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 ?
6001	13^66179+66	73720	Lelio R Paula	01/2015
6002	(82*10^73714-1)/9	73715	Robert Price	12/2014
6003	(29*2^244856-1)/186121	73706	Lelio R Paula	01/2014
6004	(13*2^244840-1)/2799	73702	Lelio R Paula	01/2014
6005	(13*10^73701+17)/3	73702	Robert Price	06/2015
6006	(2^244787-1017)/28411	73684	Lelio R Paula	07/2012
6007	(3^154421-4)/23	73677	Lelio R Paula	06/2012
6008	8*7^87170+5	73669	Lelio R Paula	10/2014
6009	(29*10^73659-113)/3	73660	Robert Price	11/2017
6010	Phi(40100,-40100)	73651	Henri Lifchitz	06/2013
6011	(4*10^73647-19)/3	73648	Robert Price	06/2017
6012	2^244618-2297	73638	Yves Minet	10/2009
6013	3*5^105344+8	73633	Lelio R Paula	10/2014
6014	5^105334-14096	73626	Enzo Doria	02/2013
6015	(2^244584-7)/13237074243033	73614	Lelio R Paula	07/2012
6016	2^244465-110185	73592	Enzo Doria	05/2014
6017	2^244443+40755	73585	Lelio R Paula	05/2013
6018	2^244404+3841	73573	Yves Minet	03/2011
6019	2^244372-110627	73564	Enzo Doria	05/2014
6020	(3*2^244255+1)/245	73527	Lelio R Paula	08/2012
6021	(11*2^244245+1)/23	73525	Lelio R Paula	08/2012
6022	(15185*2^244187-1)/6111	73509	Lelio R Paula	04/2015
6023	(91^37507+1)/92	73476	Paul Bourdelais	08/2017
6024	18^58521+65	73460	Lelio R Paula	01/2015
6025	13^65940+36	73454	Lelio R Paula	01/2015
6026	(625^26267+1)/626	73437	Richard Fischer	12/2017
6027	5^105050-14	73427	Lelio R Paula	08/2014
6028	(((((((((((((30201^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2	73401	Serge Batalov	07/2016
6029	15^62410-46	73400	Lelio R Paula	01/2015
6030	2^243733+1869707	73371	Enzo Doria	05/2016
6031	11^70439-5430	73355	Enzo Doria	01/2013
6032	2^243676-87	73354	Lelio R Paula	03/2012
6033	(101*10^73346-17)/3	73348	Robert Price	08/2016
6034	2^243621-113185	73338	Enzo Doria	07/2014
6035	(5*2^243610-1)/1669	73332	Lelio R Paula	01/2014
6036	2*5^104888-7	73314	Lelio R Paula	10/2014
6037	(58695*2^243516-1)/983	73308	Lelio R Paula	04/2015
6038	(3^153648-2)/33423138097	73299	Lelio R Paula	06/2012
6039	18^58376-5255	73278	Enzo Doria	03/2013
6040	11^70363+32	73276	Lelio R Paula	02/2015
6041	2^243413+4257	73275	Lelio R Paula	05/2013
6042	104824^5+5^104824	73269	Andrey Kulsha	07/2010
6043	7^86689-6^86689	73261	Predrag Minovic	09/2004
6044	2^243296+90195	73240	Lelio R Paula	05/2013
6046	p(15433)#/2-4	73218	Robert Price	12/2016
6045	(59*10^73217-77)/9	73218	Robert Price	11/2017
6047	2^243127+71355	73189	Lelio R Paula	05/2013
6048	2^243116-249419	73186	Paul Bourdelais	03/2013
6049	(58695*2^243085-1)/11	73180	Lelio R Paula	04/2015
6050	11^70262-98	73171	Lelio R Paula	02/2015
6051	(2^243034+47)/722703303	73152	Lelio R Paula	07/2012
6052	(2^242966+47)/46887	73136	Lelio R Paula	07/2012
6053	(43^44773-1)/42	73134	Robert Price	04/2014
6054	6^93980-158359	73131	Mike Oakes	02/2011
6055	6^93915+53	73081	Lelio R Paula	01/2015
6056	(5*10^73079+211)/9	73079	Robert Price	12/2017
6057	(74*10^73076+43)/9	73077	Robert Price	10/2015
6058	(3^153125+2)/1144955	73054	Lelio R Paula	06/2012
6059	2^242632-112199	73040	Enzo Doria	06/2014
6060	V(351646)	73029	Serge Batalov	03/2015
6061	18^58175-85	73026	Lelio R Paula	01/2015
6062	p(15395)#/2-4	73019	Robert Price	12/2016
6063	(4^121271+3^121271)/7	73012	Jean-Louis Charton	03/2011
6064	8*6^93825-5	73011	Lelio R Paula	10/2014
6066	(F(220)^1601-F(219)^1601)/F(218)	73005	Wayne Halsdorf	08/2013
6065	(73^39181+1)/74	73005	Paul Bourdelais	08/2017
6067	6^93815+143	73003	Lelio R Paula	01/2015
6068	6^93812+5	73000	Wojciech Florek	03/2006
6069	19^57078-62	72989	Lelio R Paula	01/2015
6070	(29*10^72985+91)/3	72986	Robert Price	03/2016
6071	11^70082-2520	72983	Enzo Doria	12/2012
6072	6^93773+133	72970	Lelio R Paula	01/2015
6073	2^242328-59	72948	Lelio R Paula	03/2012
6074	5^104358-13016	72944	Enzo Doria	02/2013
6075	(75*10^72941-57)/99	72941	Ray Chandler	03/2011
6076	12^67585-95	72937	Lelio R Paula	02/2015
6077	2^242230-113285	72919	Enzo Doria	07/2014
6078	(5*10^72916-11)/3	72917	Erik Branger	12/2013
6079	2^242220-110399	72916	Enzo Doria	05/2014
6080	2^242205-113413	72911	Enzo Doria	07/2014
6081	(3^152809+3^76405+1)/7	72908	Serge Batalov	03/2014
6082	2^242175+74243	72902	Yves Minet	03/2011
6083	2^242150+17659	72895	Lelio R Paula	11/2009
6084	11^69982-2340	72879	Enzo Doria	12/2012
6085	(23*2^242093+1)/10117	72875	Lelio R Paula	08/2012
6086	(67607*2^242043+1)/33263	72863	Lelio R Paula	06/2014
6087	2^242032+87	72859	Lelio R Paula	03/2012
6088	2^241968-110595	72840	Enzo Doria	05/2014
6089	(10^72821+71)/9	72821	Robert Price	11/2014
6090	2^241852-64875	72805	Lelio R Paula	05/2013
6091	F(348307)/20562890865908093	72776	Donovan Johnson	07/2007
6092	(67*10^72772+23)/9	72773	Ray Chandler	11/2010
6093	(8*10^72759+67)/3	72760	Robert Price	01/2017
6094	2^241670+145	72750	Lelio R Paula	03/2012
6095	5^104074+52	72745	Lelio R Paula	08/2014
6096	(3^152466-5)/724	72742	Lelio R Paula	06/2012
6097	20^55908-41	72738	Lelio R Paula	01/2015
6098	(73*10^72735+53)/9	72736	Robert Price	10/2015
6099	10^72730+224011	72731	Patrick De Geest	05/2013
6100	10^72730-99	72730	Robert Price	05/2011
6101	3*10^72723+67	72724	Robert Price	11/2017
6102	(11^69833+3^69833)/14	72723	Robert Price	03/2013
6103	(10^72723-79)/3	72723	Robert Price	10/2017
6104	(88*10^72711-43)/9	72712	Robert Price	11/2015
6105	3^152379+280	72704	Lelio R Paula	01/2015
6106	(25*10^72703-241)/9	72704	Robert Price	01/2017
6107	(47*10^72696+133)/9	72697	Robert Price	04/2017
6108	17^59077-90	72692	Lelio R Paula	01/2015
6109	65^40096+58	72691	Lelio R Paula	01/2016
6110	(29*2^241446-1)/245	72682	Lelio R Paula	01/2014
6112	11^69783-38400000	72672	Enzo Doria	01/2013
6111	2^241409-112903	72672	Enzo Doria	06/2014
6113	(3^152287+1)/4	72659	Paul Bourdelais	04/2008
6114	3^152249-56	72642	Lelio R Paula	01/2015
6115	10^72631+37	72632	Robert Price	01/2011
6116	10^72631-8813	72631	Patrick De Geest	05/2013
6117	(19*2^241254+1)/101	72624	Lelio R Paula	08/2012
6118	(9^76103+8^76103)/17	72620	Robert Price	12/2012
6119	2^241220-112337	72615	Enzo Doria	06/2014
6120	(82*10^72612+449)/9	72613	Robert Price	02/2017
6121	2^241169-15793	72600	Enzo Doria	04/2013
6122	9*10^72595+11	72596	Robert Kinser	01/2017
6123	(25*2^241048+1)/89	72563	Lelio R Paula	08/2012
6124	(22*10^72560+17)/3	72561	Robert Price	09/2015
6125	2^241032-23	72558	Lelio R Paula	02/2012
6126	34485*10^72550+2^241004-3	72555	Gilbert Mozzo	12/2012
6127	2^241004-3	72550	M. Frind & P. Underwood	07/2002
6128	97*10^72522-3	72524	Robert Price	01/2017
6129	(68*10^72516+7)/3	72518	Robert Price	03/2016
6130	(78557*2^240844+1)/63	72505	Lelio R Paula	06/2014
6131	67^39701-66	72497	Norbert Schneider	11/2014
6132	(185*10^72484+7)/3	72486	Robert Price	02/2017
6134	(293*27^50631-1736)/13	72473	Curtis Bright	05/2015
6133	103^36005-102	72473	Norbert Schneider	10/2016
6135	15^61616+88	72467	Lelio R Paula	01/2015
6136	45^43831+2	72462	Lelio R Paula	05/2013
6137	2^240692-492389	72456	Paul Bourdelais	03/2013
6138	(646*10^72446-7)/9	72448	Robert Price	07/2016
6139	9*6^93083+7	72434	Lelio R Paula	10/2014
6140	2^240617-3645	72433	Lelio R Paula	05/2013
6141	11^69531-24000	72410	Enzo Doria	12/2012
6142	(22699*2^240396+1)/55	72370	Lelio R Paula	06/2014
6143	6^92995+13	72365	Lelio R Paula	01/2015
6144	(11*10^72362-149)/3	72363	Robert Price	01/2017
6145	(2^240381+3)/51655	72358	Lelio R Paula	05/2012
6146	6^92974-55	72348	Lelio R Paula	01/2015
6147	2^240295+11	72337	Lelio R Paula	02/2012
6148	(14*10^72326-53)/3	72327	Robert Price	12/2016
6149	15^61493-46	72322	Lelio R Paula	01/2015
6150	lucasU(46,1,43497)-lucasU(46,1,43496)	72315	Mike Oakes	04/2009
6151	5*10^72302+9	72303	Dmitry Domanov	11/2010
6152	(9787*2^240179-1)/265	72303	Lelio R Paula	04/2015
6153	11^69419-3120	72293	Enzo Doria	12/2012
6154	4*10^72274-83	72275	Robert Price	10/2017
6155	10^72267+33	72268	Robert Price	01/2011
6156	10^72267-553947	72267	Patrick De Geest	05/2013
6157	11^69389-1380	72262	Enzo Doria	12/2012
6158	(16^60013-5^60013)/11	72262	Robert Price	07/2013
6159	7^85507-30	72262	Lelio R Paula	08/2014
6160	(19*2^240026-1)/15	72256	Lelio R Paula	02/2014
6161	(3^151426-2)/661337	72243	Lelio R Paula	06/2012
6162	gcd(V(1296375),5F(259275)(F(259275)-1)+1)	72227	Serge Batalov	04/2015
6163	2^239863-112267	72206	Enzo Doria	06/2014
6164	2^239853-114853	72203	Enzo Doria	05/2015
6165	(4*10^72174+149)/9	72174	Robert Price	03/2017
6167	(2^239671+9)/296131	72143	Lelio R Paula	05/2012
6166	2^239651-110665	72143	Enzo Doria	05/2014
6168	(29*2^239650-1)/3305	72140	Lelio R Paula	01/2014
6169	241^30280+30280^241	72128	Norbert Schneider	11/2014
6170	(68*10^72120-23)/9	72121	Robert Price	10/2015
6171	(9^75571+8^75571)/17	72112	Robert Price	12/2012
6172	(15*2^239530-1)/173	72105	Lelio R Paula	01/2014
6173	2^239513-112519	72101	Enzo Doria	06/2014
6174	(10^72097+149)/3	72097	Serge Batalov	12/2014
6175	2^239442-6555	72080	Lelio R Paula	05/2012
6176	2*5^103106+3	72069	Lelio R Paula	10/2014
6177	2^239402-197	72068	Lelio R Paula	02/2012
6178	2^239356-111875	72054	Enzo Doria	05/2014
6179	(38*10^72050-119)/9	72051	Robert Price	11/2016
6180	2^239339+15015	72049	Lelio R Paula	01/2013
6181	159^32728+2	72048	Lelio R Paula	05/2013
6182	15^61259-38	72047	Lelio R Paula	01/2015
6183	92^36683-91^36683	72038	Robert Price	08/2015
6184	2^239280+54615	72031	Lelio R Paula	05/2012
6185	(47*2^239267+1)/77	72027	Lelio R Paula	04/2015
6186	(85*10^72025-1)/3	72027	Robert Price	07/2017
6187	2^239236-97305	72018	Lelio R Paula	05/2012
6188	2^239169+59	71998	Lelio R Paula	02/2012
6189	lucasU(2010,1,21796)-lucasU(2010,1,21795)	71994	Mike Oakes	05/2009
6190	(15*2^239171-1)/106301	71994	Lelio R Paula	01/2014
6191	(29^49211-1)/28	71965	Robert Price	04/2012
6192	(299*10^71963+1)/3	71965	Robert Price	11/2017
6194	L(344293)	71953	Renaud Lifchitz	09/2003
6193	V(344293)	71953	Serge Batalov	03/2015
6195	6*10^71951+7	71952	Dmitry Domanov	11/2010
6196	3^150798+40	71949	Lelio R Paula	01/2015
6197	2^238961+95	71935	Lelio R Paula	02/2012
6198	2^238936-407	71927	Yves Minet	02/2012
6199	2^238923-28635	71923	Lelio R Paula	05/2012
6200	10^71910+25119	71911	Patrick De Geest	05/2016
6201	10^71910-801	71910	Robert Price	04/2016
6202	2^238845-112651	71900	Enzo Doria	06/2014
6203	2^238792-111245	71884	Enzo Doria	05/2014
6204	6*7^85059+5	71884	Lelio R Paula	10/2014
6205	2^238752-110589	71872	Enzo Doria	05/2014
6206	12^66581+7	71853	Lelio R Paula	07/2014
6207	(7*2^238691+1)/41229	71850	Lelio R Paula	06/2012
6208	4*3^150568-5	71840	Lelio R Paula	04/2014
6209	6^92301+67	71825	Lelio R Paula	01/2015
6210	2^238568+98765331	71817	Jason Earls	01/2009
6211	2^238541-112723	71808	Enzo Doria	06/2014
6212	2^238529-15949	71805	Enzo Doria	04/2013
6213	9*5^102721-8	71800	Lelio R Paula	10/2014
6214	2^238494-165	71794	Lelio R Paula	02/2012
6215	2^238389-110905	71763	Enzo Doria	05/2014
6216	(145*10^71760-1)/9	71762	Serge Batalov	12/2014
6217	7^84913+5062	71760	Mike Oakes	02/2010
6218	(F(11446)^31-F(11445)^31)/F(11444)	71753	Wayne Halsdorf	03/2012
6219	2^238268-97305	71726	Lelio R Paula	05/2012
6220	gcd(V(1330365),5F(266073)(F(266073)-1)+1)	71724	Serge Batalov	04/2015
6221	2^238235-113247	71716	Enzo Doria	07/2014
6222	2*12^66450-5^66450	71712	Mike Oakes	11/2010
6223	(2^238213+lucasV(1,2,238213)+1)/4	71709	Mike Oakes	11/2016
6224	2^238199-111817	71706	Enzo Doria	05/2014
6225	lucasU(46,1,43125)+lucasU(46,1,43124)	71696	Mike Oakes	04/2009
6226	2^238144+98765331	71689	Jason Earls	01/2009
6227	18^57102-4265	71679	Enzo Doria	03/2013
6228	(73*10^71670-1)/9	71671	Robert Price	01/2015
6229	2^238081+1155*238081	71670	Henri Lifchitz	02/2005
6230	2^238067-111925	71666	Enzo Doria	05/2014
6231	36^46030+35	71637	Norbert Schneider	04/2014
6232	(74*10^71621+313)/9	71622	Robert Price	11/2017
6233	2^237905-91	71617	Lelio R Paula	02/2012
6234	(31*2^237902-1)/123	71616	Lelio R Paula	01/2014
6235	(15185*2^237866-1)/43967	71605	Lelio R Paula	04/2015
6236	(24737*2^237841+1)/25	71601	Lelio R Paula	06/2014
6237	2^237846+1299	71599	Lelio R Paula	05/2012
6238	6^92004+199801	71594	Mike Oakes	02/2011
6239	159^32516+2	71581	Lelio R Paula	05/2013
6240	2^237781+855	71580	Lelio R Paula	05/2012
6241	2^237720-4079	71561	Yves Minet	06/2011
6242	2^237698-110945	71555	Enzo Doria	05/2014
6243	2^237695-113239	71554	Enzo Doria	07/2014
6244	8*5^102362-9	71549	Lelio R Paula	10/2014
6245	(4*10^71546-31)/9	71546	Erik Branger	05/2011
6246	2^237650+37	71540	Lelio R Paula	02/2012
6247	18^56977-4391	71522	Enzo Doria	03/2013
6248	(22699*2^237565+1)/4136637	71512	Lelio R Paula	06/2014
6249	((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
6250	(26*10^71503+7)/3	71504	Erik Branger	11/2013

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Probable Primes Top 10000

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