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 ?
7001	6^85481+85481	66518	Henri Lifchitz	08/2014
7002	(9179*2^220913-1)/399	66503	Lelio R Paula	04/2015
7003	13^59687+66	66488	Lelio R Paula	07/2013
7004	(49*10^66485-31)/9	66486	Robert Price	07/2015
7005	(46*10^66469+17)/9	66470	Robert Price	06/2015
7006	2^220790+97	66465	Lelio R Paula	02/2012
7007	(23*2^220790+1)/807	66463	Lelio R Paula	06/2012
7008	40009^14441-102	66460	Enzo Doria	07/2012
7009	2^220736-143	66449	Lelio R Paula	02/2012
7010	(79*10^66447-97)/99	66447	Ray Chandler	01/2011
7011	2^220675+69	66430	Lelio R Paula	02/2012
7012	2^220633-111381	66418	Enzo Doria	05/2014
7013	(2^220625-509203)/4000321	66409	Lelio R Paula	05/2012
7014	2^220596-15813	66407	Enzo Doria	04/2013
7015	(5*10^66394-17)/3	66395	Serge Batalov	05/2009
7016	2^220549-1859173	66392	Enzo Doria	04/2016
7017	2^220478-161	66371	Lelio R Paula	02/2012
7018	5^94938-14636	66359	Enzo Doria	02/2013
7019	(F(67)^4861-F(66)^4861)/F(65)	66353	Wayne Halsdorf	03/2012
7020	2^220253-114871	66303	Enzo Doria	05/2015
7021	12^61432+95	66297	Lelio R Paula	07/2013
7022	2^220192-111563	66285	Enzo Doria	05/2014
7023	2^220188-111449	66284	Enzo Doria	05/2014
7024	(4*10^66284+23)/9	66284	Robert Price	11/2014
7025	32501!2+2	66266	Robert Price	01/2015
7026	(8*10^66261-101)/3	66262	Robert Price	10/2017
7027	1530*10^66254+R(66254)	66258	Patrick De Geest	05/2016
7028	(47^39623-1)/46	66252	Robert Price	06/2014
7029	2^220044-97305	66240	Lelio R Paula	04/2012
7030	(77*10^66237-257)/9	66238	Robert Price	10/2017
7031	29^45285+2	66225	Ray Chandler	08/2011
7032	15^56289+38	66202	Lelio R Paula	08/2013
7033	3^138749+98	66201	Lelio R Paula	06/2013
7034	(21*2^219912-1)/5	66201	Lelio R Paula	01/2014
7035	2^219904-16995	66198	Lelio R Paula	10/2011
7036	(3^138712-2)/5297	66179	Lelio R Paula	04/2012
7037	Phi(198552,10)	66177	Ray Chandler	07/2010
7038	4*6^85041+7	66176	Lelio R Paula	09/2014
7039	2^219812-3149	66171	Yves Minet	10/2009
7040	2^219795-611167	66165	Paul Bourdelais	03/2013
7041	32455!2+512	66162	Robert Price	02/2015
7042	(27*2^219760-1)/227	66154	Lelio R Paula	01/2014
7044	(11^63521-4^63521)/7	66150	Robert Price	03/2013
7043	5*7^78274-6	66150	Lelio R Paula	09/2014
7045	(-lucasV(1,2,439441)-2)/(31192781359)	66134	Mike Oakes	04/2017
7046	2^219679-112015	66130	Enzo Doria	05/2014
7047	2^219653+15015*219653	66123	Henri Lifchitz	04/2005
7048	2^219600+76561	66107	Enzo Doria	05/2016
7049	2^219594+255255	66105	Lelio R Paula	10/2011
7050	4*7^78210-3	66096	Lelio R Paula	09/2014
7051	(15185*2^219557-1)/63	66096	Lelio R Paula	04/2015
7052	(19*2^219499-1)/13	66076	Lelio R Paula	01/2014
7053	2^219496+66615	66075	Lelio R Paula	10/2011
7054	(F(79021)^5-F(79020)^5)/F(79019)	66057	Wayne Halsdorf	03/2012
7055	(2^219414+7)/443657	66045	Lelio R Paula	04/2012
7056	(115*10^66043-1)/3	66045	Serge Batalov	12/2014
7057	10^66033+19	66034	Robert Price	01/2011
7058	10^66033-78309	66033	Patrick De Geest	05/2013
7059	(lucasV(1,2,438701)+2)/7599419	66025	Mike Oakes	04/2017
7060	2^219304+454245	66018	Henri Lifchitz	03/2007
7061	(27*2^219293+1)/9145	66012	Lelio R Paula	08/2012
7062	2^219273-112635	66008	Enzo Doria	06/2014
7063	2^219250+25	66001	Lelio R Paula	08/2011
7064	132^31123+131	65999	Norbert Schneider	03/2015
7065	V(319871)	65987	Serge Batalov	03/2015
7066	2^219189-195	65983	Lelio R Paula	08/2011
7067	(7*2^219143-1)/55	65968	Lelio R Paula	01/2014
7068	(73^35401-1)/72	65962	Paul Bourdelais	08/2017
7069	2^219112-17009	65960	Enzo Doria	05/2013
7070	2^219093-111201	65954	Enzo Doria	05/2014
7071	2^219089-112099	65953	Enzo Doria	06/2014
7072	46714!3+81	65950	Robert Price	09/2014
7073	(11*10^65944-131)/3	65945	Robert Price	02/2017
7074	2^219021-3553	65932	Yves Minet	03/2017
7075	Pell-LucasQ(172243)/2	65931	Eric W. Weisstein	01/2007
7076	2^218990+73519	65923	Enzo Doria	04/2016
7077	58^37378-57	65914	Norbert Schneider	09/2014
7079	(2^218945-7)/1675	65906	Lelio R Paula	04/2012
7078	5*10^65905+81	65906	Robert Price	08/2017
7080	3*10^65899-13	65900	Robert Price	11/2017
7081	(-lucasV(1,2,437845)-2)/1679917	65896	Mike Oakes	04/2017
7082	127^31322-2	65896	Lelio R Paula	10/2017
7083	2^218897-111889	65895	Enzo Doria	05/2014
7084	2^218896+1869451	65895	Enzo Doria	05/2016
7085	63^36616+2	65885	Lelio R Paula	05/2013
7086	(3*2^218822-1)/11	65872	Lelio R Paula	01/2014
7087	2^218796-113297	65865	Enzo Doria	07/2014
7088	2^218797+73727	65865	Enzo Doria	04/2016
7089	3^138040-110	65862	Lelio R Paula	06/2013
7090	11^63240-1950	65858	Enzo Doria	12/2012
7091	2^218764-111873	65855	Enzo Doria	05/2014
7092	(34*10^65839-7)/9/37	65839	Makoto Morimoto	04/2016
7093	3^137988+26	65838	Lelio R Paula	06/2013
7094	2^218680-719	65830	Yves Minet	05/2012
7095	18^52424+17	65807	Lelio R Paula	08/2013
7096	(2*15683^15683+1)/732384425	65789	David Broadhurst	09/2010
7097	(23*2^218517+1)/19003	65778	Lelio R Paula	07/2012
7098	(5*10^65773+1)/3	65774	Erik Branger	12/2013
7099	2^218457-17329	65763	Enzo Doria	05/2013
7100	151703#+223381	65759	Nicolas PALAU	10/2016
7101	2^218436+40755	65756	Lelio R Paula	10/2011
7102	(F(44)^7433-F(43)^7433)/F(42)	65744	Wayne Halsdorf	03/2012
7103	157^29934+29934^157	65733	Serge Batalov	05/2014
7104	211^28273-2	65715	Lelio R Paula	09/2013
7105	(59*10^65712+31)/9	65713	Robert Price	09/2015
7107	611^23586+23586^611	65712	Norbert Schneider	08/2016
7106	p(13991)#/2+32	65712	Robert Price	12/2016
7108	2^218282-18485	65710	Enzo Doria	05/2013
7109	2^218274-111251	65708	Enzo Doria	05/2014
7110	2*F(314335)-1	65693	Henri Lifchitz	12/2009
7111	2^218200+427	65685	Henri Lifchitz	01/2005
7112	(10199^16384+10197^16384)/2	65676	Jeppe Stig Nielsen	04/2018
7113	(10199^(2^14)+(10197)^(2^14))/2	65676	Robert Price	05/2018
7114	46532!3+3	65667	Robert Price	10/2014
7115	2^218120-147	65661	Lelio R Paula	08/2011
7116	452^24729+24729^452	65659	Norbert Schneider	09/2016
7117	2^218102-114893	65656	Enzo Doria	05/2015
7118	(15*2^218083-1)/17	65650	Lelio R Paula	01/2014
7119	(15*2^218081+1)/18941	65646	Lelio R Paula	08/2012
7120	(306^26407-1)/305	65638	Eric Chen	09/2017
7122	19^51326+36	65634	Lelio R Paula	08/2013
7121	(21*2^218045-1)/451583	65634	Lelio R Paula	01/2014
7123	2^217989-33	65622	Lelio R Paula	08/2011
7124	(13*2^217961+1)/3	65614	Lelio R Paula	06/2012
7125	4*6^84315-5	65611	Lelio R Paula	09/2014
7126	(315047^11933+1)/315048	65607	Faysal YAtim	06/2008
7127	6^84303+55	65601	Lelio R Paula	07/2013
7128	(-lucasV(1,2,435857)+2)/(1738598017)	65595	Mike Oakes	04/2017
7129	(9787*2^217873-1)/37	65589	Lelio R Paula	04/2015
7130	5*2^217858+3	65583	Lelio R Paula	04/2014
7131	(19*10^65572+119)/3	65573	Robert Price	02/2017
7132	20^50399+51	65571	Lelio R Paula	08/2013
7133	11^62946-5670	65552	Enzo Doria	01/2013
7134	2^217742-3911	65547	Yves Minet	08/2009
7135	(19*10^65545+77)/3	65546	Robert Price	08/2016
7136	2^217731+131	65544	Lelio R Paula	08/2011
7137	2^217720-111287	65541	Enzo Doria	05/2014
7138	(365^25579+1)/366	65539	Eric Chen	10/2017
7139	10^65537+27	65538	Robert Price	01/2011
7140	10^65537-76859	65537	Patrick De Geest	05/2013
7141	(28*10^65532+359)/9	65533	Robert Price	11/2017
7142	(10223*2^217676+1)/3	65531	Lelio R Paula	06/2014
7143	PadovanNumber[536485]	65518	Eric W. Weisstein	05/2009
7144	5*10^65509+23	65510	Robert Price	11/2017
7145	(8*10^65507-83)/3	65508	Robert Price	10/2017
7146	7*10^65492-47	65493	Robert Price	02/2017
7147	2^217547-1868407	65489	Enzo Doria	04/2016
7148	2^217531-111769	65484	Enzo Doria	05/2014
7149	7^77484-18	65482	Lelio R Paula	06/2013
7150	2^217488-113285	65471	Enzo Doria	07/2014
7151	151153#/30-30	65468	Henri Lifchitz	12/2011
7152	2^217466+4257	65464	Lelio R Paula	10/2011
7153	46396!3-81	65455	Robert Price	09/2014
7154	2^217421-113185	65451	Enzo Doria	07/2014
7155	(6883*2^217440-1)/1061193295893	65448	Lelio R Paula	04/2015
7156	2^217408-2145	65447	Lelio R Paula	10/2011
7157	2^217398-16947	65444	Enzo Doria	05/2013
7158	8*5^93613+3	65434	Lelio R Paula	09/2014
7159	11^62828-5310	65429	Enzo Doria	01/2013
7160	10^65426+13	65427	Robert Price	01/2011
7161	2^217341-6555	65427	Lelio R Paula	10/2011
7162	10^65426-54849	65426	Patrick De Geest	05/2013
7163	(21*2^217363-1)/56003626667	65424	Lelio R Paula	01/2014
7164	30011^14608-108	65405	Enzo Doria	07/2012
7165	119^31504-2	65389	Lelio R Paula	10/2017
7166	(43^40031-1)/42	65388	Robert Price	04/2014
7167	2^217190+94395	65381	Henri Lifchitz	02/2005
7168	15^55587+46	65376	Lelio R Paula	08/2013
7169	2^217088-111833	65350	Enzo Doria	05/2014
7170	(13*2^217069-1)/1682945	65340	Lelio R Paula	01/2014
7171	(10^65340+47)/3	65340	Robert Price	11/2017
7172	(62*10^65331+1)/9	65332	Serge Batalov	11/2010
7173	2^216947-111351	65308	Enzo Doria	05/2014
7174	-E(18022)/775201845682685322943949235068359	65307	Thomas Ritschel	02/2017
7175	(13*10^65297+83)/3	65298	Robert Price	09/2016
7176	5^93400-8	65284	Lelio R Paula	06/2013
7177	2^216802-165	65264	Lelio R Paula	08/2011
7178	2^216799-28635	65264	Lelio R Paula	10/2011
7179	5*10^65255+51	65256	Robert Price	01/2017
7180	2^216762-167	65252	Lelio R Paula	08/2011
7181	11^62657-5790	65251	Enzo Doria	01/2013
7182	3^136756-112880	65250	Enzo Doria	06/2014
7183	2^216752+21	65249	Lelio R Paula	08/2011
7184	3*10^65247+11	65248	Robert Price	11/2017
7185	11^62651-2700	65245	Enzo Doria	12/2012
7187	Pell-LucasQ(170413)/2	65230	Eric W. Weisstein	12/2006
7186	gcd(V(790525),5F(158105)(F(158105)+1)+1)	65230	Serge Batalov	04/2015
7188	(2^216676-1017)/637	65224	Lelio R Paula	04/2012
7189	2^216652-2327	65219	Yves Minet	10/2013
7190	(9179*2^216648-1)/4667	65218	Lelio R Paula	04/2015
7191	(5*10^65203-119)/3	65204	Robert Price	04/2016
7192	2^216555-113269	65190	Enzo Doria	07/2014
7193	(9513^16384+1)/2	65181	Henri Lifchitz	02/2007
7194	2^216474+12915	65166	Lelio R Paula	02/2013
7195	19^50958-32	65163	Lelio R Paula	08/2013
7196	2^216442-112133	65156	Enzo Doria	06/2014
7197	2^216437-112213	65155	Enzo Doria	06/2014
7198	2^216435-112767	65154	Enzo Doria	06/2014
7199	2^216420+12705	65149	Lelio R Paula	02/2013
7200	8*3^136507-7	65132	Lelio R Paula	04/2014
7201	(-lucasV(1,2,432719)-2)/(5*461)	65128	Mike Oakes	03/2017
7202	5*10^65086-51	65087	Robert Price	10/2017
7203	2^216197-111769	65082	Enzo Doria	05/2014
7204	6^83631-79	65078	Lelio R Paula	07/2013
7205	572^23601+23601^572	65078	Norbert Schneider	08/2016
7206	(3^136399-7)/544220	65074	Lelio R Paula	04/2012
7207	2^216154-1421	65069	Yves Minet	01/2013
7208	2^216145-112663	65067	Enzo Doria	06/2014
7209	(7*10^65064+53)/3	65065	Robert Price	10/2017
7210	132013*10^65050+2^216091-1	65056	Gilbert Mozzo	01/2014
7211	132019*10^65050+2^216091-1	65056	Gilbert Mozzo	01/2014
7212	148918*10^65050+2^216091-1	65056	Gilbert Mozzo	02/2014
7213	194014*10^65050+2^216091-1	65056	Gilbert Mozzo	02/2014
7214	223864*10^65050+2^216091-1	65056	Gilbert Mozzo	04/2014
7217	82090*10^65050+2^216091-1	65055	Gilbert Mozzo	07/2012
7216	95133*10^65050+2^216091-1	65055	Gilbert Mozzo	12/2013
7215	98142*10^65050+2^216091-1	65055	Gilbert Mozzo	12/2013
7218	((2^216091-1)*34009-48)/25	65054	Serge Batalov	01/2012
7219	5977*10^65050+2^216091-1	65054	Gilbert Mozzo	03/2012
7220	7*2^216091+2^298-13	65051	Peter Lesala	03/2007
7221	2^216091+2*29208-1	65050	Makoto Morimoto	10/2013
7222	(10^(232521+1)-610^32521-1)/3	65043	Robert Price	02/2016
7223	p(13861)#/2+256	65039	Robert Price	05/2017
7224	(2^216091-2096)/(2^432918437*5220283)	65036	Makoto Morimoto	10/2017
7225	11^62439-4380	65024	Enzo Doria	01/2013
7226	3^136244+2	65005	Mike Oakes	11/2009
7227	13^58343-50	64991	Lelio R Paula	07/2013
7228	331^25791-10002	64989	Enzo Doria	07/2012
7229	2^215877+131	64986	Lelio R Paula	08/2011
7230	4*5^92959+9	64977	Lelio R Paula	09/2014
7231	2^215789-18825	64959	Lelio R Paula	09/2011
7232	(2^215801-509203)/41327	64958	Lelio R Paula	05/2012
7233	U(315311)	64954	Serge Batalov	03/2015
7234	46072!3-59049	64951	Robert Price	12/2015
7235	2^215750-5955	64948	Lelio R Paula	09/2011
7236	13^58281+46	64922	Lelio R Paula	07/2013
7237	2^215623+183	64909	Lelio R Paula	08/2011
7238	(46*10^64904+521)/9	64905	Robert Price	08/2017
7239	(3^136043-2^136043)/(19862279*33466579)	64895	Mike Oakes	12/2016
7240	5*2^215554+3	64889	Lelio R Paula	04/2014
7241	2^215541-112075	64885	Enzo Doria	06/2014
7242	2*10^64882-3	64883	Dmitry Domanov	11/2010
7243	10^64862+342339	64863	Patrick De Geest	05/2013
7244	10^64862-47	64862	Robert Price	05/2011
7245	19^50718-84	64856	Lelio R Paula	08/2013
7246	(30452^215471-1)/(17115127067173473)	64853	Jens K. Andersen	09/2007
7248	10^64843+4278697839	64844	Robert Price	05/2015
7247	10^64843+21967	64844	Patrick De Geest	03/2016
7249	10^64843-340073	64843	Patrick De Geest	03/2016
7250	11^62254+70	64831	Lelio R Paula	07/2013

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Probable Primes Top 10000

(211563 PRPs in the top)