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	(19*2^248099-1)/29	74686	Lelio R Paula	01/2014
6502	(86*10^74676-41)/9	74677	Robert Price	11/2015
6503	(p(15711)#-4)/2	74672	Robert Price	09/2017
6504	10^74670+31	74671	Robert Price	01/2011
6505	10^74670-122463	74670	Patrick De Geest	05/2013
6506	2^248036-69	74667	Lelio R Paula	03/2012
6507	11^71698-6000	74666	Enzo Doria	12/2012
6508	58(10^(324887)-1)/111-1	74661	Robert Price	10/2014
6509	14^65139-45	74658	Lelio R Paula	01/2015
6510	6^95921-133	74642	Lelio R Paula	01/2015
6511	11^71675+78	74642	Lelio R Paula	02/2015
6512	18^59449-91	74625	Lelio R Paula	01/2015
6513	6^95864-16043	74597	Enzo Doria	02/2013
6514	5*7^88261+6	74590	Lelio R Paula	10/2014
6515	9*5^106710+4	74589	Lelio R Paula	10/2014
6516	(7772^247788+1)/(11754121)	74588	Jens K. Andersen	09/2007
6517	(265*10^74579+17)/3	74581	Robert Price	05/2016
6518	(2^247759-1017)/3318311717	74574	Lelio R Paula	07/2012
6519	5^106682-24	74568	Lelio R Paula	08/2014
6520	474^27863+27863^474	74556	Norbert Schneider	01/2017
6521	(14*10^74540+79)/3	74541	Robert Price	11/2017
6522	(35365^16384+1)/2	74524	Lelio R Paula	11/2011
6523	3^156161+2660	74508	Lelio R Paula	01/2015
6524	2^247474-58695	74498	Lelio R Paula	05/2013
6525	11^71519-90	74480	Enzo Doria	07/2012
6526	(19*2^247419-1)/23202983	74475	Lelio R Paula	01/2014
6528	(2^247394-7)/3	74473	Lelio R Paula	06/2012
6527	18^59328+17	74473	Lelio R Paula	01/2015
6529	2^247379-181	74469	Lelio R Paula	03/2012
6530	(15*2^247370-1)/479	74465	Lelio R Paula	01/2014
6531	2^247344+2047	74458	Lelio R Paula	05/2013
6532	2^247311-1017	74449	Lelio R Paula	05/2013
6533	2^247280+7	74439	Lelio R Paula	03/2012
6534	(68*10^74434+13)/9	74435	Ray Chandler	11/2010
6535	3^156004-62	74433	Lelio R Paula	01/2015
6536	36095!2-64	74416	Robert Price	06/2015
6537	2^247165-3	74405	M. Frind & P. Underwood	07/2002
6538	2^247150+32769	74400	Lelio R Paula	05/2013
6539	12^68911+73	74368	Lelio R Paula	01/2015
6540	2^246999+74903	74355	Enzo Doria	04/2016
6541	2^246989-110643	74352	Enzo Doria	05/2014
6542	10^74350+279439	74351	Patrick De Geest	07/2017
6545	(10^74350+11)/3	74350	Robert Price	11/2014
6543	10^74350-400000001	74350	Robert Price	07/2017
6544	10^74350-716241	74350	Patrick De Geest	07/2017
6546	10^74335+13659	74336	Patrick De Geest	05/2013
6547	10^74335-53	74335	Robert Price	05/2011
6548	2^246906-1215	74327	Lelio R Paula	05/2013
6549	2^246848+111	74309	Lelio R Paula	03/2012
6550	6^95490-18443	74306	Enzo Doria	03/2013
6551	18^59188-2369	74298	Enzo Doria	03/2013
6552	(13632^246767+1)/(35713^2*743)	74281	Jens K. Andersen	09/2007
6553	2^246744+40755	74278	Lelio R Paula	05/2013
6554	(29*10^74276+91)/3	74277	Robert Price	03/2016
6555	6^95441+163	74268	Lelio R Paula	01/2015
6556	V(390863)	74258	Serge Batalov	03/2015
6557	10^74254+91	74255	Robert Price	03/2011
6558	(19*10^74253-1)/9	74254	Ray Chandler	02/2012
6559	10^74254-130569	74254	Patrick De Geest	05/2013
6560	771^25718+25718^771	74250	Norbert Schneider	10/2016
6561	2^246618+427	74240	Henri Lifchitz	02/2005
6562	88*10^74234+3	74236	Robert Price	11/2016
6563	8*10^74234-49	74235	Robert Price	04/2016
6564	2^246578+12285	74228	Lelio R Paula	05/2013
6565	(3^155569-5)/2	74225	Lelio R Paula	06/2012
6566	13^66628+46	74220	Lelio R Paula	01/2015
6567	2^246476-17295	74197	Lelio R Paula	05/2013
6568	(61*10^74189-1)/3	74191	Robert Price	11/2017
6569	(15185*2^246432-1)/13	74187	Lelio R Paula	04/2015
6570	5*2^246413-3	74179	Lelio R Paula	05/2014
6571	2^246386-28635	74170	Lelio R Paula	05/2013
6572	2^246334-111245	74154	Enzo Doria	05/2014
6573	39^77708+7^77708-24^77708-3	74153	Mike Oakes	12/2010
6574	15^63045+82	74147	Lelio R Paula	01/2015
6575	19255!+19255#+1	74140	D. Gazzoni Filho & Lucas Teixeira	06/2005
6576	2^246268-110507	74135	Enzo Doria	05/2014
6577	3^155328+2660	74111	Lelio R Paula	01/2015
6578	2^246148-2786249	74098	Enzo Doria	03/2016
6579	(16*10^74092-19)/3	74093	Robert Price	03/2016
6580	2^246115-110767	74088	Enzo Doria	05/2014
6581	7^87666-68	74087	Lelio R Paula	08/2014
6582	10^74079+1145141919	74080	Marisa Kirisame	03/2015
6583	10^74079+6219	74080	Patrick De Geest	03/2016
6584	10^74079-282707	74079	Patrick De Geest	03/2016
6585	129^35098+2	74078	Lelio R Paula	05/2013
6586	2^246025-112123	74061	Enzo Doria	06/2014
6587	(67*10^74045+17)/3	74047	Robert Price	02/2017
6588	2^245823+66831	74001	Marek Hubal	02/2017
6589	5^105869+42	74000	Lelio R Paula	08/2014
6590	(21*2^245806+1)/634555	73991	Lelio R Paula	08/2012
6591	(22699*2^245762+1)/119	73985	Lelio R Paula	06/2014
6592	(3^155048-7)/262	73975	Lelio R Paula	06/2012
6593	9998*2^245696+3	73966	Donovan Johnson	10/2004
6594	13^66400-80	73966	Lelio R Paula	01/2015
6595	(2^245704+9)/25	73963	Lelio R Paula	07/2012
6597	11^71023-7170	73963	Enzo Doria	01/2013
6596	3*10^73962+13	73963	Robert Price	08/2017
6598	(31*2^245660-1)/114195	73948	Lelio R Paula	01/2014
6599	2^245629-2797813	73942	Eric Chen	03/2016
6600	2^245557-153	73921	Lelio R Paula	03/2012
6601	(77*10^73917-59)/9	73918	Robert Price	11/2017
6602	2^245525+1869881	73911	Enzo Doria	06/2016
6603	2^245522+159	73910	Lelio R Paula	03/2012
6604	(13*10^73891-43)/3	73892	Robert Price	08/2017
6605	19^57783-56	73891	Lelio R Paula	01/2015
6606	7*10^73888+79	73889	Robert Price	02/2017
6607	6^94948+174281	73884	Mike Oakes	02/2011
6608	11^70939-4860	73876	Enzo Doria	01/2013
6609	2^245372+54615	73865	Lelio R Paula	05/2013
6610	2^245362-143	73862	Lelio R Paula	03/2012
6611	7^87396+6^(87396-1)	73859	Robert Price	03/2016
6612	(22*10^73853-37)/3	73854	Robert Price	05/2017
6613	5^105646-14246	73844	Enzo Doria	02/2013
6615	2^245290-41	73840	Lelio R Paula	03/2012
6614	2^245290-94395	73840	Lelio R Paula	05/2013
6616	8*5^105600-7	73813	Lelio R Paula	10/2014
6617	7*5^105573-4	73794	Lelio R Paula	10/2014
6618	18^58742-4805	73738	Enzo Doria	03/2013
6619	13^66179+66	73720	Lelio R Paula	01/2015
6620	(82*10^73714-1)/9	73715	Robert Price	12/2014
6621	(29*2^244856-1)/186121	73706	Lelio R Paula	01/2014
6622	(13*2^244840-1)/2799	73702	Lelio R Paula	01/2014
6623	(13*10^73701+17)/3	73702	Robert Price	06/2015
6624	(2^244787-1017)/28411	73684	Lelio R Paula	07/2012
6625	(3^154421-4)/23	73677	Lelio R Paula	06/2012
6626	8*7^87170+5	73669	Lelio R Paula	10/2014
6627	(29*10^73659-113)/3	73660	Robert Price	11/2017
6628	Phi(40100,-40100)	73651	Henri Lifchitz	06/2013
6629	(4*10^73647-19)/3	73648	Robert Price	06/2017
6630	2^244618-2297	73638	Yves Minet	10/2009
6631	3*5^105344+8	73633	Lelio R Paula	10/2014
6632	5^105334-14096	73626	Enzo Doria	02/2013
6633	(2^244584-7)/13237074243033	73614	Lelio R Paula	07/2012
6634	2^244465-110185	73592	Enzo Doria	05/2014
6635	2^244443+40755	73585	Lelio R Paula	05/2013
6636	2^244404+3841	73573	Yves Minet	03/2011
6637	2^244372-110627	73564	Enzo Doria	05/2014
6638	(3*2^244255+1)/245	73527	Lelio R Paula	08/2012
6639	(11*2^244245+1)/23	73525	Lelio R Paula	08/2012
6640	(15185*2^244187-1)/6111	73509	Lelio R Paula	04/2015
6641	(91^37507+1)/92	73476	Paul Bourdelais	08/2017
6642	18^58521+65	73460	Lelio R Paula	01/2015
6643	13^65940+36	73454	Lelio R Paula	01/2015
6644	(625^26267+1)/626	73437	Richard Fischer	12/2017
6645	5^105050-14	73427	Lelio R Paula	08/2014
6646	(((((((((((((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
6647	15^62410-46	73400	Lelio R Paula	01/2015
6648	2^243733+1869707	73371	Enzo Doria	05/2016
6649	11^70439-5430	73355	Enzo Doria	01/2013
6650	2^243676-87	73354	Lelio R Paula	03/2012
6651	(101*10^73346-17)/3	73348	Robert Price	08/2016
6652	2^243621-113185	73338	Enzo Doria	07/2014
6653	(5*2^243610-1)/1669	73332	Lelio R Paula	01/2014
6654	2*5^104888-7	73314	Lelio R Paula	10/2014
6655	(58695*2^243516-1)/983	73308	Lelio R Paula	04/2015
6656	(3^153648-2)/33423138097	73299	Lelio R Paula	06/2012
6657	18^58376-5255	73278	Enzo Doria	03/2013
6658	11^70363+32	73276	Lelio R Paula	02/2015
6659	2^243413+4257	73275	Lelio R Paula	05/2013
6660	104824^5+5^104824	73269	Andrey Kulsha	07/2010
6661	7^86689-6^86689	73261	Predrag Minovic	09/2004
6662	2^243296+90195	73240	Lelio R Paula	05/2013
6664	p(15433)#/2-4	73218	Robert Price	12/2016
6663	(59*10^73217-77)/9	73218	Robert Price	11/2017
6665	2^243127+71355	73189	Lelio R Paula	05/2013
6666	2^243116-249419	73186	Paul Bourdelais	03/2013
6667	(58695*2^243085-1)/11	73180	Lelio R Paula	04/2015
6668	11^70262-98	73171	Lelio R Paula	02/2015
6669	(2^243034+47)/722703303	73152	Lelio R Paula	07/2012
6670	(2^242966+47)/46887	73136	Lelio R Paula	07/2012
6671	(43^44773-1)/42	73134	Robert Price	04/2014
6672	6^93980-158359	73131	Mike Oakes	02/2011
6673	6^93915+53	73081	Lelio R Paula	01/2015
6674	(5*10^73079+211)/9	73079	Robert Price	12/2017
6675	(74*10^73076+43)/9	73077	Robert Price	10/2015
6676	(3^153125+2)/1144955	73054	Lelio R Paula	06/2012
6677	2^242632-112199	73040	Enzo Doria	06/2014
6678	V(351646)	73029	Serge Batalov	03/2015
6679	18^58175-85	73026	Lelio R Paula	01/2015
6680	p(15395)#/2-4	73019	Robert Price	12/2016
6681	(4^121271+3^121271)/7	73012	Jean-Louis Charton	03/2011
6682	8*6^93825-5	73011	Lelio R Paula	10/2014
6683	(F(220)^1601-F(219)^1601)/F(218)	73005	Wayne Halsdorf	08/2013
6684	(73^39181+1)/74	73005	Paul Bourdelais	08/2017
6685	6^93815+143	73003	Lelio R Paula	01/2015
6686	6^93812+5	73000	Wojciech Florek	03/2006
6687	19^57078-62	72989	Lelio R Paula	01/2015
6688	(29*10^72985+91)/3	72986	Robert Price	03/2016
6689	11^70082-2520	72983	Enzo Doria	12/2012
6690	6^93773+133	72970	Lelio R Paula	01/2015
6691	2^242328-59	72948	Lelio R Paula	03/2012
6692	5^104358-13016	72944	Enzo Doria	02/2013
6693	(75*10^72941-57)/99	72941	Ray Chandler	03/2011
6694	12^67585-95	72937	Lelio R Paula	02/2015
6695	2^242230-113285	72919	Enzo Doria	07/2014
6696	(5*10^72916-11)/3	72917	Erik Branger	12/2013
6697	2^242220-110399	72916	Enzo Doria	05/2014
6698	2^242205-113413	72911	Enzo Doria	07/2014
6699	(3^152809+3^76405+1)/7	72908	Serge Batalov	03/2014
6700	2^242175+74243	72902	Yves Minet	03/2011
6701	2^242150+17659	72895	Lelio R Paula	11/2009
6702	11^69982-2340	72879	Enzo Doria	12/2012
6703	(23*2^242093+1)/10117	72875	Lelio R Paula	08/2012
6704	(67607*2^242043+1)/33263	72863	Lelio R Paula	06/2014
6705	2^242032+87	72859	Lelio R Paula	03/2012
6706	2^241968-110595	72840	Enzo Doria	05/2014
6707	(10^72821+71)/9	72821	Robert Price	11/2014
6708	2^241852-64875	72805	Lelio R Paula	05/2013
6709	F(348307)/20562890865908093	72776	Donovan Johnson	07/2007
6710	(67*10^72772+23)/9	72773	Ray Chandler	11/2010
6711	(8*10^72759+67)/3	72760	Robert Price	01/2017
6712	2^241670+145	72750	Lelio R Paula	03/2012
6713	5^104074+52	72745	Lelio R Paula	08/2014
6714	(3^152466-5)/724	72742	Lelio R Paula	06/2012
6715	20^55908-41	72738	Lelio R Paula	01/2015
6716	(73*10^72735+53)/9	72736	Robert Price	10/2015
6717	10^72730+224011	72731	Patrick De Geest	05/2013
6718	10^72730-99	72730	Robert Price	05/2011
6719	3*10^72723+67	72724	Robert Price	11/2017
6720	(11^69833+3^69833)/14	72723	Robert Price	03/2013
6721	(10^72723-79)/3	72723	Robert Price	10/2017
6722	(88*10^72711-43)/9	72712	Robert Price	11/2015
6723	3^152379+280	72704	Lelio R Paula	01/2015
6724	(25*10^72703-241)/9	72704	Robert Price	01/2017
6725	(47*10^72696+133)/9	72697	Robert Price	04/2017
6726	17^59077-90	72692	Lelio R Paula	01/2015
6727	65^40096+58	72691	Lelio R Paula	01/2016
6728	(29*2^241446-1)/245	72682	Lelio R Paula	01/2014
6730	11^69783-38400000	72672	Enzo Doria	01/2013
6729	2^241409-112903	72672	Enzo Doria	06/2014
6731	(3^152287+1)/4	72659	Paul Bourdelais	04/2008
6732	3^152249-56	72642	Lelio R Paula	01/2015
6733	10^72631+37	72632	Robert Price	01/2011
6734	10^72631-8813	72631	Patrick De Geest	05/2013
6735	(19*2^241254+1)/101	72624	Lelio R Paula	08/2012
6736	(9^76103+8^76103)/17	72620	Robert Price	12/2012
6737	2^241220-112337	72615	Enzo Doria	06/2014
6738	(82*10^72612+449)/9	72613	Robert Price	02/2017
6739	2^241169-15793	72600	Enzo Doria	04/2013
6740	9*10^72595+11	72596	Robert Kinser	01/2017
6741	(25*2^241048+1)/89	72563	Lelio R Paula	08/2012
6742	(22*10^72560+17)/3	72561	Robert Price	09/2015
6743	2^241032-23	72558	Lelio R Paula	02/2012
6744	34485*10^72550+2^241004-3	72555	Gilbert Mozzo	12/2012
6745	2^241004-3	72550	M. Frind & P. Underwood	07/2002
6746	97*10^72522-3	72524	Robert Price	01/2017
6747	(68*10^72516+7)/3	72518	Robert Price	03/2016
6748	(78557*2^240844+1)/63	72505	Lelio R Paula	06/2014
6749	67^39701-66	72497	Norbert Schneider	11/2014
6750	(185*10^72484+7)/3	72486	Robert Price	02/2017

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Probable Primes Top 10000

(252675 PRPs in the top)