805	Enzo Doria	04/2013
6930	9*5^102721-8	71800	Lelio R Paula	10/2014
6931	2^238494-165	71794	Lelio R Paula	02/2012
6932	2^238389-110905	71763	Enzo Doria	05/2014
6933	(145*10^71760-1)/9	71762	Serge Batalov	12/2014
6934	7^84913+5062	71760	Mike Oakes	02/2010
6935	(F(11446)^31-F(11445)^31)/F(11444)	71753	Wayne Halsdorf	03/2012
6936	2^238268-97305	71726	Lelio R Paula	05/2012
6937	gcd(V(1330365),5F(266073)(F(266073)-1)+1)	71724	Serge Batalov	04/2015
6938	2^238235-113247	71716	Enzo Doria	07/2014
6939	2*12^66450-5^66450	71712	Mike Oakes	11/2010
6940	(2^238213+lucasV(1,2,238213)+1)/4	71709	Mike Oakes	11/2016
6941	2^238199-111817	71706	Enzo Doria	05/2014
6942	lucasU(46,1,43125)+lucasU(46,1,43124)	71696	Mike Oakes	04/2009
6943	2^238144+98765331	71689	Jason Earls	01/2009
6944	18^57102-4265	71679	Enzo Doria	03/2013
6945	(73*10^71670-1)/9	71671	Robert Price	01/2015
6946	2^238081+1155*238081	71670	Henri Lifchitz	02/2005
6947	2^238067-111925	71666	Enzo Doria	05/2014
6948	36^46030+35	71637	Norbert Schneider	04/2014
6949	(74*10^71621+313)/9	71622	Robert Price	11/2017
6950	2^237905-91	71617	Lelio R Paula	02/2012
6951	(31*2^237902-1)/123	71616	Lelio R Paula	01/2014
6952	(15185*2^237866-1)/43967	71605	Lelio R Paula	04/2015
6953	(24737*2^237841+1)/25	71601	Lelio R Paula	06/2014
6954	2^237846+1299	71599	Lelio R Paula	05/2012
6955	6^92004+199801	71594	Mike Oakes	02/2011
6956	159^32516+2	71581	Lelio R Paula	05/2013
6957	2^237781+855	71580	Lelio R Paula	05/2012
6958	2^237720-4079	71561	Yves Minet	06/2011
6959	2^237698-110945	71555	Enzo Doria	05/2014
6960	2^237695-113239	71554	Enzo Doria	07/2014
6961	8*5^102362-9	71549	Lelio R Paula	10/2014
6962	(4*10^71546-31)/9	71546	Erik Branger	05/2011
6963	2^237650+37	71540	Lelio R Paula	02/2012
6964	18^56977-4391	71522	Enzo Doria	03/2013
6965	(22699*2^237565+1)/4136637	71512	Lelio R Paula	06/2014
6966	((1+sqrt(7)+sqrt(6))^48479-1)((1+sqrt(7)-sqrt(6))^48479-1)((1-sqrt(7)+sqrt(6))^48479-1)*((1-sqrt(7	71512	Mike Oakes	05/2009
6967	(26*10^71503+7)/3	71504	Erik Branger	11/2013
6968	(4*10^71498+173)/3	71499	Robert Price	01/2017
6969	3^149848+110	71496	Lelio R Paula	11/2014
6970	2^237498+513	71495	Lelio R Paula	05/2012
6971	2^237485+107	71491	Lelio R Paula	02/2012
6972	(2^237465+9)/2419	71481	Lelio R Paula	05/2012
6973	2^237439-112237	71477	Enzo Doria	06/2014
6974	2^237407-9787	71467	Lelio R Paula	11/2009
6975	2^237383+72953	71460	Enzo Doria	04/2016
6976	82^37337-81^37337	71457	Robert Price	01/2015
6977	(1017*2^237313-1)/19	71441	Lelio R Paula	04/2015
6978	2^237311+191	71438	Lelio R Paula	02/2012
6979	2^237280-59	71429	Lelio R Paula	02/2012
6980	11^68564-98	71403	Lelio R Paula	01/2015
6981	2^237173+74801	71397	Enzo Doria	04/2016
6982	15^60697+56	71386	Lelio R Paula	01/2015
6983	2^237118+177	71380	Lelio R Paula	02/2012
6984	2^237110+69	71378	Lelio R Paula	02/2012
6985	15^60690-58	71377	Lelio R Paula	01/2015
6986	(5*2^237125-1)/599851191	71374	Lelio R Paula	01/2014
6987	(3^149567+2)/539	71359	Lelio R Paula	06/2012
6988	(5*10^71357-143)/3	71358	Robert Price	04/2016
6989	2^237039-114621	71356	Enzo Doria	05/2015
6990	12^66116-37	71352	Lelio R Paula	02/2015
6991	(3^149497+2^149497)/5	71328	Jean-Louis Charton	10/2010
6992	2^236941-66945	71327	Lelio R Paula	05/2012
6993	2^236911-1147	71318	Yves Minet	10/2009
6994	65^39337+42	71315	Lelio R Paula	01/2016
6995	6*10^71299+7	71300	Dmitry Domanov	11/2010
6996	(25*2^236843+1)/3753	71295	Lelio R Paula	06/2012
6997	10^71291+15187	71292	Patrick De Geest	03/2016
6999	10^71291-5587309119	71291	Robert Price	03/2015
6998	10^71291-273581	71291	Patrick De Geest	03/2016
7000	-numer(bernoulli(22808)/22808)	71290	T. D. Noe	09/2005

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Probable Primes Top 10000

(252932 PRPs in the top)