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 ?
6501	3^138040-110	65862	Lelio R Paula	06/2013
6502	11^63240-1950	65858	Enzo Doria	12/2012
6503	2^218764-111873	65855	Enzo Doria	05/2014
6504	(34*10^65839-7)/9/37	65839	Makoto Morimoto	04/2016
6505	3^137988+26	65838	Lelio R Paula	06/2013
6506	2^218680-719	65830	Yves Minet	05/2012
6507	18^52424+17	65807	Lelio R Paula	08/2013
6508	(2*15683^15683+1)/732384425	65789	David Broadhurst	09/2010
6509	(23*2^218517+1)/19003	65778	Lelio R Paula	07/2012
6510	(5*10^65773+1)/3	65774	Erik Branger	12/2013
6511	2^218457-17329	65763	Enzo Doria	05/2013
6512	151703#+223381	65759	Nicolas PALAU	10/2016
6513	2^218436+40755	65756	Lelio R Paula	10/2011
6514	(F(44)^7433-F(43)^7433)/F(42)	65744	Wayne Halsdorf	03/2012
6515	157^29934+29934^157	65733	Serge Batalov	05/2014
6516	211^28273-2	65715	Lelio R Paula	09/2013
6517	(59*10^65712+31)/9	65713	Robert Price	09/2015
6518	611^23586+23586^611	65712	Norbert Schneider	08/2016
6519	p(13991)#/2+32	65712	Robert Price	12/2016
6520	2^218282-18485	65710	Enzo Doria	05/2013
6521	2^218274-111251	65708	Enzo Doria	05/2014
6522	2*F(314335)-1	65693	Henri Lifchitz	12/2009
6523	2^218200+427	65685	Henri Lifchitz	01/2005
6524	46532!3+3	65667	Robert Price	10/2014
6525	2^218120-147	65661	Lelio R Paula	08/2011
6526	452^24729+24729^452	65659	Norbert Schneider	09/2016
6527	2^218102-114893	65656	Enzo Doria	05/2015
6528	(15*2^218083-1)/17	65650	Lelio R Paula	01/2014
6529	(15*2^218081+1)/18941	65646	Lelio R Paula	08/2012
6531	19^51326+36	65634	Lelio R Paula	08/2013
6530	(21*2^218045-1)/451583	65634	Lelio R Paula	01/2014
6532	2^217989-33	65622	Lelio R Paula	08/2011
6533	(13*2^217961+1)/3	65614	Lelio R Paula	06/2012
6534	4*6^84315-5	65611	Lelio R Paula	09/2014
6535	(315047^11933+1)/315048	65607	Faysal YAtim	06/2008
6536	6^84303+55	65601	Lelio R Paula	07/2013
6537	(-lucasV(1,2,435857)+2)/(1738598017)	65595	Mike Oakes	04/2017
6538	(9787*2^217873-1)/37	65589	Lelio R Paula	04/2015
6539	5*2^217858+3	65583	Lelio R Paula	04/2014
6540	(19*10^65572+119)/3	65573	Robert Price	02/2017
6541	20^50399+51	65571	Lelio R Paula	08/2013
6542	11^62946-5670	65552	Enzo Doria	01/2013
6543	2^217742-3911	65547	Yves Minet	08/2009
6544	(19*10^65545+77)/3	65546	Robert Price	08/2016
6545	2^217731+131	65544	Lelio R Paula	08/2011
6546	2^217720-111287	65541	Enzo Doria	05/2014
6547	10^65537+27	65538	Robert Price	01/2011
6548	10^65537-76859	65537	Patrick De Geest	05/2013
6549	(10223*2^217676+1)/3	65531	Lelio R Paula	06/2014
6550	PadovanNumber[536485]	65518	Eric W. Weisstein	05/2009
6551	7*10^65492-47	65493	Robert Price	02/2017
6552	2^217547-1868407	65489	Enzo Doria	04/2016
6553	2^217531-111769	65484	Enzo Doria	05/2014
6554	7^77484-18	65482	Lelio R Paula	06/2013
6555	2^217488-113285	65471	Enzo Doria	07/2014
6556	151153#/30-30	65468	Henri Lifchitz	12/2011
6557	2^217466+4257	65464	Lelio R Paula	10/2011
6558	46396!3-81	65455	Robert Price	09/2014
6559	2^217421-113185	65451	Enzo Doria	07/2014
6560	(6883*2^217440-1)/1061193295893	65448	Lelio R Paula	04/2015
6561	2^217408-2145	65447	Lelio R Paula	10/2011
6562	2^217398-16947	65444	Enzo Doria	05/2013
6563	8*5^93613+3	65434	Lelio R Paula	09/2014
6564	11^62828-5310	65429	Enzo Doria	01/2013
6565	10^65426+13	65427	Robert Price	01/2011
6566	2^217341-6555	65427	Lelio R Paula	10/2011
6567	10^65426-54849	65426	Patrick De Geest	05/2013
6568	(21*2^217363-1)/56003626667	65424	Lelio R Paula	01/2014
6569	30011^14608-108	65405	Enzo Doria	07/2012
6570	(43^40031-1)/42	65388	Robert Price	04/2014
6571	2^217190+94395	65381	Henri Lifchitz	02/2005
6572	15^55587+46	65376	Lelio R Paula	08/2013
6573	2^217088-111833	65350	Enzo Doria	05/2014
6574	(13*2^217069-1)/1682945	65340	Lelio R Paula	01/2014
6575	(62*10^65331+1)/9	65332	Serge Batalov	11/2010
6576	2^216947-111351	65308	Enzo Doria	05/2014
6577	-E(18022)/775201845682685322943949235068359	65307	Thomas Ritschel	02/2017
6578	(13*10^65297+83)/3	65298	Robert Price	09/2016
6579	5^93400-8	65284	Lelio R Paula	06/2013
6580	2^216802-165	65264	Lelio R Paula	08/2011
6581	2^216799-28635	65264	Lelio R Paula	10/2011
6582	5*10^65255+51	65256	Robert Price	01/2017
6583	2^216762-167	65252	Lelio R Paula	08/2011
6584	11^62657-5790	65251	Enzo Doria	01/2013
6585	3^136756-112880	65250	Enzo Doria	06/2014
6586	2^216752+21	65249	Lelio R Paula	08/2011
6587	11^62651-2700	65245	Enzo Doria	12/2012
6589	Pell-LucasQ(170413)/2	65230	Eric W. Weisstein	12/2006
6588	gcd(V(790525),5F(158105)(F(158105)+1)+1)	65230	Serge Batalov	04/2015
6590	(2^216676-1017)/637	65224	Lelio R Paula	04/2012
6591	2^216652-2327	65219	Yves Minet	10/2013
6592	(9179*2^216648-1)/4667	65218	Lelio R Paula	04/2015
6593	(5*10^65203-119)/3	65204	Robert Price	04/2016
6594	2^216555-113269	65190	Enzo Doria	07/2014
6595	(9513^16384+1)/2	65181	Henri Lifchitz	02/2007
6596	2^216474+12915	65166	Lelio R Paula	02/2013
6597	19^50958-32	65163	Lelio R Paula	08/2013
6598	2^216442-112133	65156	Enzo Doria	06/2014
6599	2^216437-112213	65155	Enzo Doria	06/2014
6600	2^216435-112767	65154	Enzo Doria	06/2014
6601	2^216420+12705	65149	Lelio R Paula	02/2013
6602	8*3^136507-7	65132	Lelio R Paula	04/2014
6603	(-lucasV(1,2,432719)-2)/(5*461)	65128	Mike Oakes	03/2017
6604	2^216197-111769	65082	Enzo Doria	05/2014
6606	6^83631-79	65078	Lelio R Paula	07/2013
6605	572^23601+23601^572	65078	Norbert Schneider	08/2016
6607	(3^136399-7)/544220	65074	Lelio R Paula	04/2012
6608	2^216154-1421	65069	Yves Minet	01/2013
6609	2^216145-112663	65067	Enzo Doria	06/2014
6610	132013*10^65050+2^216091-1	65056	Gilbert Mozzo	01/2014
6611	132019*10^65050+2^216091-1	65056	Gilbert Mozzo	01/2014
6612	148918*10^65050+2^216091-1	65056	Gilbert Mozzo	02/2014
6613	194014*10^65050+2^216091-1	65056	Gilbert Mozzo	02/2014
6614	223864*10^65050+2^216091-1	65056	Gilbert Mozzo	04/2014
6616	82090*10^65050+2^216091-1	65055	Gilbert Mozzo	07/2012
6617	95133*10^65050+2^216091-1	65055	Gilbert Mozzo	12/2013
6615	98142*10^65050+2^216091-1	65055	Gilbert Mozzo	12/2013
6618	((2^216091-1)*34009-48)/25	65054	Serge Batalov	01/2012
6619	5977*10^65050+2^216091-1	65054	Gilbert Mozzo	03/2012
6620	7*2^216091+2^298-13	65051	Peter Lesala	03/2007
6621	2^216091+2*29208-1	65050	Makoto Morimoto	10/2013
6622	(10^(232521+1)-610^32521-1)/3	65043	Robert Price	02/2016
6623	p(13861)#/2+256	65039	Robert Price	05/2017
6624	11^62439-4380	65024	Enzo Doria	01/2013
6625	3^136244+2	65005	Mike Oakes	11/2009
6626	13^58343-50	64991	Lelio R Paula	07/2013
6627	331^25791-10002	64989	Enzo Doria	07/2012
6628	2^215877+131	64986	Lelio R Paula	08/2011
6629	4*5^92959+9	64977	Lelio R Paula	09/2014
6630	2^215789-18825	64959	Lelio R Paula	09/2011
6631	(2^215801-509203)/41327	64958	Lelio R Paula	05/2012
6632	U(315311)	64954	Serge Batalov	03/2015
6633	46072!3-59049	64951	Robert Price	12/2015
6634	2^215750-5955	64948	Lelio R Paula	09/2011
6635	13^58281+46	64922	Lelio R Paula	07/2013
6636	2^215623+183	64909	Lelio R Paula	08/2011
6637	(3^136043-2^136043)/(19862279*33466579)	64895	Mike Oakes	12/2016
6638	5*2^215554+3	64889	Lelio R Paula	04/2014
6639	2^215541-112075	64885	Enzo Doria	06/2014
6640	2*10^64882-3	64883	Dmitry Domanov	11/2010
6641	10^64862+342339	64863	Patrick De Geest	05/2013
6642	10^64862-47	64862	Robert Price	05/2011
6643	19^50718-84	64856	Lelio R Paula	08/2013
6644	(30452^215471-1)/(17115127067173473)	64853	Jens K. Andersen	09/2007
6646	10^64843+4278697839	64844	Robert Price	05/2015
6645	10^64843+21967	64844	Patrick De Geest	03/2016
6647	10^64843-340073	64843	Patrick De Geest	03/2016
6648	11^62254+70	64831	Lelio R Paula	07/2013
6649	2^215351-111925	64828	Enzo Doria	05/2014
6650	2^215310-117	64815	Lelio R Paula	08/2011
6651	124^30958-123	64809	Norbert Schneider	02/2015
6652	(7*10^64807+17)/3	64808	Erik Branger	03/2014
6653	(710^(232400+1)-27*10^32400-7)/9	64801	Robert Price	11/2015
6654	2^215243-15949	64795	Enzo Doria	04/2013
6655	23^47581-22^47581	64793	Robert Price	08/2012
6656	(62*10^64783-17)/9	64784	Robert Price	09/2015
6657	5*3^135747-4	64769	Lelio R Paula	04/2014
6658	(59*10^64767-41)/9	64768	Robert Price	09/2015
6660	(2^215140+3)/19	64763	Lelio R Paula	04/2012
6659	2^215135-17169	64763	Enzo Doria	05/2013
6661	2^215115-111277	64757	Enzo Doria	05/2014
6662	9*5^92641+2	64755	Lelio R Paula	09/2014
6663	(lucasV(1,2,430086)-2)/(7*1033)	64731	Mike Oakes	03/2017
6664	(5*10^64715-23)/9	64715	Robert Price	11/2014
6665	2^214938-1781	64703	Yves Minet	03/2013
6666	11^62111-420	64682	Enzo Doria	08/2012
6667	5^92525+42	64673	Lelio R Paula	06/2013
6668	2^214824+71893	64669	Enzo Doria	04/2016
6669	2^214799-2221	64661	Yves Minet	08/2013
6670	(21*2^214688+1)/293	64627	Lelio R Paula	08/2012
6671	92^32907+32907^92	64623	Serge Batalov	05/2014
6672	6^83013+101	64597	Lelio R Paula	07/2013
6673	p(13775)#/2+8	64594	Robert Price	01/2017
6674	(7*10^64568-43)/9	64568	Robert Price	10/2014
6675	Pell-LucasQ(168677)/2	64566	Eric W. Weisstein	11/2006
6676	(24737*2^214476+1)/2877	64565	Lelio R Paula	06/2014
6677	(47*2^214463+1)/7	64561	Lelio R Paula	04/2015
6678	2^214458+54615	64559	Lelio R Paula	10/2011
6679	(3^135322+7)/122911408	64557	Lelio R Paula	04/2012
6680	2^214389-683113	64538	Paul Bourdelais	03/2013
6681	2^214369-111241	64532	Enzo Doria	05/2014
6682	(19^50461+3^50461)/22	64526	Robert Price	07/2013
6683	11^61954-3660	64519	Enzo Doria	12/2012
6684	(23*2^214319-1)/21	64517	Lelio R Paula	01/2014
6685	(58695*2^214310-1)/571	64516	Lelio R Paula	04/2015
6686	35^41779-34	64510	Norbert Schneider	04/2014
6687	11^61939-5220	64503	Enzo Doria	01/2013
6688	(2^214271+78557)/35	64501	Lelio R Paula	05/2012
6689	126^30706-125	64494	Norbert Schneider	02/2015
6690	gcd(V(1157265),5F(231453)(F(231453)-1)+1)	64492	Serge Batalov	04/2015
6691	2^214215+12909	64486	Lelio R Paula	10/2011
6692	5^92225+66	64463	Lelio R Paula	06/2013
6693	2^214126-240551	64459	Paul Bourdelais	03/2013
6694	8*6^82827+5	64453	Lelio R Paula	09/2014
6695	(31*2^214120-1)/2170485	64452	Lelio R Paula	01/2014
6696	(31*2^214088-1)/5955	64445	Lelio R Paula	01/2014
6697	14^56227+89	64444	Lelio R Paula	08/2013
6700	2^214055-159	64437	Lelio R Paula	08/2011
6698	10^64436+2667	64437	Patrick De Geest	05/2013
6699	65^35543-64^35543	64437	Robert Price	08/2013
6701	10^64436-53	64436	Robert Price	05/2011
6702	Phi(128878,10)/39503297927	64428	Maksym Voznyy	11/2015
6703	3^135027+100	64425	Lelio R Paula	05/2013
6704	(3^134972-7)/2	64398	Lelio R Paula	04/2012
6705	6*10^64387+7	64388	Dmitry Domanov	11/2010
6706	2^213864-18377	64380	Enzo Doria	05/2013
6707	(2^213821+9)/209	64365	Lelio R Paula	04/2012
6708	2^213788+135	64357	Lelio R Paula	08/2011
6709	(3^134883+2)/48313	64351	Lelio R Paula	04/2012
6710	(49^38069-46^38069)/3	64344	Serge Batalov	12/2016
6711	(11^61781+2^61781)/13	64338	Robert Price	02/2013
6712	6^82670+37	64330	Lelio R Paula	07/2013
6713	(3^134839+4)/32312959	64328	Lelio R Paula	04/2012
6714	(22*10^64326+161)/3	64327	Robert Price	02/2017
6715	11^61767-4050	64324	Enzo Doria	12/2012
6716	2^213645-114853	64314	Enzo Doria	05/2015
6717	13^57733+18	64312	Lelio R Paula	07/2013
6718	2^213621+72707	64307	Enzo Doria	04/2016
6719	10^64305+136791	64306	Patrick De Geest	05/2011
6720	10^64305-9	64305	Alexander Gramolin	01/2011
6721	V(307652)	64295	Serge Batalov	03/2015
6722	(2^213546-5)/2221	64281	Lelio R Paula	04/2012
6723	2^213438-58695	64252	Lelio R Paula	10/2011
6724	2^213367-105	64230	Lelio R Paula	08/2011
6725	595^23148+23148^595	64225	Norbert Schneider	07/2016
6726	3^134601+8680	64221	Lelio R Paula	05/2013
6727	(26*10^64220+61)/3	64221	Robert Price	06/2017
6728	500^23793+23793^500	64217	Norbert Schneider	08/2016
6730	2^213314-455	64214	Yves Minet	02/2012
6729	39^40359-38	64214	Norbert Schneider	05/2014
6731	2^213292-16085	64208	Enzo Doria	04/2013
6732	2^213274-77	64202	Lelio R Paula	08/2011
6733	19^50203+78	64198	Lelio R Paula	08/2013
6734	2^213240-112865	64192	Enzo Doria	06/2014
6735	2^213190-112391	64177	Enzo Doria	06/2014
6736	(9913*2^213184-1)/9657	64175	Lelio R Paula	04/2015
6737	14^55991+27	64173	Lelio R Paula	07/2013
6738	2^213158-112581	64167	Enzo Doria	06/2014
6739	2^213148+91	64164	Lelio R Paula	08/2011
6741	6^82439+125	64151	Lelio R Paula	07/2013
6740	7*2^213102+9	64151	Lelio R Paula	04/2014
6742	L(306854)+F(306855)	64129	Henri Lifchitz	01/2007
6743	610^23017+23017^610	64110	Norbert Schneider	07/2016
6744	2^212950-64875	64105	Lelio R Paula	10/2011
6745	(266*10^64102-17)/3	64104	Robert Price	06/2016
6746	p(13679)#/2+64	64097	Robert Price	03/2017
6747	19^50119+94	64090	Lelio R Paula	08/2013
6748	2^212880-147	64084	Lelio R Paula	08/2011
6749	11^61523-4590	64070	Enzo Doria	01/2013
6750	5^91663+38	64070	Lelio R Paula	05/2013

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Probable Primes Top 10000

(174961 PRPs in the top)