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 ?
7501	46396!3-81	65455	Robert Price	09/2014
7502	2^217421-113185	65451	Enzo Doria	07/2014
7503	(6883*2^217440-1)/1061193295893	65448	Lelio R Paula	04/2015
7504	2^217408-2145	65447	Lelio R Paula	10/2011
7505	2^217398-16947	65444	Enzo Doria	05/2013
7506	8*5^93613+3	65434	Lelio R Paula	09/2014
7507	11^62828-5310	65429	Enzo Doria	01/2013
7508	10^65426+13	65427	Robert Price	01/2011
7509	2^217341-6555	65427	Lelio R Paula	10/2011
7510	10^65426-54849	65426	Patrick De Geest	05/2013
7511	(21*2^217363-1)/56003626667	65424	Lelio R Paula	01/2014
7512	30011^14608-108	65405	Enzo Doria	07/2012
7513	119^31504-2	65389	Lelio R Paula	10/2017
7514	(43^40031-1)/42	65388	Robert Price	04/2014
7515	2^217190+94395	65381	Henri Lifchitz	02/2005
7516	15^55587+46	65376	Lelio R Paula	08/2013
7517	2^217088-111833	65350	Enzo Doria	05/2014
7518	(13*2^217069-1)/1682945	65340	Lelio R Paula	01/2014
7519	(10^65340+47)/3	65340	Robert Price	11/2017
7520	(62*10^65331+1)/9	65332	Serge Batalov	11/2010
7521	2^216947-111351	65308	Enzo Doria	05/2014
7522	-E(18022)/775201845682685322943949235068359	65307	Thomas Ritschel	02/2017
7523	(13*10^65297+83)/3	65298	Robert Price	09/2016
7524	5^93400-8	65284	Lelio R Paula	06/2013
7525	2^216802-165	65264	Lelio R Paula	08/2011
7526	2^216799-28635	65264	Lelio R Paula	10/2011
7527	5*10^65255+51	65256	Robert Price	01/2017
7528	2^216762-167	65252	Lelio R Paula	08/2011
7529	11^62657-5790	65251	Enzo Doria	01/2013
7530	3^136756-112880	65250	Enzo Doria	06/2014
7531	2^216752+21	65249	Lelio R Paula	08/2011
7532	3*10^65247+11	65248	Robert Price	11/2017
7533	11^62651-2700	65245	Enzo Doria	12/2012
7534	15130^15609-15609^15130	65244	Norbert Schneider	07/2018
7536	Pell-LucasQ(170413)/2	65230	Eric W. Weisstein	12/2006
7535	gcd(V(790525),5F(158105)(F(158105)+1)+1)	65230	Serge Batalov	04/2015
7537	(2^216676-1017)/637	65224	Lelio R Paula	04/2012
7538	2^216652-2327	65219	Yves Minet	10/2013
7539	(9179*2^216648-1)/4667	65218	Lelio R Paula	04/2015
7540	(5*10^65203-119)/3	65204	Robert Price	04/2016
7541	2^216555-113269	65190	Enzo Doria	07/2014
7542	(9513^16384+1)/2	65181	Henri Lifchitz	02/2007
7543	2^216474+12915	65166	Lelio R Paula	02/2013
7544	19^50958-32	65163	Lelio R Paula	08/2013
7545	2^216442-112133	65156	Enzo Doria	06/2014
7546	2^216437-112213	65155	Enzo Doria	06/2014
7547	2^216435-112767	65154	Enzo Doria	06/2014
7548	2^216420+12705	65149	Lelio R Paula	02/2013
7549	8*3^136507-7	65132	Lelio R Paula	04/2014
7550	(-lucasV(1,2,432719)-2)/(5*461)	65128	Mike Oakes	03/2017
7551	15132^15575-15575^15132	65102	Norbert Schneider	07/2018
7552	5*10^65086-51	65087	Robert Price	10/2017
7553	2^216197-111769	65082	Enzo Doria	05/2014
7554	6^83631-79	65078	Lelio R Paula	07/2013
7555	572^23601+23601^572	65078	Norbert Schneider	08/2016
7556	(3^136399-7)/544220	65074	Lelio R Paula	04/2012
7557	2^216154-1421	65069	Yves Minet	01/2013
7558	2^216145-112663	65067	Enzo Doria	06/2014
7559	(7*10^65064+53)/3	65065	Robert Price	10/2017
7560	132013*10^65050+2^216091-1	65056	Gilbert Mozzo	01/2014
7561	132019*10^65050+2^216091-1	65056	Gilbert Mozzo	01/2014
7562	148918*10^65050+2^216091-1	65056	Gilbert Mozzo	02/2014
7563	194014*10^65050+2^216091-1	65056	Gilbert Mozzo	02/2014
7564	223864*10^65050+2^216091-1	65056	Gilbert Mozzo	04/2014
7567	82090*10^65050+2^216091-1	65055	Gilbert Mozzo	07/2012
7566	95133*10^65050+2^216091-1	65055	Gilbert Mozzo	12/2013
7565	98142*10^65050+2^216091-1	65055	Gilbert Mozzo	12/2013
7568	((2^216091-1)*34009-48)/25	65054	Serge Batalov	01/2012
7569	5977*10^65050+2^216091-1	65054	Gilbert Mozzo	03/2012
7570	7*2^216091+2^298-13	65051	Peter Lesala	03/2007
7571	2^216091+2*29208-1	65050	Makoto Morimoto	10/2013
7572	(10^(232521+1)-610^32521-1)/3	65043	Robert Price	02/2016
7573	p(13861)#/2+256	65039	Robert Price	05/2017
7574	(2^216091-2096)/(2^432918437*5220283)	65036	Makoto Morimoto	10/2017
7575	11^62439-4380	65024	Enzo Doria	01/2013
7576	3^136244+2	65005	Mike Oakes	11/2009
7577	13^58343-50	64991	Lelio R Paula	07/2013
7578	331^25791-10002	64989	Enzo Doria	07/2012
7579	2^215877+131	64986	Lelio R Paula	08/2011
7580	4*5^92959+9	64977	Lelio R Paula	09/2014
7581	2^215789-18825	64959	Lelio R Paula	09/2011
7582	(2^215801-509203)/41327	64958	Lelio R Paula	05/2012
7583	U(315311)	64954	Serge Batalov	03/2015
7584	46072!3-59049	64951	Robert Price	12/2015
7585	2^215750-5955	64948	Lelio R Paula	09/2011
7586	13^58281+46	64922	Lelio R Paula	07/2013
7587	2^215623+183	64909	Lelio R Paula	08/2011
7588	(46*10^64904+521)/9	64905	Robert Price	08/2017
7589	(3^136043-2^136043)/(19862279*33466579)	64895	Mike Oakes	12/2016
7590	5*2^215554+3	64889	Lelio R Paula	04/2014
7591	2^215541-112075	64885	Enzo Doria	06/2014
7592	2*10^64882-3	64883	Dmitry Domanov	11/2010
7593	10^64862+342339	64863	Patrick De Geest	05/2013
7594	10^64862-47	64862	Robert Price	05/2011
7595	19^50718-84	64856	Lelio R Paula	08/2013
7596	(30452^215471-1)/(17115127067173473)	64853	Jens K. Andersen	09/2007
7597	86413!6-12	64846	Robert Price	08/2018
7598	10^64843+4278697839	64844	Robert Price	05/2015
7599	10^64843+21967	64844	Patrick De Geest	03/2016
7600	10^64843-340073	64843	Patrick De Geest	03/2016
7601	11^62254+70	64831	Lelio R Paula	07/2013
7602	2^215351-111925	64828	Enzo Doria	05/2014
7603	2^215310-117	64815	Lelio R Paula	08/2011
7604	124^30958-123	64809	Norbert Schneider	02/2015
7605	(7*10^64807+17)/3	64808	Erik Branger	03/2014
7606	(710^(232400+1)-27*10^32400-7)/9	64801	Robert Price	11/2015
7607	2^215243-15949	64795	Enzo Doria	04/2013
7608	23^47581-22^47581	64793	Robert Price	08/2012
7609	(62*10^64783-17)/9	64784	Robert Price	09/2015
7610	5*3^135747-4	64769	Lelio R Paula	04/2014
7611	(59*10^64767-41)/9	64768	Robert Price	09/2015
7613	(2^215140+3)/19	64763	Lelio R Paula	04/2012
7612	2^215135-17169	64763	Enzo Doria	05/2013
7614	2^215115-111277	64757	Enzo Doria	05/2014
7615	9*5^92641+2	64755	Lelio R Paula	09/2014
7616	(lucasV(1,2,430086)-2)/(7*1033)	64731	Mike Oakes	03/2017
7617	5791^17200+17200^5791	64720	Norbert Schneider	12/2018
7618	(5*10^64715-23)/9	64715	Robert Price	11/2014
7619	2^214938-1781	64703	Yves Minet	03/2013
7620	11^62111-420	64682	Enzo Doria	08/2012
7621	5^92525+42	64673	Lelio R Paula	06/2013
7622	2^214824+71893	64669	Enzo Doria	04/2016
7623	2^214799-2221	64661	Yves Minet	08/2013
7624	5939^17128+17128^5939	64637	Norbert Schneider	10/2018
7625	(21*2^214688+1)/293	64627	Lelio R Paula	08/2012
7626	92^32907+32907^92	64623	Serge Batalov	05/2014
7627	(89*10^64608-539)/9	64609	Robert Price	11/2017
7628	6^83013+101	64597	Lelio R Paula	07/2013
7629	p(13775)#/2+8	64594	Robert Price	01/2017
7630	(7*10^64568-43)/9	64568	Robert Price	10/2014
7631	Pell-LucasQ(168677)/2	64566	Eric W. Weisstein	11/2006
7632	(24737*2^214476+1)/2877	64565	Lelio R Paula	06/2014
7633	(47*2^214463+1)/7	64561	Lelio R Paula	04/2015
7634	2^214458+54615	64559	Lelio R Paula	10/2011
7635	(3^135322+7)/122911408	64557	Lelio R Paula	04/2012
7636	2^214389-683113	64538	Paul Bourdelais	03/2013
7637	(76*10^64534+113)/9	64535	Robert Price	11/2017
7638	2^214369-111241	64532	Enzo Doria	05/2014
7639	(19^50461+3^50461)/22	64526	Robert Price	07/2013
7640	11^61954-3660	64519	Enzo Doria	12/2012
7641	(23*2^214319-1)/21	64517	Lelio R Paula	01/2014
7642	(58695*2^214310-1)/571	64516	Lelio R Paula	04/2015
7643	35^41779-34	64510	Norbert Schneider	04/2014
7644	(159^29303+1)/160	64506	Eric Chen	12/2017
7645	(89*10^64504-179)/9	64505	Robert Price	11/2017
7646	11^61939-5220	64503	Enzo Doria	01/2013
7647	(2^214271+78557)/35	64501	Lelio R Paula	05/2012
7648	L(308604)+P(308604)	64495	Robert Price	12/2017
7649	126^30706-125	64494	Norbert Schneider	02/2015
7650	gcd(V(1157265),5F(231453)(F(231453)-1)+1)	64492	Serge Batalov	04/2015
7651	2^214215+12909	64486	Lelio R Paula	10/2011
7652	5^92225+66	64463	Lelio R Paula	06/2013
7653	2^214126-240551	64459	Paul Bourdelais	03/2013
7654	8*6^82827+5	64453	Lelio R Paula	09/2014
7655	(31*2^214120-1)/2170485	64452	Lelio R Paula	01/2014
7656	(31*2^214088-1)/5955	64445	Lelio R Paula	01/2014
7657	14^56227+89	64444	Lelio R Paula	08/2013
7660	2^214055-159	64437	Lelio R Paula	08/2011
7658	10^64436+2667	64437	Patrick De Geest	05/2013
7659	65^35543-64^35543	64437	Robert Price	08/2013
7661	10^64436-53	64436	Robert Price	05/2011
7662	(3^135043-lucasV(1,3,135043)+1)/3	64432	Paul Vanderveen	11/2017
7663	Phi(128878,10)/39503297927	64428	Maksym Voznyy	11/2015
7664	3^135027+100	64425	Lelio R Paula	05/2013
7665	(3^134972-7)/2	64398	Lelio R Paula	04/2012
7666	6*10^64387+7	64388	Dmitry Domanov	11/2010
7667	2^213864-18377	64380	Enzo Doria	05/2013
7668	(2^213821+9)/209	64365	Lelio R Paula	04/2012
7669	2^213788+135	64357	Lelio R Paula	08/2011
7670	(3^134883+2)/48313	64351	Lelio R Paula	04/2012
7671	(49^38069-46^38069)/3	64344	Serge Batalov	12/2016
7672	(11^61781+2^61781)/13	64338	Robert Price	02/2013
7673	6^82670+37	64330	Lelio R Paula	07/2013
7674	(3^134839+4)/32312959	64328	Lelio R Paula	04/2012
7675	(22*10^64326+161)/3	64327	Robert Price	02/2017
7676	11^61767-4050	64324	Enzo Doria	12/2012
7677	2^213645-114853	64314	Enzo Doria	05/2015
7678	13^57733+18	64312	Lelio R Paula	07/2013
7679	2^213621+72707	64307	Enzo Doria	04/2016
7680	10^64305+136791	64306	Patrick De Geest	05/2011
7681	10^64305-9	64305	Alexander Gramolin	01/2011
7682	V(307652)	64295	Serge Batalov	03/2015
7683	4*10^64286-89	64287	Robert Price	08/2017
7684	(2^213546-5)/2221	64281	Lelio R Paula	04/2012
7685	2^213438-58695	64252	Lelio R Paula	10/2011
7686	2^213367-105	64230	Lelio R Paula	08/2011
7687	595^23148+23148^595	64225	Norbert Schneider	07/2016
7689	3^134601+8680	64221	Lelio R Paula	05/2013
7688	(26*10^64220+61)/3	64221	Robert Price	06/2017
7690	500^23793+23793^500	64217	Norbert Schneider	08/2016
7691	179^28504-2	64216	Lelio R Paula	10/2017
7693	2^213314-455	64214	Yves Minet	02/2012
7692	39^40359-38	64214	Norbert Schneider	05/2014
7694	2^213292-16085	64208	Enzo Doria	04/2013
7695	(72524!5+1)/25	64203	Joe McLean	10/2018
7696	2^213274-77	64202	Lelio R Paula	08/2011
7697	19^50203+78	64198	Lelio R Paula	08/2013
7698	(44*10^64192-233)/9	64193	Robert Price	10/2017
7699	2^213240-112865	64192	Enzo Doria	06/2014
7700	2^213190-112391	64177	Enzo Doria	06/2014
7701	(9913*2^213184-1)/9657	64175	Lelio R Paula	04/2015
7702	14^55991+27	64173	Lelio R Paula	07/2013
7703	2^213158-112581	64167	Enzo Doria	06/2014
7704	2^213148+91	64164	Lelio R Paula	08/2011
7705	(96^32369+1)/97	64163	Paul Bourdelais	08/2017
7707	6^82439+125	64151	Lelio R Paula	07/2013
7706	7*2^213102+9	64151	Lelio R Paula	04/2014
7708	L(306854)+F(306855)	64129	Henri Lifchitz	01/2007
7709	610^23017+23017^610	64110	Norbert Schneider	07/2016
7710	2^212950-64875	64105	Lelio R Paula	10/2011
7711	(266*10^64102-17)/3	64104	Robert Price	06/2016
7712	p(13679)#/2+64	64097	Robert Price	03/2017
7713	19^50119+94	64090	Lelio R Paula	08/2013
7714	2^212880-147	64084	Lelio R Paula	08/2011
7715	11^61523-4590	64070	Enzo Doria	01/2013
7716	5^91663+38	64070	Lelio R Paula	05/2013
7717	5^91650+52	64061	Lelio R Paula	05/2013
7718	2^212770+69	64051	Lelio R Paula	08/2011
7719	(3^134227+1)/4	64042	Paul Bourdelais	11/2007
7720	(2*10^64041-17)/3	64041	Robert Price	08/2014
7721	(15^54449+1)/16	64036	Paul Bourdelais	03/2010
7722	(29*10^64027+91)/3	64028	Robert Price	03/2016
7723	(lucasV(1,2,425405)+2)/(17*89)	64027	Mike Oakes	03/2017
7724	16878!+16878#-1	64022	D. Gazzoni Filho & Lucas Teixeira	05/2005
7725	2^212663+53	64018	Lelio R Paula	08/2011
7726	(4*10^64014+197)/3	64015	Robert Price	03/2017
7727	85402!6-3	64014	Robert Price	08/2018
7728	(140^29819+1)/141	63994	Richard Fischer	05/2018
7729	10^63986+63	63987	Robert Price	01/2011
7730	10^63986-31557	63986	Patrick De Geest	05/2013
7731	31487!2-2^31487	63982	Robert Price	09/2015
7732	(21*2^212522-1)/1416323	63971	Lelio R Paula	01/2014
7733	5^91517+98	63968	Lelio R Paula	04/2013
7734	(19*10^63960-43)/3	63961	Robert Price	10/2017
7735	(62*10^63954-17)/9	63955	Robert Price	09/2015
7737	5^91493-4^91493	63951	Predrag Minovic	04/2004
7736	V(364793)	63951	Serge Batalov	03/2015
7740	19^50004+58	63943	Lelio R Paula	05/2013
7738	5*6^82172-7	63943	Lelio R Paula	09/2014
7739	(56*10^63942+223)/9	63943	Robert Price	07/2016
7741	19^50000-24	63938	Lelio R Paula	05/2013
7742	(23*2^212374-1)/27019	63928	Lelio R Paula	01/2014
7743	(9*2^212355-1)/761	63924	Lelio R Paula	01/2014
7745	2^212344-183	63922	Lelio R Paula	08/2011
7744	(58695*2^212336-1)/379	63922	Lelio R Paula	04/2015
7746	10^63916+79	63917	Robert Price	01/2011
7747	10^63916-76823	63916	Patrick De Geest	05/2013
7748	2^212295-25	63908	Lelio R Paula	08/2011
7750	2^212285-2383	63905	Yves Minet	10/2013
7749	267^26336+26336^267	63905	Norbert Schneider	09/2014

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Probable Primes Top 10000

(252402 PRPs in the top)