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) !!!

Submit your PRPs

See the Top discoverers
See the Latest PRPs
Search by form


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	2^219021-3553	65932	Yves Minet	03/2017
7002	Pell-LucasQ(172243)/2	65931	Eric W. Weisstein	01/2007
7003	2^218990+73519	65923	Enzo Doria	04/2016
7004	58^37378-57	65914	Norbert Schneider	09/2014
7006	(2^218945-7)/1675	65906	Lelio R Paula	04/2012
7005	5*10^65905+81	65906	Robert Price	08/2017
7007	3*10^65899-13	65900	Robert Price	11/2017
7008	(-lucasV(1,2,437845)-2)/1679917	65896	Mike Oakes	04/2017
7009	127^31322-2	65896	Lelio R Paula	10/2017
7010	2^218897-111889	65895	Enzo Doria	05/2014
7011	2^218896+1869451	65895	Enzo Doria	05/2016
7012	63^36616+2	65885	Lelio R Paula	05/2013
7013	(3*2^218822-1)/11	65872	Lelio R Paula	01/2014
7014	2^218796-113297	65865	Enzo Doria	07/2014
7015	2^218797+73727	65865	Enzo Doria	04/2016
7016	3^138040-110	65862	Lelio R Paula	06/2013
7017	11^63240-1950	65858	Enzo Doria	12/2012
7018	2^218764-111873	65855	Enzo Doria	05/2014
7019	(34*10^65839-7)/9/37	65839	Makoto Morimoto	04/2016
7020	3^137988+26	65838	Lelio R Paula	06/2013
7021	2^218680-719	65830	Yves Minet	05/2012
7022	18^52424+17	65807	Lelio R Paula	08/2013
7023	(2*15683^15683+1)/732384425	65789	David Broadhurst	09/2010
7024	(23*2^218517+1)/19003	65778	Lelio R Paula	07/2012
7025	(5*10^65773+1)/3	65774	Erik Branger	12/2013
7026	2^218457-17329	65763	Enzo Doria	05/2013
7027	151703#+223381	65759	Nicolas PALAU	10/2016
7028	2^218436+40755	65756	Lelio R Paula	10/2011
7029	(F(44)^7433-F(43)^7433)/F(42)	65744	Wayne Halsdorf	03/2012
7030	157^29934+29934^157	65733	Serge Batalov	05/2014
7031	211^28273-2	65715	Lelio R Paula	09/2013
7032	(59*10^65712+31)/9	65713	Robert Price	09/2015
7034	611^23586+23586^611	65712	Norbert Schneider	08/2016
7033	p(13991)#/2+32	65712	Robert Price	12/2016
7035	2^218282-18485	65710	Enzo Doria	05/2013
7036	2^218274-111251	65708	Enzo Doria	05/2014
7037	2*F(314335)-1	65693	Henri Lifchitz	12/2009
7038	2^218200+427	65685	Henri Lifchitz	01/2005
7039	(10199^16384+10197^16384)/2	65676	Jeppe Stig Nielsen	04/2018
7040	46532!3+3	65667	Robert Price	10/2014
7041	2^218120-147	65661	Lelio R Paula	08/2011
7042	452^24729+24729^452	65659	Norbert Schneider	09/2016
7043	2^218102-114893	65656	Enzo Doria	05/2015
7044	(15*2^218083-1)/17	65650	Lelio R Paula	01/2014
7045	(15*2^218081+1)/18941	65646	Lelio R Paula	08/2012
7046	(306^26407-1)/305	65638	Eric Chen	09/2017
7048	19^51326+36	65634	Lelio R Paula	08/2013
7047	(21*2^218045-1)/451583	65634	Lelio R Paula	01/2014
7049	2^217989-33	65622	Lelio R Paula	08/2011
7050	(13*2^217961+1)/3	65614	Lelio R Paula	06/2012
7051	4*6^84315-5	65611	Lelio R Paula	09/2014
7052	(315047^11933+1)/315048	65607	Faysal YAtim	06/2008
7053	6^84303+55	65601	Lelio R Paula	07/2013
7054	(-lucasV(1,2,435857)+2)/(1738598017)	65595	Mike Oakes	04/2017
7055	(9787*2^217873-1)/37	65589	Lelio R Paula	04/2015
7056	5*2^217858+3	65583	Lelio R Paula	04/2014
7057	(19*10^65572+119)/3	65573	Robert Price	02/2017
7058	20^50399+51	65571	Lelio R Paula	08/2013
7059	11^62946-5670	65552	Enzo Doria	01/2013
7060	2^217742-3911	65547	Yves Minet	08/2009
7061	(19*10^65545+77)/3	65546	Robert Price	08/2016
7062	2^217731+131	65544	Lelio R Paula	08/2011
7063	2^217720-111287	65541	Enzo Doria	05/2014
7064	(365^25579+1)/366	65539	Eric Chen	10/2017
7065	10^65537+27	65538	Robert Price	01/2011
7066	10^65537-76859	65537	Patrick De Geest	05/2013
7067	(28*10^65532+359)/9	65533	Robert Price	11/2017
7068	(10223*2^217676+1)/3	65531	Lelio R Paula	06/2014
7069	PadovanNumber[536485]	65518	Eric W. Weisstein	05/2009
7070	5*10^65509+23	65510	Robert Price	11/2017
7071	(8*10^65507-83)/3	65508	Robert Price	10/2017
7072	7*10^65492-47	65493	Robert Price	02/2017
7073	2^217547-1868407	65489	Enzo Doria	04/2016
7074	2^217531-111769	65484	Enzo Doria	05/2014
7075	7^77484-18	65482	Lelio R Paula	06/2013
7076	2^217488-113285	65471	Enzo Doria	07/2014
7077	151153#/30-30	65468	Henri Lifchitz	12/2011
7078	2^217466+4257	65464	Lelio R Paula	10/2011
7079	46396!3-81	65455	Robert Price	09/2014
7080	2^217421-113185	65451	Enzo Doria	07/2014
7081	(6883*2^217440-1)/1061193295893	65448	Lelio R Paula	04/2015
7082	2^217408-2145	65447	Lelio R Paula	10/2011
7083	2^217398-16947	65444	Enzo Doria	05/2013
7084	8*5^93613+3	65434	Lelio R Paula	09/2014
7085	11^62828-5310	65429	Enzo Doria	01/2013
7086	10^65426+13	65427	Robert Price	01/2011
7087	2^217341-6555	65427	Lelio R Paula	10/2011
7088	10^65426-54849	65426	Patrick De Geest	05/2013
7089	(21*2^217363-1)/56003626667	65424	Lelio R Paula	01/2014
7090	30011^14608-108	65405	Enzo Doria	07/2012
7091	119^31504-2	65389	Lelio R Paula	10/2017
7092	(43^40031-1)/42	65388	Robert Price	04/2014
7093	2^217190+94395	65381	Henri Lifchitz	02/2005
7094	15^55587+46	65376	Lelio R Paula	08/2013
7095	2^217088-111833	65350	Enzo Doria	05/2014
7096	(13*2^217069-1)/1682945	65340	Lelio R Paula	01/2014
7097	(10^65340+47)/3	65340	Robert Price	11/2017
7098	(62*10^65331+1)/9	65332	Serge Batalov	11/2010
7099	2^216947-111351	65308	Enzo Doria	05/2014
7100	-E(18022)/775201845682685322943949235068359	65307	Thomas Ritschel	02/2017
7101	(13*10^65297+83)/3	65298	Robert Price	09/2016
7102	5^93400-8	65284	Lelio R Paula	06/2013
7103	2^216802-165	65264	Lelio R Paula	08/2011
7104	2^216799-28635	65264	Lelio R Paula	10/2011
7105	5*10^65255+51	65256	Robert Price	01/2017
7106	2^216762-167	65252	Lelio R Paula	08/2011
7107	11^62657-5790	65251	Enzo Doria	01/2013
7108	3^136756-112880	65250	Enzo Doria	06/2014
7109	2^216752+21	65249	Lelio R Paula	08/2011
7110	3*10^65247+11	65248	Robert Price	11/2017
7111	11^62651-2700	65245	Enzo Doria	12/2012
7113	Pell-LucasQ(170413)/2	65230	Eric W. Weisstein	12/2006
7112	gcd(V(790525),5F(158105)(F(158105)+1)+1)	65230	Serge Batalov	04/2015
7114	(2^216676-1017)/637	65224	Lelio R Paula	04/2012
7115	2^216652-2327	65219	Yves Minet	10/2013
7116	(9179*2^216648-1)/4667	65218	Lelio R Paula	04/2015
7117	(5*10^65203-119)/3	65204	Robert Price	04/2016
7118	2^216555-113269	65190	Enzo Doria	07/2014
7119	(9513^16384+1)/2	65181	Henri Lifchitz	02/2007
7120	2^216474+12915	65166	Lelio R Paula	02/2013
7121	19^50958-32	65163	Lelio R Paula	08/2013
7122	2^216442-112133	65156	Enzo Doria	06/2014
7123	2^216437-112213	65155	Enzo Doria	06/2014
7124	2^216435-112767	65154	Enzo Doria	06/2014
7125	2^216420+12705	65149	Lelio R Paula	02/2013
7126	8*3^136507-7	65132	Lelio R Paula	04/2014
7127	(-lucasV(1,2,432719)-2)/(5*461)	65128	Mike Oakes	03/2017
7128	5*10^65086-51	65087	Robert Price	10/2017
7129	2^216197-111769	65082	Enzo Doria	05/2014
7130	6^83631-79	65078	Lelio R Paula	07/2013
7131	572^23601+23601^572	65078	Norbert Schneider	08/2016
7132	(3^136399-7)/544220	65074	Lelio R Paula	04/2012
7133	2^216154-1421	65069	Yves Minet	01/2013
7134	2^216145-112663	65067	Enzo Doria	06/2014
7135	(7*10^65064+53)/3	65065	Robert Price	10/2017
7136	132013*10^65050+2^216091-1	65056	Gilbert Mozzo	01/2014
7137	132019*10^65050+2^216091-1	65056	Gilbert Mozzo	01/2014
7138	148918*10^65050+2^216091-1	65056	Gilbert Mozzo	02/2014
7139	194014*10^65050+2^216091-1	65056	Gilbert Mozzo	02/2014
7140	223864*10^65050+2^216091-1	65056	Gilbert Mozzo	04/2014
7142	82090*10^65050+2^216091-1	65055	Gilbert Mozzo	07/2012
7143	95133*10^65050+2^216091-1	65055	Gilbert Mozzo	12/2013
7141	98142*10^65050+2^216091-1	65055	Gilbert Mozzo	12/2013
7144	((2^216091-1)*34009-48)/25	65054	Serge Batalov	01/2012
7145	5977*10^65050+2^216091-1	65054	Gilbert Mozzo	03/2012
7146	7*2^216091+2^298-13	65051	Peter Lesala	03/2007
7147	2^216091+2*29208-1	65050	Makoto Morimoto	10/2013
7148	(10^(232521+1)-610^32521-1)/3	65043	Robert Price	02/2016
7149	p(13861)#/2+256	65039	Robert Price	05/2017
7150	(2^216091-2096)/(2^432918437*5220283)	65036	Makoto Morimoto	10/2017
7151	11^62439-4380	65024	Enzo Doria	01/2013
7152	3^136244+2	65005	Mike Oakes	11/2009
7153	13^58343-50	64991	Lelio R Paula	07/2013
7154	331^25791-10002	64989	Enzo Doria	07/2012
7155	2^215877+131	64986	Lelio R Paula	08/2011
7156	4*5^92959+9	64977	Lelio R Paula	09/2014
7157	2^215789-18825	64959	Lelio R Paula	09/2011
7158	(2^215801-509203)/41327	64958	Lelio R Paula	05/2012
7159	U(315311)	64954	Serge Batalov	03/2015
7160	46072!3-59049	64951	Robert Price	12/2015
7161	2^215750-5955	64948	Lelio R Paula	09/2011
7162	13^58281+46	64922	Lelio R Paula	07/2013
7163	2^215623+183	64909	Lelio R Paula	08/2011
7164	(46*10^64904+521)/9	64905	Robert Price	08/2017
7165	(3^136043-2^136043)/(19862279*33466579)	64895	Mike Oakes	12/2016
7166	5*2^215554+3	64889	Lelio R Paula	04/2014
7167	2^215541-112075	64885	Enzo Doria	06/2014
7168	2*10^64882-3	64883	Dmitry Domanov	11/2010
7169	10^64862+342339	64863	Patrick De Geest	05/2013
7170	10^64862-47	64862	Robert Price	05/2011
7171	19^50718-84	64856	Lelio R Paula	08/2013
7172	(30452^215471-1)/(17115127067173473)	64853	Jens K. Andersen	09/2007
7174	10^64843+4278697839	64844	Robert Price	05/2015
7173	10^64843+21967	64844	Patrick De Geest	03/2016
7175	10^64843-340073	64843	Patrick De Geest	03/2016
7176	11^62254+70	64831	Lelio R Paula	07/2013
7177	2^215351-111925	64828	Enzo Doria	05/2014
7178	2^215310-117	64815	Lelio R Paula	08/2011
7179	124^30958-123	64809	Norbert Schneider	02/2015
7180	(7*10^64807+17)/3	64808	Erik Branger	03/2014
7181	(710^(232400+1)-27*10^32400-7)/9	64801	Robert Price	11/2015
7182	2^215243-15949	64795	Enzo Doria	04/2013
7183	23^47581-22^47581	64793	Robert Price	08/2012
7184	(62*10^64783-17)/9	64784	Robert Price	09/2015
7185	5*3^135747-4	64769	Lelio R Paula	04/2014
7186	(59*10^64767-41)/9	64768	Robert Price	09/2015
7188	(2^215140+3)/19	64763	Lelio R Paula	04/2012
7187	2^215135-17169	64763	Enzo Doria	05/2013
7189	2^215115-111277	64757	Enzo Doria	05/2014
7190	9*5^92641+2	64755	Lelio R Paula	09/2014
7191	(lucasV(1,2,430086)-2)/(7*1033)	64731	Mike Oakes	03/2017
7192	(5*10^64715-23)/9	64715	Robert Price	11/2014
7193	2^214938-1781	64703	Yves Minet	03/2013
7194	11^62111-420	64682	Enzo Doria	08/2012
7195	5^92525+42	64673	Lelio R Paula	06/2013
7196	2^214824+71893	64669	Enzo Doria	04/2016
7197	2^214799-2221	64661	Yves Minet	08/2013
7198	(21*2^214688+1)/293	64627	Lelio R Paula	08/2012
7199	92^32907+32907^92	64623	Serge Batalov	05/2014
7200	(89*10^64608-539)/9	64609	Robert Price	11/2017
7201	6^83013+101	64597	Lelio R Paula	07/2013
7202	p(13775)#/2+8	64594	Robert Price	01/2017
7203	(7*10^64568-43)/9	64568	Robert Price	10/2014
7204	Pell-LucasQ(168677)/2	64566	Eric W. Weisstein	11/2006
7205	(24737*2^214476+1)/2877	64565	Lelio R Paula	06/2014
7206	(47*2^214463+1)/7	64561	Lelio R Paula	04/2015
7207	2^214458+54615	64559	Lelio R Paula	10/2011
7208	(3^135322+7)/122911408	64557	Lelio R Paula	04/2012
7209	2^214389-683113	64538	Paul Bourdelais	03/2013
7210	(76*10^64534+113)/9	64535	Robert Price	11/2017
7211	2^214369-111241	64532	Enzo Doria	05/2014
7212	(19^50461+3^50461)/22	64526	Robert Price	07/2013
7213	11^61954-3660	64519	Enzo Doria	12/2012
7214	(23*2^214319-1)/21	64517	Lelio R Paula	01/2014
7215	(58695*2^214310-1)/571	64516	Lelio R Paula	04/2015
7216	35^41779-34	64510	Norbert Schneider	04/2014
7217	(159^29303+1)/160	64506	Eric Chen	12/2017
7218	(89*10^64504-179)/9	64505	Robert Price	11/2017
7219	11^61939-5220	64503	Enzo Doria	01/2013
7220	(2^214271+78557)/35	64501	Lelio R Paula	05/2012
7221	L(308604)+P(308604)	64495	Robert Price	12/2017
7222	126^30706-125	64494	Norbert Schneider	02/2015
7223	gcd(V(1157265),5F(231453)(F(231453)-1)+1)	64492	Serge Batalov	04/2015
7224	2^214215+12909	64486	Lelio R Paula	10/2011
7225	5^92225+66	64463	Lelio R Paula	06/2013
7226	2^214126-240551	64459	Paul Bourdelais	03/2013
7227	8*6^82827+5	64453	Lelio R Paula	09/2014
7228	(31*2^214120-1)/2170485	64452	Lelio R Paula	01/2014
7229	(31*2^214088-1)/5955	64445	Lelio R Paula	01/2014
7230	14^56227+89	64444	Lelio R Paula	08/2013
7233	2^214055-159	64437	Lelio R Paula	08/2011
7231	10^64436+2667	64437	Patrick De Geest	05/2013
7232	65^35543-64^35543	64437	Robert Price	08/2013
7234	10^64436-53	64436	Robert Price	05/2011
7235	(3^135043-lucasV(1,3,135043)+1)/3	64432	Paul Vanderveen	11/2017
7236	Phi(128878,10)/39503297927	64428	Maksym Voznyy	11/2015
7237	3^135027+100	64425	Lelio R Paula	05/2013
7238	(3^134972-7)/2	64398	Lelio R Paula	04/2012
7239	6*10^64387+7	64388	Dmitry Domanov	11/2010
7240	2^213864-18377	64380	Enzo Doria	05/2013
7241	(2^213821+9)/209	64365	Lelio R Paula	04/2012
7242	2^213788+135	64357	Lelio R Paula	08/2011
7243	(3^134883+2)/48313	64351	Lelio R Paula	04/2012
7244	(49^38069-46^38069)/3	64344	Serge Batalov	12/2016
7245	(11^61781+2^61781)/13	64338	Robert Price	02/2013
7246	6^82670+37	64330	Lelio R Paula	07/2013
7247	(3^134839+4)/32312959	64328	Lelio R Paula	04/2012
7248	(22*10^64326+161)/3	64327	Robert Price	02/2017
7249	11^61767-4050	64324	Enzo Doria	12/2012
7250	2^213645-114853	64314	Enzo Doria	05/2015

Find by discoverer :

PRP Records

Probable Primes Top 10000

(205869 PRPs in the top)