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	(4*10^66284+23)/9	66284	Robert Price	11/2014
6502	32501!2+2	66266	Robert Price	01/2015
6503	1530*10^66254+R(66254)	66258	Patrick De Geest	05/2016
6504	(47^39623-1)/46	66252	Robert Price	06/2014
6505	2^220044-97305	66240	Lelio R Paula	04/2012
6506	29^45285+2	66225	Ray Chandler	08/2011
6507	15^56289+38	66202	Lelio R Paula	08/2013
6508	3^138749+98	66201	Lelio R Paula	06/2013
6509	(21*2^219912-1)/5	66201	Lelio R Paula	01/2014
6510	2^219904-16995	66198	Lelio R Paula	10/2011
6511	(3^138712-2)/5297	66179	Lelio R Paula	04/2012
6512	Phi(198552,10)	66177	Ray Chandler	07/2010
6513	4*6^85041+7	66176	Lelio R Paula	09/2014
6514	2^219812-3149	66171	Yves Minet	10/2009
6515	2^219795-611167	66165	Paul Bourdelais	03/2013
6516	32455!2+512	66162	Robert Price	02/2015
6517	(27*2^219760-1)/227	66154	Lelio R Paula	01/2014
6519	(11^63521-4^63521)/7	66150	Robert Price	03/2013
6518	5*7^78274-6	66150	Lelio R Paula	09/2014
6520	(-lucasV(1,2,439441)-2)/(31192781359)	66134	Mike Oakes	04/2017
6521	2^219679-112015	66130	Enzo Doria	05/2014
6522	2^219653+15015*219653	66123	Henri Lifchitz	04/2005
6523	2^219600+76561	66107	Enzo Doria	05/2016
6524	2^219594+255255	66105	Lelio R Paula	10/2011
6525	4*7^78210-3	66096	Lelio R Paula	09/2014
6526	(15185*2^219557-1)/63	66096	Lelio R Paula	04/2015
6527	(19*2^219499-1)/13	66076	Lelio R Paula	01/2014
6528	2^219496+66615	66075	Lelio R Paula	10/2011
6529	(F(79021)^5-F(79020)^5)/F(79019)	66057	Wayne Halsdorf	03/2012
6530	(2^219414+7)/443657	66045	Lelio R Paula	04/2012
6531	(115*10^66043-1)/3	66045	Serge Batalov	12/2014
6532	10^66033+19	66034	Robert Price	01/2011
6533	10^66033-78309	66033	Patrick De Geest	05/2013
6534	(lucasV(1,2,438701)+2)/7599419	66025	Mike Oakes	04/2017
6535	2^219304+454245	66018	Henri Lifchitz	03/2007
6536	(27*2^219293+1)/9145	66012	Lelio R Paula	08/2012
6537	2^219273-112635	66008	Enzo Doria	06/2014
6538	2^219250+25	66001	Lelio R Paula	08/2011
6539	132^31123+131	65999	Norbert Schneider	03/2015
6540	V(319871)	65987	Serge Batalov	03/2015
6541	2^219189-195	65983	Lelio R Paula	08/2011
6542	(7*2^219143-1)/55	65968	Lelio R Paula	01/2014
6543	2^219112-17009	65960	Enzo Doria	05/2013
6544	2^219093-111201	65954	Enzo Doria	05/2014
6545	2^219089-112099	65953	Enzo Doria	06/2014
6546	46714!3+81	65950	Robert Price	09/2014
6547	(11*10^65944-131)/3	65945	Robert Price	02/2017
6548	2^219021-3553	65932	Yves Minet	03/2017
6549	Pell-LucasQ(172243)/2	65931	Eric W. Weisstein	01/2007
6550	2^218990+73519	65923	Enzo Doria	04/2016
6551	58^37378-57	65914	Norbert Schneider	09/2014
6552	(2^218945-7)/1675	65906	Lelio R Paula	04/2012
6553	(-lucasV(1,2,437845)-2)/1679917	65896	Mike Oakes	04/2017
6555	2^218897-111889	65895	Enzo Doria	05/2014
6554	2^218896+1869451	65895	Enzo Doria	05/2016
6556	63^36616+2	65885	Lelio R Paula	05/2013
6557	(3*2^218822-1)/11	65872	Lelio R Paula	01/2014
6558	2^218796-113297	65865	Enzo Doria	07/2014
6559	2^218797+73727	65865	Enzo Doria	04/2016
6560	3^138040-110	65862	Lelio R Paula	06/2013
6561	11^63240-1950	65858	Enzo Doria	12/2012
6562	2^218764-111873	65855	Enzo Doria	05/2014
6563	(34*10^65839-7)/9/37	65839	Makoto Morimoto	04/2016
6564	3^137988+26	65838	Lelio R Paula	06/2013
6565	2^218680-719	65830	Yves Minet	05/2012
6566	18^52424+17	65807	Lelio R Paula	08/2013
6567	(2*15683^15683+1)/732384425	65789	David Broadhurst	09/2010
6568	(23*2^218517+1)/19003	65778	Lelio R Paula	07/2012
6569	(5*10^65773+1)/3	65774	Erik Branger	12/2013
6570	2^218457-17329	65763	Enzo Doria	05/2013
6571	151703#+223381	65759	Nicolas PALAU	10/2016
6572	2^218436+40755	65756	Lelio R Paula	10/2011
6573	(F(44)^7433-F(43)^7433)/F(42)	65744	Wayne Halsdorf	03/2012
6574	157^29934+29934^157	65733	Serge Batalov	05/2014
6575	211^28273-2	65715	Lelio R Paula	09/2013
6576	(59*10^65712+31)/9	65713	Robert Price	09/2015
6578	611^23586+23586^611	65712	Norbert Schneider	08/2016
6577	p(13991)#/2+32	65712	Robert Price	12/2016
6579	2^218282-18485	65710	Enzo Doria	05/2013
6580	2^218274-111251	65708	Enzo Doria	05/2014
6581	2*F(314335)-1	65693	Henri Lifchitz	12/2009
6582	2^218200+427	65685	Henri Lifchitz	01/2005
6583	46532!3+3	65667	Robert Price	10/2014
6584	2^218120-147	65661	Lelio R Paula	08/2011
6585	452^24729+24729^452	65659	Norbert Schneider	09/2016
6586	2^218102-114893	65656	Enzo Doria	05/2015
6587	(15*2^218083-1)/17	65650	Lelio R Paula	01/2014
6588	(15*2^218081+1)/18941	65646	Lelio R Paula	08/2012
6589	19^51326+36	65634	Lelio R Paula	08/2013
6590	(21*2^218045-1)/451583	65634	Lelio R Paula	01/2014
6591	2^217989-33	65622	Lelio R Paula	08/2011
6592	(13*2^217961+1)/3	65614	Lelio R Paula	06/2012
6593	4*6^84315-5	65611	Lelio R Paula	09/2014
6594	(315047^11933+1)/315048	65607	Faysal YAtim	06/2008
6595	6^84303+55	65601	Lelio R Paula	07/2013
6596	(-lucasV(1,2,435857)+2)/(1738598017)	65595	Mike Oakes	04/2017
6597	(9787*2^217873-1)/37	65589	Lelio R Paula	04/2015
6598	5*2^217858+3	65583	Lelio R Paula	04/2014
6599	(19*10^65572+119)/3	65573	Robert Price	02/2017
6600	20^50399+51	65571	Lelio R Paula	08/2013
6601	11^62946-5670	65552	Enzo Doria	01/2013
6602	2^217742-3911	65547	Yves Minet	08/2009
6603	(19*10^65545+77)/3	65546	Robert Price	08/2016
6604	2^217731+131	65544	Lelio R Paula	08/2011
6605	2^217720-111287	65541	Enzo Doria	05/2014
6606	10^65537+27	65538	Robert Price	01/2011
6607	10^65537-76859	65537	Patrick De Geest	05/2013
6608	(10223*2^217676+1)/3	65531	Lelio R Paula	06/2014
6609	PadovanNumber[536485]	65518	Eric W. Weisstein	05/2009
6610	7*10^65492-47	65493	Robert Price	02/2017
6611	2^217547-1868407	65489	Enzo Doria	04/2016
6612	2^217531-111769	65484	Enzo Doria	05/2014
6613	7^77484-18	65482	Lelio R Paula	06/2013
6614	2^217488-113285	65471	Enzo Doria	07/2014
6615	151153#/30-30	65468	Henri Lifchitz	12/2011
6616	2^217466+4257	65464	Lelio R Paula	10/2011
6617	46396!3-81	65455	Robert Price	09/2014
6618	2^217421-113185	65451	Enzo Doria	07/2014
6619	(6883*2^217440-1)/1061193295893	65448	Lelio R Paula	04/2015
6620	2^217408-2145	65447	Lelio R Paula	10/2011
6621	2^217398-16947	65444	Enzo Doria	05/2013
6622	8*5^93613+3	65434	Lelio R Paula	09/2014
6623	11^62828-5310	65429	Enzo Doria	01/2013
6624	10^65426+13	65427	Robert Price	01/2011
6625	2^217341-6555	65427	Lelio R Paula	10/2011
6626	10^65426-54849	65426	Patrick De Geest	05/2013
6627	(21*2^217363-1)/56003626667	65424	Lelio R Paula	01/2014
6628	30011^14608-108	65405	Enzo Doria	07/2012
6629	(43^40031-1)/42	65388	Robert Price	04/2014
6630	2^217190+94395	65381	Henri Lifchitz	02/2005
6631	15^55587+46	65376	Lelio R Paula	08/2013
6632	2^217088-111833	65350	Enzo Doria	05/2014
6633	(13*2^217069-1)/1682945	65340	Lelio R Paula	01/2014
6634	(62*10^65331+1)/9	65332	Serge Batalov	11/2010
6635	2^216947-111351	65308	Enzo Doria	05/2014
6636	-E(18022)/775201845682685322943949235068359	65307	Thomas Ritschel	02/2017
6637	(13*10^65297+83)/3	65298	Robert Price	09/2016
6638	5^93400-8	65284	Lelio R Paula	06/2013
6639	2^216802-165	65264	Lelio R Paula	08/2011
6640	2^216799-28635	65264	Lelio R Paula	10/2011
6641	5*10^65255+51	65256	Robert Price	01/2017
6642	2^216762-167	65252	Lelio R Paula	08/2011
6643	11^62657-5790	65251	Enzo Doria	01/2013
6644	3^136756-112880	65250	Enzo Doria	06/2014
6645	2^216752+21	65249	Lelio R Paula	08/2011
6646	11^62651-2700	65245	Enzo Doria	12/2012
6648	Pell-LucasQ(170413)/2	65230	Eric W. Weisstein	12/2006
6647	gcd(V(790525),5F(158105)(F(158105)+1)+1)	65230	Serge Batalov	04/2015
6649	(2^216676-1017)/637	65224	Lelio R Paula	04/2012
6650	2^216652-2327	65219	Yves Minet	10/2013
6651	(9179*2^216648-1)/4667	65218	Lelio R Paula	04/2015
6652	(5*10^65203-119)/3	65204	Robert Price	04/2016
6653	2^216555-113269	65190	Enzo Doria	07/2014
6654	(9513^16384+1)/2	65181	Henri Lifchitz	02/2007
6655	2^216474+12915	65166	Lelio R Paula	02/2013
6656	19^50958-32	65163	Lelio R Paula	08/2013
6657	2^216442-112133	65156	Enzo Doria	06/2014
6658	2^216437-112213	65155	Enzo Doria	06/2014
6659	2^216435-112767	65154	Enzo Doria	06/2014
6660	2^216420+12705	65149	Lelio R Paula	02/2013
6661	8*3^136507-7	65132	Lelio R Paula	04/2014
6662	(-lucasV(1,2,432719)-2)/(5*461)	65128	Mike Oakes	03/2017
6663	2^216197-111769	65082	Enzo Doria	05/2014
6664	6^83631-79	65078	Lelio R Paula	07/2013
6665	572^23601+23601^572	65078	Norbert Schneider	08/2016
6666	(3^136399-7)/544220	65074	Lelio R Paula	04/2012
6667	2^216154-1421	65069	Yves Minet	01/2013
6668	2^216145-112663	65067	Enzo Doria	06/2014
6669	132013*10^65050+2^216091-1	65056	Gilbert Mozzo	01/2014
6670	132019*10^65050+2^216091-1	65056	Gilbert Mozzo	01/2014
6671	148918*10^65050+2^216091-1	65056	Gilbert Mozzo	02/2014
6672	194014*10^65050+2^216091-1	65056	Gilbert Mozzo	02/2014
6673	223864*10^65050+2^216091-1	65056	Gilbert Mozzo	04/2014
6676	82090*10^65050+2^216091-1	65055	Gilbert Mozzo	07/2012
6675	95133*10^65050+2^216091-1	65055	Gilbert Mozzo	12/2013
6674	98142*10^65050+2^216091-1	65055	Gilbert Mozzo	12/2013
6677	((2^216091-1)*34009-48)/25	65054	Serge Batalov	01/2012
6678	5977*10^65050+2^216091-1	65054	Gilbert Mozzo	03/2012
6679	7*2^216091+2^298-13	65051	Peter Lesala	03/2007
6680	2^216091+2*29208-1	65050	Makoto Morimoto	10/2013
6681	(10^(232521+1)-610^32521-1)/3	65043	Robert Price	02/2016
6682	p(13861)#/2+256	65039	Robert Price	05/2017
6683	11^62439-4380	65024	Enzo Doria	01/2013
6684	3^136244+2	65005	Mike Oakes	11/2009
6685	13^58343-50	64991	Lelio R Paula	07/2013
6686	331^25791-10002	64989	Enzo Doria	07/2012
6687	2^215877+131	64986	Lelio R Paula	08/2011
6688	4*5^92959+9	64977	Lelio R Paula	09/2014
6689	2^215789-18825	64959	Lelio R Paula	09/2011
6690	(2^215801-509203)/41327	64958	Lelio R Paula	05/2012
6691	U(315311)	64954	Serge Batalov	03/2015
6692	46072!3-59049	64951	Robert Price	12/2015
6693	2^215750-5955	64948	Lelio R Paula	09/2011
6694	13^58281+46	64922	Lelio R Paula	07/2013
6695	2^215623+183	64909	Lelio R Paula	08/2011
6696	(3^136043-2^136043)/(19862279*33466579)	64895	Mike Oakes	12/2016
6697	5*2^215554+3	64889	Lelio R Paula	04/2014
6698	2^215541-112075	64885	Enzo Doria	06/2014
6699	2*10^64882-3	64883	Dmitry Domanov	11/2010
6700	10^64862+342339	64863	Patrick De Geest	05/2013
6701	10^64862-47	64862	Robert Price	05/2011
6702	19^50718-84	64856	Lelio R Paula	08/2013
6703	(30452^215471-1)/(17115127067173473)	64853	Jens K. Andersen	09/2007
6705	10^64843+4278697839	64844	Robert Price	05/2015
6704	10^64843+21967	64844	Patrick De Geest	03/2016
6706	10^64843-340073	64843	Patrick De Geest	03/2016
6707	11^62254+70	64831	Lelio R Paula	07/2013
6708	2^215351-111925	64828	Enzo Doria	05/2014
6709	2^215310-117	64815	Lelio R Paula	08/2011
6710	124^30958-123	64809	Norbert Schneider	02/2015
6711	(7*10^64807+17)/3	64808	Erik Branger	03/2014
6712	(710^(232400+1)-27*10^32400-7)/9	64801	Robert Price	11/2015
6713	2^215243-15949	64795	Enzo Doria	04/2013
6714	23^47581-22^47581	64793	Robert Price	08/2012
6715	(62*10^64783-17)/9	64784	Robert Price	09/2015
6716	5*3^135747-4	64769	Lelio R Paula	04/2014
6717	(59*10^64767-41)/9	64768	Robert Price	09/2015
6719	(2^215140+3)/19	64763	Lelio R Paula	04/2012
6718	2^215135-17169	64763	Enzo Doria	05/2013
6720	2^215115-111277	64757	Enzo Doria	05/2014
6721	9*5^92641+2	64755	Lelio R Paula	09/2014
6722	(lucasV(1,2,430086)-2)/(7*1033)	64731	Mike Oakes	03/2017
6723	(5*10^64715-23)/9	64715	Robert Price	11/2014
6724	2^214938-1781	64703	Yves Minet	03/2013
6725	11^62111-420	64682	Enzo Doria	08/2012
6726	5^92525+42	64673	Lelio R Paula	06/2013
6727	2^214824+71893	64669	Enzo Doria	04/2016
6728	2^214799-2221	64661	Yves Minet	08/2013
6729	(21*2^214688+1)/293	64627	Lelio R Paula	08/2012
6730	92^32907+32907^92	64623	Serge Batalov	05/2014
6731	6^83013+101	64597	Lelio R Paula	07/2013
6732	p(13775)#/2+8	64594	Robert Price	01/2017
6733	(7*10^64568-43)/9	64568	Robert Price	10/2014
6734	Pell-LucasQ(168677)/2	64566	Eric W. Weisstein	11/2006
6735	(24737*2^214476+1)/2877	64565	Lelio R Paula	06/2014
6736	(47*2^214463+1)/7	64561	Lelio R Paula	04/2015
6737	2^214458+54615	64559	Lelio R Paula	10/2011
6738	(3^135322+7)/122911408	64557	Lelio R Paula	04/2012
6739	2^214389-683113	64538	Paul Bourdelais	03/2013
6740	2^214369-111241	64532	Enzo Doria	05/2014
6741	(19^50461+3^50461)/22	64526	Robert Price	07/2013
6742	11^61954-3660	64519	Enzo Doria	12/2012
6743	(23*2^214319-1)/21	64517	Lelio R Paula	01/2014
6744	(58695*2^214310-1)/571	64516	Lelio R Paula	04/2015
6745	35^41779-34	64510	Norbert Schneider	04/2014
6746	11^61939-5220	64503	Enzo Doria	01/2013
6747	(2^214271+78557)/35	64501	Lelio R Paula	05/2012
6748	126^30706-125	64494	Norbert Schneider	02/2015
6749	gcd(V(1157265),5F(231453)(F(231453)-1)+1)	64492	Serge Batalov	04/2015
6750	2^214215+12909	64486	Lelio R Paula	10/2011

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Probable Primes Top 10000

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