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 ?
6501	9998*2^245696+3	73966	Donovan Johnson	10/2004
6502	13^66400-80	73966	Lelio R Paula	01/2015
6503	(2^245704+9)/25	73963	Lelio R Paula	07/2012
6505	11^71023-7170	73963	Enzo Doria	01/2013
6504	3*10^73962+13	73963	Robert Price	08/2017
6506	(31*2^245660-1)/114195	73948	Lelio R Paula	01/2014
6507	2^245629-2797813	73942	Eric Chen	03/2016
6508	2^245557-153	73921	Lelio R Paula	03/2012
6509	(77*10^73917-59)/9	73918	Robert Price	11/2017
6510	2^245525+1869881	73911	Enzo Doria	06/2016
6511	2^245522+159	73910	Lelio R Paula	03/2012
6512	(13*10^73891-43)/3	73892	Robert Price	08/2017
6513	19^57783-56	73891	Lelio R Paula	01/2015
6514	7*10^73888+79	73889	Robert Price	02/2017
6515	6^94948+174281	73884	Mike Oakes	02/2011
6516	11^70939-4860	73876	Enzo Doria	01/2013
6517	2^245372+54615	73865	Lelio R Paula	05/2013
6518	2^245362-143	73862	Lelio R Paula	03/2012
6519	7^87396+6^(87396-1)	73859	Robert Price	03/2016
6520	(22*10^73853-37)/3	73854	Robert Price	05/2017
6521	5^105646-14246	73844	Enzo Doria	02/2013
6523	2^245290-41	73840	Lelio R Paula	03/2012
6522	2^245290-94395	73840	Lelio R Paula	05/2013
6524	8*5^105600-7	73813	Lelio R Paula	10/2014
6525	7*5^105573-4	73794	Lelio R Paula	10/2014
6526	18^58742-4805	73738	Enzo Doria	03/2013
6527	13^66179+66	73720	Lelio R Paula	01/2015
6528	(82*10^73714-1)/9	73715	Robert Price	12/2014
6529	(29*2^244856-1)/186121	73706	Lelio R Paula	01/2014
6530	(13*2^244840-1)/2799	73702	Lelio R Paula	01/2014
6531	(13*10^73701+17)/3	73702	Robert Price	06/2015
6532	(2^244787-1017)/28411	73684	Lelio R Paula	07/2012
6533	(3^154421-4)/23	73677	Lelio R Paula	06/2012
6534	8*7^87170+5	73669	Lelio R Paula	10/2014
6535	(29*10^73659-113)/3	73660	Robert Price	11/2017
6536	Phi(40100,-40100)	73651	Henri Lifchitz	06/2013
6537	(4*10^73647-19)/3	73648	Robert Price	06/2017
6538	2^244618-2297	73638	Yves Minet	10/2009
6539	3*5^105344+8	73633	Lelio R Paula	10/2014
6540	5^105334-14096	73626	Enzo Doria	02/2013
6541	(2^244584-7)/13237074243033	73614	Lelio R Paula	07/2012
6542	2^244465-110185	73592	Enzo Doria	05/2014
6543	2^244443+40755	73585	Lelio R Paula	05/2013
6544	2^244404+3841	73573	Yves Minet	03/2011
6545	2^244372-110627	73564	Enzo Doria	05/2014
6546	(3*2^244255+1)/245	73527	Lelio R Paula	08/2012
6547	(11*2^244245+1)/23	73525	Lelio R Paula	08/2012
6548	(15185*2^244187-1)/6111	73509	Lelio R Paula	04/2015
6549	(91^37507+1)/92	73476	Paul Bourdelais	08/2017
6550	18^58521+65	73460	Lelio R Paula	01/2015
6551	13^65940+36	73454	Lelio R Paula	01/2015
6552	(625^26267+1)/626	73437	Richard Fischer	12/2017
6553	5^105050-14	73427	Lelio R Paula	08/2014
6554	(((((((((((((30201^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2	73401	Serge Batalov	07/2016
6555	15^62410-46	73400	Lelio R Paula	01/2015
6556	2^243733+1869707	73371	Enzo Doria	05/2016
6557	11^70439-5430	73355	Enzo Doria	01/2013
6558	2^243676-87	73354	Lelio R Paula	03/2012
6559	(101*10^73346-17)/3	73348	Robert Price	08/2016
6560	2^243621-113185	73338	Enzo Doria	07/2014
6561	(5*2^243610-1)/1669	73332	Lelio R Paula	01/2014
6562	2*5^104888-7	73314	Lelio R Paula	10/2014
6563	(58695*2^243516-1)/983	73308	Lelio R Paula	04/2015
6564	(3^153648-2)/33423138097	73299	Lelio R Paula	06/2012
6565	18^58376-5255	73278	Enzo Doria	03/2013
6566	11^70363+32	73276	Lelio R Paula	02/2015
6567	2^243413+4257	73275	Lelio R Paula	05/2013
6568	104824^5+5^104824	73269	Andrey Kulsha	07/2010
6569	7^86689-6^86689	73261	Predrag Minovic	09/2004
6570	2^243296+90195	73240	Lelio R Paula	05/2013
6572	p(15433)#/2-4	73218	Robert Price	12/2016
6571	(59*10^73217-77)/9	73218	Robert Price	11/2017
6573	2^243127+71355	73189	Lelio R Paula	05/2013
6574	2^243116-249419	73186	Paul Bourdelais	03/2013
6575	(58695*2^243085-1)/11	73180	Lelio R Paula	04/2015
6576	11^70262-98	73171	Lelio R Paula	02/2015
6577	(2^243034+47)/722703303	73152	Lelio R Paula	07/2012
6578	(2^242966+47)/46887	73136	Lelio R Paula	07/2012
6579	(43^44773-1)/42	73134	Robert Price	04/2014
6580	6^93980-158359	73131	Mike Oakes	02/2011
6581	6^93915+53	73081	Lelio R Paula	01/2015
6582	(5*10^73079+211)/9	73079	Robert Price	12/2017
6583	(74*10^73076+43)/9	73077	Robert Price	10/2015
6584	(3^153125+2)/1144955	73054	Lelio R Paula	06/2012
6585	2^242632-112199	73040	Enzo Doria	06/2014
6586	V(351646)	73029	Serge Batalov	03/2015
6587	18^58175-85	73026	Lelio R Paula	01/2015
6588	p(15395)#/2-4	73019	Robert Price	12/2016
6589	(4^121271+3^121271)/7	73012	Jean-Louis Charton	03/2011
6590	8*6^93825-5	73011	Lelio R Paula	10/2014
6591	(F(220)^1601-F(219)^1601)/F(218)	73005	Wayne Halsdorf	08/2013
6592	(73^39181+1)/74	73005	Paul Bourdelais	08/2017
6593	6^93815+143	73003	Lelio R Paula	01/2015
6594	6^93812+5	73000	Wojciech Florek	03/2006
6595	19^57078-62	72989	Lelio R Paula	01/2015
6596	(29*10^72985+91)/3	72986	Robert Price	03/2016
6597	11^70082-2520	72983	Enzo Doria	12/2012
6598	6^93773+133	72970	Lelio R Paula	01/2015
6599	2^242328-59	72948	Lelio R Paula	03/2012
6600	5^104358-13016	72944	Enzo Doria	02/2013
6601	(75*10^72941-57)/99	72941	Ray Chandler	03/2011
6602	12^67585-95	72937	Lelio R Paula	02/2015
6603	2^242230-113285	72919	Enzo Doria	07/2014
6604	(5*10^72916-11)/3	72917	Erik Branger	12/2013
6605	2^242220-110399	72916	Enzo Doria	05/2014
6606	2^242205-113413	72911	Enzo Doria	07/2014
6607	(3^152809+3^76405+1)/7	72908	Serge Batalov	03/2014
6608	2^242175+74243	72902	Yves Minet	03/2011
6609	2^242150+17659	72895	Lelio R Paula	11/2009
6610	11^69982-2340	72879	Enzo Doria	12/2012
6611	(23*2^242093+1)/10117	72875	Lelio R Paula	08/2012
6612	(67607*2^242043+1)/33263	72863	Lelio R Paula	06/2014
6613	2^242032+87	72859	Lelio R Paula	03/2012
6614	2^241968-110595	72840	Enzo Doria	05/2014
6615	(10^72821+71)/9	72821	Robert Price	11/2014
6616	2^241852-64875	72805	Lelio R Paula	05/2013
6617	F(348307)/20562890865908093	72776	Donovan Johnson	07/2007
6618	(67*10^72772+23)/9	72773	Ray Chandler	11/2010
6619	(8*10^72759+67)/3	72760	Robert Price	01/2017
6620	2^241670+145	72750	Lelio R Paula	03/2012
6621	5^104074+52	72745	Lelio R Paula	08/2014
6622	(3^152466-5)/724	72742	Lelio R Paula	06/2012
6623	20^55908-41	72738	Lelio R Paula	01/2015
6624	(73*10^72735+53)/9	72736	Robert Price	10/2015
6625	10^72730+224011	72731	Patrick De Geest	05/2013
6626	10^72730-99	72730	Robert Price	05/2011
6627	3*10^72723+67	72724	Robert Price	11/2017
6628	(11^69833+3^69833)/14	72723	Robert Price	03/2013
6629	(10^72723-79)/3	72723	Robert Price	10/2017
6630	(88*10^72711-43)/9	72712	Robert Price	11/2015
6631	3^152379+280	72704	Lelio R Paula	01/2015
6632	(25*10^72703-241)/9	72704	Robert Price	01/2017
6633	(47*10^72696+133)/9	72697	Robert Price	04/2017
6634	17^59077-90	72692	Lelio R Paula	01/2015
6635	65^40096+58	72691	Lelio R Paula	01/2016
6636	(29*2^241446-1)/245	72682	Lelio R Paula	01/2014
6638	11^69783-38400000	72672	Enzo Doria	01/2013
6637	2^241409-112903	72672	Enzo Doria	06/2014
6639	(3^152287+1)/4	72659	Paul Bourdelais	04/2008
6640	3^152249-56	72642	Lelio R Paula	01/2015
6641	10^72631+37	72632	Robert Price	01/2011
6642	10^72631-8813	72631	Patrick De Geest	05/2013
6643	(19*2^241254+1)/101	72624	Lelio R Paula	08/2012
6644	(9^76103+8^76103)/17	72620	Robert Price	12/2012
6645	2^241220-112337	72615	Enzo Doria	06/2014
6646	(82*10^72612+449)/9	72613	Robert Price	02/2017
6647	2^241169-15793	72600	Enzo Doria	04/2013
6648	9*10^72595+11	72596	Robert Kinser	01/2017
6649	(25*2^241048+1)/89	72563	Lelio R Paula	08/2012
6650	(22*10^72560+17)/3	72561	Robert Price	09/2015
6651	2^241032-23	72558	Lelio R Paula	02/2012
6652	34485*10^72550+2^241004-3	72555	Gilbert Mozzo	12/2012
6653	2^241004-3	72550	M. Frind & P. Underwood	07/2002
6654	97*10^72522-3	72524	Robert Price	01/2017
6655	(68*10^72516+7)/3	72518	Robert Price	03/2016
6656	(78557*2^240844+1)/63	72505	Lelio R Paula	06/2014
6657	67^39701-66	72497	Norbert Schneider	11/2014
6658	(185*10^72484+7)/3	72486	Robert Price	02/2017
6660	(293*27^50631-1736)/13	72473	Curtis Bright	05/2015
6659	103^36005-102	72473	Norbert Schneider	10/2016
6661	15^61616+88	72467	Lelio R Paula	01/2015
6662	45^43831+2	72462	Lelio R Paula	05/2013
6663	2^240692-492389	72456	Paul Bourdelais	03/2013
6664	(646*10^72446-7)/9	72448	Robert Price	07/2016
6665	9*6^93083+7	72434	Lelio R Paula	10/2014
6666	2^240617-3645	72433	Lelio R Paula	05/2013
6667	11^69531-24000	72410	Enzo Doria	12/2012
6668	(22699*2^240396+1)/55	72370	Lelio R Paula	06/2014
6669	6^92995+13	72365	Lelio R Paula	01/2015
6670	(11*10^72362-149)/3	72363	Robert Price	01/2017
6671	(2^240381+3)/51655	72358	Lelio R Paula	05/2012
6672	6^92974-55	72348	Lelio R Paula	01/2015
6673	2^240295+11	72337	Lelio R Paula	02/2012
6674	(14*10^72326-53)/3	72327	Robert Price	12/2016
6675	15^61493-46	72322	Lelio R Paula	01/2015
6676	lucasU(46,1,43497)-lucasU(46,1,43496)	72315	Mike Oakes	04/2009
6677	5*10^72302+9	72303	Dmitry Domanov	11/2010
6678	(9787*2^240179-1)/265	72303	Lelio R Paula	04/2015
6679	11^69419-3120	72293	Enzo Doria	12/2012
6680	4*10^72274-83	72275	Robert Price	10/2017
6681	10^72267+33	72268	Robert Price	01/2011
6682	10^72267-553947	72267	Patrick De Geest	05/2013
6683	11^69389-1380	72262	Enzo Doria	12/2012
6684	(16^60013-5^60013)/11	72262	Robert Price	07/2013
6685	7^85507-30	72262	Lelio R Paula	08/2014
6686	(19*2^240026-1)/15	72256	Lelio R Paula	02/2014
6687	(3^151426-2)/661337	72243	Lelio R Paula	06/2012
6688	gcd(V(1296375),5F(259275)(F(259275)-1)+1)	72227	Serge Batalov	04/2015
6689	2^239863-112267	72206	Enzo Doria	06/2014
6690	2^239853-114853	72203	Enzo Doria	05/2015
6691	(4*10^72174+149)/9	72174	Robert Price	03/2017
6692	(2^239671+9)/296131	72143	Lelio R Paula	05/2012
6693	2^239651-110665	72143	Enzo Doria	05/2014
6694	(29*2^239650-1)/3305	72140	Lelio R Paula	01/2014
6695	241^30280+30280^241	72128	Norbert Schneider	11/2014
6696	(68*10^72120-23)/9	72121	Robert Price	10/2015
6697	(9^75571+8^75571)/17	72112	Robert Price	12/2012
6698	(15*2^239530-1)/173	72105	Lelio R Paula	01/2014
6699	2^239513-112519	72101	Enzo Doria	06/2014
6700	(10^72097+149)/3	72097	Serge Batalov	12/2014
6701	2^239442-6555	72080	Lelio R Paula	05/2012
6702	2*5^103106+3	72069	Lelio R Paula	10/2014
6703	2^239402-197	72068	Lelio R Paula	02/2012
6704	2^239356-111875	72054	Enzo Doria	05/2014
6705	(38*10^72050-119)/9	72051	Robert Price	11/2016
6706	2^239339+15015	72049	Lelio R Paula	01/2013
6707	159^32728+2	72048	Lelio R Paula	05/2013
6708	15^61259-38	72047	Lelio R Paula	01/2015
6709	92^36683-91^36683	72038	Robert Price	08/2015
6710	2^239280+54615	72031	Lelio R Paula	05/2012
6712	(47*2^239267+1)/77	72027	Lelio R Paula	04/2015
6711	(85*10^72025-1)/3	72027	Robert Price	07/2017
6713	2^239236-97305	72018	Lelio R Paula	05/2012
6714	144^33361-143	72006	Norbert Schneider	11/2018
6715	2^239169+59	71998	Lelio R Paula	02/2012
6717	lucasU(2010,1,21796)-lucasU(2010,1,21795)	71994	Mike Oakes	05/2009
6716	(15*2^239171-1)/106301	71994	Lelio R Paula	01/2014
6718	(29^49211-1)/28	71965	Robert Price	04/2012
6719	(299*10^71963+1)/3	71965	Robert Price	11/2017
6721	L(344293)	71953	Renaud Lifchitz	09/2003
6720	V(344293)	71953	Serge Batalov	03/2015
6722	6*10^71951+7	71952	Dmitry Domanov	11/2010
6723	3^150798+40	71949	Lelio R Paula	01/2015
6724	2^238961+95	71935	Lelio R Paula	02/2012
6725	2^238936-407	71927	Yves Minet	02/2012
6726	2^238923-28635	71923	Lelio R Paula	05/2012
6727	10^71910+25119	71911	Patrick De Geest	05/2016
6728	10^71910-801	71910	Robert Price	04/2016
6729	2^238845-112651	71900	Enzo Doria	06/2014
6730	2^238792-111245	71884	Enzo Doria	05/2014
6731	6*7^85059+5	71884	Lelio R Paula	10/2014
6732	2^238752-110589	71872	Enzo Doria	05/2014
6733	12^66581+7	71853	Lelio R Paula	07/2014
6734	(7*2^238691+1)/41229	71850	Lelio R Paula	06/2012
6735	4*3^150568-5	71840	Lelio R Paula	04/2014
6736	6^92301+67	71825	Lelio R Paula	01/2015
6737	2^238568+98765331	71817	Jason Earls	01/2009
6738	2^238541-112723	71808	Enzo Doria	06/2014
6739	2^238529-15949	71805	Enzo Doria	04/2013
6740	9*5^102721-8	71800	Lelio R Paula	10/2014
6741	2^238494-165	71794	Lelio R Paula	02/2012
6742	2^238389-110905	71763	Enzo Doria	05/2014
6743	(145*10^71760-1)/9	71762	Serge Batalov	12/2014
6744	7^84913+5062	71760	Mike Oakes	02/2010
6745	(F(11446)^31-F(11445)^31)/F(11444)	71753	Wayne Halsdorf	03/2012
6746	2^238268-97305	71726	Lelio R Paula	05/2012
6747	gcd(V(1330365),5F(266073)(F(266073)-1)+1)	71724	Serge Batalov	04/2015
6748	2^238235-113247	71716	Enzo Doria	07/2014
6749	2*12^66450-5^66450	71712	Mike Oakes	11/2010
6750	(2^238213+lucasV(1,2,238213)+1)/4	71709	Mike Oakes	11/2016

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