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 ?
7251	10^65426+13	65427	Robert Price	01/2011
7252	2^217341-6555	65427	Lelio R Paula	10/2011
7253	10^65426-54849	65426	Patrick De Geest	05/2013
7254	(21*2^217363-1)/56003626667	65424	Lelio R Paula	01/2014
7255	30011^14608-108	65405	Enzo Doria	07/2012
7256	119^31504-2	65389	Lelio R Paula	10/2017
7257	(43^40031-1)/42	65388	Robert Price	04/2014
7258	2^217190+94395	65381	Henri Lifchitz	02/2005
7259	15^55587+46	65376	Lelio R Paula	08/2013
7260	2^217088-111833	65350	Enzo Doria	05/2014
7261	(13*2^217069-1)/1682945	65340	Lelio R Paula	01/2014
7262	(10^65340+47)/3	65340	Robert Price	11/2017
7263	(62*10^65331+1)/9	65332	Serge Batalov	11/2010
7264	2^216947-111351	65308	Enzo Doria	05/2014
7265	-E(18022)/775201845682685322943949235068359	65307	Thomas Ritschel	02/2017
7266	(13*10^65297+83)/3	65298	Robert Price	09/2016
7267	5^93400-8	65284	Lelio R Paula	06/2013
7268	2^216802-165	65264	Lelio R Paula	08/2011
7269	2^216799-28635	65264	Lelio R Paula	10/2011
7270	5*10^65255+51	65256	Robert Price	01/2017
7271	2^216762-167	65252	Lelio R Paula	08/2011
7272	11^62657-5790	65251	Enzo Doria	01/2013
7273	3^136756-112880	65250	Enzo Doria	06/2014
7274	2^216752+21	65249	Lelio R Paula	08/2011
7275	3*10^65247+11	65248	Robert Price	11/2017
7276	11^62651-2700	65245	Enzo Doria	12/2012
7277	15130^15609-15609^15130	65244	Norbert Schneider	07/2018
7278	Pell-LucasQ(170413)/2	65230	Eric W. Weisstein	12/2006
7279	gcd(V(790525),5F(158105)(F(158105)+1)+1)	65230	Serge Batalov	04/2015
7280	(2^216676-1017)/637	65224	Lelio R Paula	04/2012
7281	2^216652-2327	65219	Yves Minet	10/2013
7282	(9179*2^216648-1)/4667	65218	Lelio R Paula	04/2015
7283	(5*10^65203-119)/3	65204	Robert Price	04/2016
7284	2^216555-113269	65190	Enzo Doria	07/2014
7285	(9513^16384+1)/2	65181	Henri Lifchitz	02/2007
7286	2^216474+12915	65166	Lelio R Paula	02/2013
7287	19^50958-32	65163	Lelio R Paula	08/2013
7288	2^216442-112133	65156	Enzo Doria	06/2014
7289	2^216437-112213	65155	Enzo Doria	06/2014
7290	2^216435-112767	65154	Enzo Doria	06/2014
7291	2^216420+12705	65149	Lelio R Paula	02/2013
7292	8*3^136507-7	65132	Lelio R Paula	04/2014
7293	(-lucasV(1,2,432719)-2)/(5*461)	65128	Mike Oakes	03/2017
7294	15132^15575-15575^15132	65102	Norbert Schneider	07/2018
7295	5*10^65086-51	65087	Robert Price	10/2017
7296	2^216197-111769	65082	Enzo Doria	05/2014
7297	6^83631-79	65078	Lelio R Paula	07/2013
7298	572^23601+23601^572	65078	Norbert Schneider	08/2016
7299	(3^136399-7)/544220	65074	Lelio R Paula	04/2012
7300	2^216154-1421	65069	Yves Minet	01/2013
7301	2^216145-112663	65067	Enzo Doria	06/2014
7302	(7*10^65064+53)/3	65065	Robert Price	10/2017
7303	132013*10^65050+2^216091-1	65056	Gilbert Mozzo	01/2014
7304	132019*10^65050+2^216091-1	65056	Gilbert Mozzo	01/2014
7305	148918*10^65050+2^216091-1	65056	Gilbert Mozzo	02/2014
7306	194014*10^65050+2^216091-1	65056	Gilbert Mozzo	02/2014
7307	223864*10^65050+2^216091-1	65056	Gilbert Mozzo	04/2014
7309	82090*10^65050+2^216091-1	65055	Gilbert Mozzo	07/2012
7310	95133*10^65050+2^216091-1	65055	Gilbert Mozzo	12/2013
7308	98142*10^65050+2^216091-1	65055	Gilbert Mozzo	12/2013
7311	((2^216091-1)*34009-48)/25	65054	Serge Batalov	01/2012
7312	5977*10^65050+2^216091-1	65054	Gilbert Mozzo	03/2012
7313	7*2^216091+2^298-13	65051	Peter Lesala	03/2007
7314	2^216091+2*29208-1	65050	Makoto Morimoto	10/2013
7315	(10^(232521+1)-610^32521-1)/3	65043	Robert Price	02/2016
7316	p(13861)#/2+256	65039	Robert Price	05/2017
7317	(2^216091-2096)/(2^432918437*5220283)	65036	Makoto Morimoto	10/2017
7318	11^62439-4380	65024	Enzo Doria	01/2013
7319	3^136244+2	65005	Mike Oakes	11/2009
7320	13^58343-50	64991	Lelio R Paula	07/2013
7321	331^25791-10002	64989	Enzo Doria	07/2012
7322	2^215877+131	64986	Lelio R Paula	08/2011
7323	4*5^92959+9	64977	Lelio R Paula	09/2014
7324	2^215789-18825	64959	Lelio R Paula	09/2011
7325	(2^215801-509203)/41327	64958	Lelio R Paula	05/2012
7326	U(315311)	64954	Serge Batalov	03/2015
7327	46072!3-59049	64951	Robert Price	12/2015
7328	2^215750-5955	64948	Lelio R Paula	09/2011
7329	13^58281+46	64922	Lelio R Paula	07/2013
7330	2^215623+183	64909	Lelio R Paula	08/2011
7331	(46*10^64904+521)/9	64905	Robert Price	08/2017
7332	(3^136043-2^136043)/(19862279*33466579)	64895	Mike Oakes	12/2016
7333	5*2^215554+3	64889	Lelio R Paula	04/2014
7334	2^215541-112075	64885	Enzo Doria	06/2014
7335	2*10^64882-3	64883	Dmitry Domanov	11/2010
7336	10^64862+342339	64863	Patrick De Geest	05/2013
7337	10^64862-47	64862	Robert Price	05/2011
7338	19^50718-84	64856	Lelio R Paula	08/2013
7339	(30452^215471-1)/(17115127067173473)	64853	Jens K. Andersen	09/2007
7340	86413!6-12	64846	Robert Price	08/2018
7341	10^64843+4278697839	64844	Robert Price	05/2015
7342	10^64843+21967	64844	Patrick De Geest	03/2016
7343	10^64843-340073	64843	Patrick De Geest	03/2016
7344	11^62254+70	64831	Lelio R Paula	07/2013
7345	2^215351-111925	64828	Enzo Doria	05/2014
7346	2^215310-117	64815	Lelio R Paula	08/2011
7347	124^30958-123	64809	Norbert Schneider	02/2015
7348	(7*10^64807+17)/3	64808	Erik Branger	03/2014
7349	(710^(232400+1)-27*10^32400-7)/9	64801	Robert Price	11/2015
7350	2^215243-15949	64795	Enzo Doria	04/2013
7351	23^47581-22^47581	64793	Robert Price	08/2012
7352	(62*10^64783-17)/9	64784	Robert Price	09/2015
7353	5*3^135747-4	64769	Lelio R Paula	04/2014
7354	(59*10^64767-41)/9	64768	Robert Price	09/2015
7356	(2^215140+3)/19	64763	Lelio R Paula	04/2012
7355	2^215135-17169	64763	Enzo Doria	05/2013
7357	2^215115-111277	64757	Enzo Doria	05/2014
7358	9*5^92641+2	64755	Lelio R Paula	09/2014
7359	(lucasV(1,2,430086)-2)/(7*1033)	64731	Mike Oakes	03/2017
7360	(5*10^64715-23)/9	64715	Robert Price	11/2014
7361	2^214938-1781	64703	Yves Minet	03/2013
7362	11^62111-420	64682	Enzo Doria	08/2012
7363	5^92525+42	64673	Lelio R Paula	06/2013
7364	2^214824+71893	64669	Enzo Doria	04/2016
7365	2^214799-2221	64661	Yves Minet	08/2013
7366	(21*2^214688+1)/293	64627	Lelio R Paula	08/2012
7367	92^32907+32907^92	64623	Serge Batalov	05/2014
7368	(89*10^64608-539)/9	64609	Robert Price	11/2017
7369	6^83013+101	64597	Lelio R Paula	07/2013
7370	p(13775)#/2+8	64594	Robert Price	01/2017
7371	(7*10^64568-43)/9	64568	Robert Price	10/2014
7372	Pell-LucasQ(168677)/2	64566	Eric W. Weisstein	11/2006
7373	(24737*2^214476+1)/2877	64565	Lelio R Paula	06/2014
7374	(47*2^214463+1)/7	64561	Lelio R Paula	04/2015
7375	2^214458+54615	64559	Lelio R Paula	10/2011
7376	(3^135322+7)/122911408	64557	Lelio R Paula	04/2012
7377	2^214389-683113	64538	Paul Bourdelais	03/2013
7378	(76*10^64534+113)/9	64535	Robert Price	11/2017
7379	2^214369-111241	64532	Enzo Doria	05/2014
7380	(19^50461+3^50461)/22	64526	Robert Price	07/2013
7381	11^61954-3660	64519	Enzo Doria	12/2012
7382	(23*2^214319-1)/21	64517	Lelio R Paula	01/2014
7383	(58695*2^214310-1)/571	64516	Lelio R Paula	04/2015
7384	35^41779-34	64510	Norbert Schneider	04/2014
7385	(159^29303+1)/160	64506	Eric Chen	12/2017
7386	(89*10^64504-179)/9	64505	Robert Price	11/2017
7387	11^61939-5220	64503	Enzo Doria	01/2013
7388	(2^214271+78557)/35	64501	Lelio R Paula	05/2012
7389	L(308604)+P(308604)	64495	Robert Price	12/2017
7390	126^30706-125	64494	Norbert Schneider	02/2015
7391	gcd(V(1157265),5F(231453)(F(231453)-1)+1)	64492	Serge Batalov	04/2015
7392	2^214215+12909	64486	Lelio R Paula	10/2011
7393	5^92225+66	64463	Lelio R Paula	06/2013
7394	2^214126-240551	64459	Paul Bourdelais	03/2013
7395	8*6^82827+5	64453	Lelio R Paula	09/2014
7396	(31*2^214120-1)/2170485	64452	Lelio R Paula	01/2014
7397	(31*2^214088-1)/5955	64445	Lelio R Paula	01/2014
7398	14^56227+89	64444	Lelio R Paula	08/2013
7401	2^214055-159	64437	Lelio R Paula	08/2011
7399	10^64436+2667	64437	Patrick De Geest	05/2013
7400	65^35543-64^35543	64437	Robert Price	08/2013
7402	10^64436-53	64436	Robert Price	05/2011
7403	(3^135043-lucasV(1,3,135043)+1)/3	64432	Paul Vanderveen	11/2017
7404	Phi(128878,10)/39503297927	64428	Maksym Voznyy	11/2015
7405	3^135027+100	64425	Lelio R Paula	05/2013
7406	(3^134972-7)/2	64398	Lelio R Paula	04/2012
7407	6*10^64387+7	64388	Dmitry Domanov	11/2010
7408	2^213864-18377	64380	Enzo Doria	05/2013
7409	(2^213821+9)/209	64365	Lelio R Paula	04/2012
7410	2^213788+135	64357	Lelio R Paula	08/2011
7411	(3^134883+2)/48313	64351	Lelio R Paula	04/2012
7412	(49^38069-46^38069)/3	64344	Serge Batalov	12/2016
7413	(11^61781+2^61781)/13	64338	Robert Price	02/2013
7414	6^82670+37	64330	Lelio R Paula	07/2013
7415	(3^134839+4)/32312959	64328	Lelio R Paula	04/2012
7416	(22*10^64326+161)/3	64327	Robert Price	02/2017
7417	11^61767-4050	64324	Enzo Doria	12/2012
7418	2^213645-114853	64314	Enzo Doria	05/2015
7419	13^57733+18	64312	Lelio R Paula	07/2013
7420	2^213621+72707	64307	Enzo Doria	04/2016
7421	10^64305+136791	64306	Patrick De Geest	05/2011
7422	10^64305-9	64305	Alexander Gramolin	01/2011
7423	V(307652)	64295	Serge Batalov	03/2015
7424	4*10^64286-89	64287	Robert Price	08/2017
7425	(2^213546-5)/2221	64281	Lelio R Paula	04/2012
7426	2^213438-58695	64252	Lelio R Paula	10/2011
7427	2^213367-105	64230	Lelio R Paula	08/2011
7428	595^23148+23148^595	64225	Norbert Schneider	07/2016
7430	3^134601+8680	64221	Lelio R Paula	05/2013
7429	(26*10^64220+61)/3	64221	Robert Price	06/2017
7431	500^23793+23793^500	64217	Norbert Schneider	08/2016
7432	179^28504-2	64216	Lelio R Paula	10/2017
7434	2^213314-455	64214	Yves Minet	02/2012
7433	39^40359-38	64214	Norbert Schneider	05/2014
7435	2^213292-16085	64208	Enzo Doria	04/2013
7436	2^213274-77	64202	Lelio R Paula	08/2011
7437	19^50203+78	64198	Lelio R Paula	08/2013
7438	(44*10^64192-233)/9	64193	Robert Price	10/2017
7439	2^213240-112865	64192	Enzo Doria	06/2014
7440	2^213190-112391	64177	Enzo Doria	06/2014
7441	(9913*2^213184-1)/9657	64175	Lelio R Paula	04/2015
7442	14^55991+27	64173	Lelio R Paula	07/2013
7443	2^213158-112581	64167	Enzo Doria	06/2014
7444	2^213148+91	64164	Lelio R Paula	08/2011
7445	(96^32369+1)/97	64163	Paul Bourdelais	08/2017
7447	6^82439+125	64151	Lelio R Paula	07/2013
7446	7*2^213102+9	64151	Lelio R Paula	04/2014
7448	L(306854)+F(306855)	64129	Henri Lifchitz	01/2007
7449	610^23017+23017^610	64110	Norbert Schneider	07/2016
7450	2^212950-64875	64105	Lelio R Paula	10/2011
7451	(266*10^64102-17)/3	64104	Robert Price	06/2016
7452	p(13679)#/2+64	64097	Robert Price	03/2017
7453	19^50119+94	64090	Lelio R Paula	08/2013
7454	2^212880-147	64084	Lelio R Paula	08/2011
7455	11^61523-4590	64070	Enzo Doria	01/2013
7456	5^91663+38	64070	Lelio R Paula	05/2013
7457	5^91650+52	64061	Lelio R Paula	05/2013
7458	2^212770+69	64051	Lelio R Paula	08/2011
7459	(3^134227+1)/4	64042	Paul Bourdelais	11/2007
7460	(2*10^64041-17)/3	64041	Robert Price	08/2014
7461	(15^54449+1)/16	64036	Paul Bourdelais	03/2010
7462	(29*10^64027+91)/3	64028	Robert Price	03/2016
7463	(lucasV(1,2,425405)+2)/(17*89)	64027	Mike Oakes	03/2017
7464	16878!+16878#-1	64022	D. Gazzoni Filho & Lucas Teixeira	05/2005
7465	2^212663+53	64018	Lelio R Paula	08/2011
7466	(4*10^64014+197)/3	64015	Robert Price	03/2017
7467	85402!6-3	64014	Robert Price	08/2018
7468	(140^29819+1)/141	63994	Richard Fischer	05/2018
7469	10^63986+63	63987	Robert Price	01/2011
7470	10^63986-31557	63986	Patrick De Geest	05/2013
7471	31487!2-2^31487	63982	Robert Price	09/2015
7472	(21*2^212522-1)/1416323	63971	Lelio R Paula	01/2014
7473	5^91517+98	63968	Lelio R Paula	04/2013
7474	(19*10^63960-43)/3	63961	Robert Price	10/2017
7475	(62*10^63954-17)/9	63955	Robert Price	09/2015
7477	5^91493-4^91493	63951	Predrag Minovic	04/2004
7476	V(364793)	63951	Serge Batalov	03/2015
7479	19^50004+58	63943	Lelio R Paula	05/2013
7478	5*6^82172-7	63943	Lelio R Paula	09/2014
7480	(56*10^63942+223)/9	63943	Robert Price	07/2016
7481	19^50000-24	63938	Lelio R Paula	05/2013
7482	(23*2^212374-1)/27019	63928	Lelio R Paula	01/2014
7483	(9*2^212355-1)/761	63924	Lelio R Paula	01/2014
7485	2^212344-183	63922	Lelio R Paula	08/2011
7484	(58695*2^212336-1)/379	63922	Lelio R Paula	04/2015
7486	10^63916+79	63917	Robert Price	01/2011
7487	10^63916-76823	63916	Patrick De Geest	05/2013
7488	2^212295-25	63908	Lelio R Paula	08/2011
7490	2^212285-2383	63905	Yves Minet	10/2013
7489	267^26336+26336^267	63905	Norbert Schneider	09/2014
7491	(-lucasV(1,2,424552)-2)/1601	63899	Mike Oakes	03/2017
7492	19^49962+60	63890	Lelio R Paula	05/2013
7493	3^133906-113056	63890	Enzo Doria	07/2014
7494	(lucasV(1,2,424451)+2)/3	63886	Mike Oakes	03/2017
7495	3*6^82092+5	63881	Lelio R Paula	09/2014
7496	15441^13706+13706^15441	63879	Hans Havermann	02/2017
7497	2^212154-776351	63865	Paul Bourdelais	03/2013
7498	35^41359+2	63862	Lelio R Paula	05/2013
7499	(61*10^63857-43)/9	63858	Robert Price	09/2015
7500	(2^212131-3)/485	63856	Lelio R Paula	04/2012

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PRP Records

Probable Primes Top 10000

(218736 PRPs in the top)