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 ?
9501	(12113^12113+3627)/2^2/5/19/14496299	49451	Makoto Morimoto	07/2016
9502	5^70746-16016	49450	Enzo Doria	02/2013
9504	(2^164258+9)/13	49446	Lelio R Paula	01/2012
9503	2^164255-112687	49446	Enzo Doria	06/2014
9505	(21*2^164222-1)/1717	49434	Lelio R Paula	01/2014
9506	2^164212+12705	49433	Lelio R Paula	11/2011
9507	3*2^164205+7	49432	Lelio R Paula	02/2014
9508	2^164203+577294575	49431	Lelio R Paula	02/2013
9509	(12109^12109+2534)/3^2/23/24763/781021	49430	Makoto Morimoto	07/2016
9510	Pell-LucasQ(129127)/2	49427	Eric W. Weisstein	05/2006
9511	2^164187+7695	49426	Lelio R Paula	11/2011
9512	3^103585-26	49423	Lelio R Paula	07/2012
9513	(3*2^164194+1)/14255017	49421	Lelio R Paula	07/2012
9514	10^49415+76837	49416	Patrick De Geest	01/2016
9517	10^49415-6^49415-4^49415-1	49415	Mike Oakes	01/2010
9515	10^49415-32813	49415	Patrick De Geest	01/2016
9516	12943^6574+6574^12943	49415	Hans Havermann	02/2016
9518	(6^63497-61)/25	49409	Lelio R Paula	05/2014
9519	11376^12181+12181^11376	49407	Norbert Schneider	12/2013
9520	2^164110-17	49403	Lelio R Paula	08/2010
9521	12^45773+41	49398	Lelio R Paula	10/2012
9522	2^164090+4257	49397	Lelio R Paula	04/2009
9523	(12101^12101+1403)/2^4/193/349/160231/6927689	49389	Makoto Morimoto	07/2016
9524	2^164061-3889	49388	Yves Minet	04/2017
9525	2^164046+25	49383	Lelio R Paula	01/2009
9526	(24737*2^164045+1)/5906585	49381	Lelio R Paula	05/2014
9527	(12097^12097+1922)/3/139/2253409	49380	Makoto Morimoto	07/2016
9528	5^70640-18296	49376	Enzo Doria	02/2013
9529	(9179*2^164010-1)/5	49376	Lelio R Paula	03/2015
9530	(-lucasV(1,2,328052)+2)/108961	49372	Mike Oakes	02/2017
9531	9*2^164002-7	49371	Lelio R Paula	02/2014
9532	5^70626-44	49366	Lelio R Paula	06/2012
9533	11^47396-1050	49358	Enzo Doria	11/2012
9534	(13*2^163956+1)/7	49356	Lelio R Paula	07/2012
9536	2^163934-135	49350	Lelio R Paula	01/2011
9535	3^103431+20	49350	Lelio R Paula	07/2012
9537	7192^12795-12795^7192	49349	Norbert Schneider	03/2017
9538	13^44300+22	49348	Lelio R Paula	11/2012
9539	(2^163904+3)/7	49340	Lelio R Paula	01/2012
9540	2^163872+12915	49331	Lelio R Paula	11/2011
9541	130^23332-129	49323	Norbert Schneider	03/2015
9542	7^58357-38	49318	Lelio R Paula	06/2012
9543	7760^12677-12677^7760	49312	Norbert Schneider	01/2017
9544	13^44265-2	49309	Lelio R Paula	11/2012
9546	(19*2^163785+1)/2043	49303	Lelio R Paula	01/2012
9545	2^163781-1741	49303	Yves Minet	09/2012
9547	4*5^70529+3	49299	Lelio R Paula	09/2014
9548	(2^163742-3)/131	49290	Lelio R Paula	01/2012
9549	5^70514-17216	49288	Enzo Doria	02/2013
9550	2^163727-1741	49287	Yves Minet	09/2012
9551	Linear(0,1,1,-1,327433)	49283	Henri Lifchitz	04/2007
9552	5^70498-17576	49276	Enzo Doria	02/2013
9553	(12073^12073+1070)/3/13/31063	49274	Makoto Morimoto	07/2016
9554	2^163667+72113	49269	Enzo Doria	04/2016
9555	5^70484-17696	49267	Enzo Doria	02/2013
9556	(12071^12071+4263)/2/101/11489	49265	Makoto Morimoto	07/2016
9557	7^58293+66	49264	Lelio R Paula	06/2012
9558	(52*10^49261-1)/3	49263	Robert Price	02/2017
9559	2671^14376-114	49262	Enzo Doria	06/2012
9560	(15185*2^163636-1)/209	49262	Lelio R Paula	03/2015
9561	2^163630+183	49258	Lelio R Paula	01/2011
9562	2^163560+15	49237	Lelio R Paula	08/2010
9564	3^103189+110	49234	Lelio R Paula	07/2012
9563	(41*10^49233+31)/9	49234	Erik Branger	05/2013
9565	(1023052^8192+1)/65537	49229	Syoichiro Yamada	05/2008
9566	2*10^49216+93	49217	Robert Price	07/2016
9567	(107^24251-1)/106	49213	Richard Fischer	07/2017
9568	2^163453+885	49205	Lelio R Paula	10/2011
9569	(67607*2^163432+1)/3	49203	Lelio R Paula	05/2014
9570	15^41835-46	49202	Lelio R Paula	11/2012
9571	10^49190+45507	49191	Patrick De Geest	01/2016
9573	10^49190-6018659	49190	Marisa Kirisame	02/2015
9572	10^49190-154431	49190	Patrick De Geest	01/2016
9574	2^163385+94395	49184	Henri Lifchitz	01/2005
9575	2^163382-2021	49183	Yves Minet	03/2013
9577	(55*10^49169-1)/9	49170	Ray Chandler	02/2012
9576	2^163336-15177	49170	Enzo Doria	04/2013
9578	8323^12542-12542^8323	49169	Norbert Schneider	11/2016
9579	(10^49165-991)/9	49165	Serge Batalov	07/2010
9580	7^58169-6^(58169+1)	49159	Robert Price	06/2016
9581	(F(5)^70327-F(4)^70327)/F(3)	49157	Wayne Halsdorf	01/2010
9582	(5^70327-3^70327)/2	49157	Robert Price	08/2011
9583	2^163283+54615	49154	Lelio R Paula	04/2009
9584	18388^471+471^18388	49152	Anatoly F. Selevich	12/2006
9585	(782*10^49148-71)/9	49150	Robert Price	06/2017
9586	(12043^12043+799)/2/157	49142	Makoto Morimoto	07/2016
9587	14^42875+69	49141	Lelio R Paula	11/2012
9588	(2^163243+9)/17	49140	Lelio R Paula	01/2012
9589	(F(770)^307-F(769)^307)/F(768)	49136	Wayne Halsdorf	02/2010
9590	(12041^12041+467)/2^2/23/47	49132	Makoto Morimoto	07/2016
9591	5^70290-19446	49131	Enzo Doria	03/2013
9592	(F(760)^311-F(759)^311)/F(758)	49130	Wayne Halsdorf	02/2010
9593	5^70286-20046	49128	Enzo Doria	03/2013
9594	12^45519-91	49124	Lelio R Paula	10/2012
9595	7^58126+72	49123	Lelio R Paula	06/2012
9596	7^58125+4	49122	Lelio R Paula	06/2012
9597	(991537^8192+1)/2	49122	Lelio R Paula	12/2014
9598	(14*10^49119-11)/3	49120	Erik Branger	05/2013
9599	t(185595)	49118	Robert Price	12/2013
9600	(2*10^49117+457)/9	49117	Robert Price	01/2017
9601	(988635^8192+1)/2	49112	Lelio R Paula	12/2014
9602	(26*10^49106-23)/3	49107	Robert Price	08/2016
9603	(986617^8192+1)/2	49104	Lelio R Paula	12/2014
9604	14313^2696+2696^14313	49104	Hans Havermann	08/2015
9605	(89*10^49101-53)/9	49102	Erik Branger	05/2013
9606	9*7^58099-4	49101	Lelio R Paula	09/2014
9607	(-lucasV(1,2,326291)+2)/(5835637935289)	49100	Mike Oakes	02/2017
9608	23^36054-1050	49096	Enzo Doria	08/2012
9609	(984325^8192+1)/131074	49091	Lelio R Paula	12/2014
9610	(3^51443-87)^2-89	49090	Jorge Menendez	02/2017
9611	9286492((10^49081-1)/9)+1	49087	Danilo Nitsche	01/2016
9612	5922712((10^49081-1)/9)+1	49087	Danilo Nitsche	01/2016
9613	5800432((10^49081-1)/9)+1	49087	Danilo Nitsche	01/2016
9614	5555002((10^49081-1)/9)+1	49087	Danilo Nitsche	01/2016
9615	5126512((10^49081-1)/9)+1	49087	Danilo Nitsche	01/2016
9616	1433582((10^49081-1)/9)+1	49086	Danilo Nitsche	01/2016
9617	1074452((10^49081-1)/9)+1	49086	Danilo Nitsche	01/2016
9618	1173602((10^49081-1)/9)+1	49086	Danilo Nitsche	01/2016
9619	281242((10^49081-1)/9)+1	49085	Danilo Nitsche	01/2016
9620	18^39100-29	49082	Lelio R Paula	11/2012
9621	(10^49081-1)/9	49081	Harvey Dubner	09/1999
9622	(978811^8192+1)/2	49076	Lelio R Paula	12/2014
9623	17200^713+713^17200	49074	Anatoly F. Selevich	07/2006
9624	9*2^163006+5	49071	Lelio R Paula	02/2014
9625	11^47113-1710	49064	Enzo Doria	11/2012
9626	11^47106-1410	49056	Enzo Doria	11/2012
9627	2^162954-23	49055	Lelio R Paula	08/2010
9628	2^162924-28635	49046	Lelio R Paula	04/2009
9629	24771!2-8	49045	Robert Price	06/2015
9630	(26*10^49039-77)/3	49040	Robert Price	02/2017
9631	5^70155-4	49037	Theodore Burton	11/2005
9632	3^102763-14	49031	Lelio R Paula	06/2012
9633	(21*2^162876+1)/23	49031	Lelio R Paula	07/2012
9634	5^70146+58	49030	Lelio R Paula	06/2012
9635	2^162864-744389	49027	Paul Bourdelais	11/2012
9636	2^162860-112859	49026	Enzo Doria	06/2014
9637	(10^49025-1)/3-2*10^24512	49025	Patrick De Geest	07/2005
9638	2^162856-229209	49025	Enzo Doria	01/2013
9639	(10^(224512+1)-610^24512-1)/3	49025	Robert Price	02/2016
9640	(965897^8192+1)/327682	49024	Lelio R Paula	12/2014
9641	(5*2^162859-1)/53919	49022	Lelio R Paula	01/2014
9642	6^62990+31	49016	Lelio R Paula	06/2012
9643	46329!4+2	49014	Robert Price	03/2017
9644	2^162816-219209	49013	Enzo Doria	11/2012
9645	(127^23297-1)/126	49011	Alexander Zhirkov	10/2010
9646	(13^43997+12^43997)/25	49009	Robert Price	04/2013
9647	10^49008+66669	49009	Patrick De Geest	01/2016
9648	10^49008-5037	49008	Robert Price	09/2015
9649	5^70110+52	49005	Lelio R Paula	06/2012
9650	10^49000+213037	49001	Patrick De Geest	07/2012
9651	15^41664-94	49001	Lelio R Paula	11/2012
9652	3^102699-340	49000	Lelio R Paula	06/2012
9653	10^49000-621	49000	Patrick De Geest	07/2012
9654	10^48999+268791	49000	Patrick De Geest	07/2012
9655	10^48999-74639	48999	Patrick De Geest	07/2012
9656	(21181*2^162764+1)/65583709	48994	Lelio R Paula	05/2014
9657	1033^16254+16254^1033	48992	Serge Batalov	05/2014
9658	8602^12451+12451^8602	48990	Norbert Schneider	07/2014
9659	12^45385+5	48979	Lelio R Paula	10/2012
9660	(951919^8192+1)/2	48977	Lelio R Paula	12/2014
9661	(12007^12007+2128)/37/11801	48977	Makoto Morimoto	07/2016
9662	2^162669-1795	48969	Lelio R Paula	01/2009
9663	2^162668-112757	48968	Enzo Doria	06/2014
9664	13527^4168+4168^13527	48967	Hans Havermann	04/2016
9665	(6883*2^162649-1)/5	48966	Lelio R Paula	03/2015
9666	(944123^8192+1)/2	48948	Lelio R Paula	12/2014
9667	(229*10^48944-1)/3	48946	Robert Price	12/2016
9668	2003^14821-102	48935	Enzo Doria	06/2012
9669	7^57901+82	48933	Lelio R Paula	06/2012
9670	t(166683)	48933	Robert Price	10/2014
9671	11^46985-18	48930	Lelio R Paula	10/2012
9672	2^162521+98765331	48924	Jason Earls	12/2008
9673	V(380406)	48914	Serge Batalov	03/2015
9674	2^162482+65835	48912	Lelio R Paula	10/2011
9675	12^45317+7	48906	Lelio R Paula	10/2012
9676	(4^81223+3^81223)/7	48901	Jean-Louis Charton	03/2011
9677	(2^162474-5)/1353094831	48901	Lelio R Paula	01/2012
9678	3^102477+2660	48894	Lelio R Paula	07/2012
9679	2^162412+29835	48891	Lelio R Paula	10/2011
9680	9*6^62820+7	48885	Lelio R Paula	09/2014
9681	(169^21943+1)/170	48885	Richard Fischer	11/2015
9682	(11987^11987+3067)/2/3/5^2/11/13/2857	48884	Makoto Morimoto	07/2016
9683	13^43881-50	48881	Lelio R Paula	11/2012
9684	8173^12492-12492^8173	48874	Norbert Schneider	05/2013
9685	20^37563-1363	48871	Enzo Doria	03/2013
9686	(923522^8192+1)/114689	48864	Lelio R Paula	11/2014
9687	13137^5242+5242^13137	48864	Hans Havermann	04/2016
9688	15^41545+92	48861	Lelio R Paula	11/2012
9689	(11981^11981+632)/97/1709	48860	Makoto Morimoto	07/2016
9690	(919695^8192+1)/131074	48850	Lelio R Paula	12/2014
9691	(917697^8192+1)/2	48847	Lelio R Paula	12/2014
9692	(12^45259-5^45259)/7	48842	Robert Price	03/2013
9693	9*5^69862+8	48833	Lelio R Paula	09/2014
9694	12^45244-95	48827	Lelio R Paula	10/2012
9695	(29*2^162182-1)/5	48823	Lelio R Paula	01/2014
9696	(2^162167-3)6+10^4881813803-7	48823	Gilbert Mozzo	11/2016
9697	(2^162167-3)*6-7	48818	Gilbert Mozzo	03/2016
9698	7*10^48816-69	48817	Robert Price	01/2017
9699	(11971^11971+3180)/103/7577	48814	Makoto Morimoto	07/2016
9700	2^162143-51	48810	Lelio R Paula	08/2010
9702	2^162136-284519	48808	Gary Barnes	08/2009
9701	5^69828-15386	48808	Enzo Doria	02/2013
9703	5^69826-3*4^69826	48807	Mike Oakes	02/2010
9704	2^162123+74063	48804	Enzo Doria	04/2016
9705	21001^11289-104	48794	Enzo Doria	07/2012
9706	5^69802-32	48790	Lelio R Paula	05/2012
9707	(902939^8192+1)/2	48789	Lelio R Paula	12/2014
9708	(2^162059+78557)/35	48784	Lelio R Paula	05/2012
9709	(900239^8192+1)/2	48778	Lelio R Paula	12/2014
9710	138^22794-137	48777	Norbert Schneider	10/2015
9711	2^162033+76757	48777	Enzo Doria	05/2016
9712	18^38850-37	48768	Lelio R Paula	11/2012
9713	(898286^8192+1)/786433	48765	Lelio R Paula	11/2014
9714	68^26610+67	48764	Norbert Schneider	10/2012
9715	2^161987+15015	48763	Lelio R Paula	10/2011
9716	(11959^11959+6523)/2/5581	48762	Makoto Morimoto	07/2016
9717	3^102198-86	48761	Lelio R Paula	06/2012
9718	(13224!+1)/221497	48755	Donovan Johnson	04/2006
9719	18^38838-13	48753	Lelio R Paula	11/2012
9720	161923*2^161923+161923+2	48749	Robert Price	05/2016
9721	(892493^8192+1)/131074	48743	Lelio R Paula	12/2014
9722	(11953^11953+133)/2/46861	48734	Makoto Morimoto	06/2016
9723	2^161881-14941	48732	Enzo Doria	04/2013
9724	(888215^8192+1)/2	48730	Lelio R Paula	12/2014
9725	-lucasV(1,2,323749)-2	48730	Mike Oakes	02/2017
9726	10268^12147+12147^10268	48728	Norbert Schneider	11/2013
9727	(26*10^48726-11)/3	48727	Erik Branger	05/2013
9728	3*6^62618-7	48727	Lelio R Paula	09/2014
9730	2^161857-45	48724	Lelio R Paula	08/2010
9729	(889160^8192+1)/73283633153	48724	Lelio R Paula	11/2014
9731	2^161837+467	48718	Lelio R Paula	11/2007
9732	3^102102+10	48716	Lelio R Paula	01/2007
9733	2^161806-8295	48709	Lelio R Paula	04/2009
9734	(25*2^161811-1)/457	48709	Lelio R Paula	01/2014
9735	13311^4558+4558^13311	48702	Hans Havermann	05/2016
9736	24^35284-457	48700	Enzo Doria	03/2013
9737	3^102058+8680	48695	Lelio R Paula	06/2012
9738	13537^3948+3948^13537	48685	Hans Havermann	05/2016
9739	(11941^11941+6414)/5	48684	Makoto Morimoto	07/2016
9740	2^161719-15097	48683	Enzo Doria	04/2013
9741	(41*10^48678+373)/9	48679	Robert Price	04/2017
9742	3*10^48668-7^48668	48669	Mike Oakes	01/2010
9743	13201!+13201!2+13201#-2	48666	Joe McLean	10/2007
9744	2*3^101994-5	48664	Lelio R Paula	03/2014
9745	(11939^11939+2801)/2^2/5/19/307/2210473	48664	Makoto Morimoto	07/2016
9746	11933^11933+1316	48648	Makoto Morimoto	07/2016
9747	(-lucasV(1,2,323096)+2)/(3*193)	48629	Mike Oakes	02/2017
9748	(lucasV(1,2,323208)-2)/(3^3571137173320111660317957*80803)	48622	Mike Oakes	02/2017
9749	95^24584+94	48621	Norbert Schneider	05/2013
9750	(11927^11927+2091)/2/2273/62683	48613	Makoto Morimoto	07/2016

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