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	7^58126+72	49123	Lelio R Paula	06/2012
9502	7^58125+4	49122	Lelio R Paula	06/2012
9503	(991537^8192+1)/2	49122	Lelio R Paula	12/2014
9504	(14*10^49119-11)/3	49120	Erik Branger	05/2013
9505	t(185595)	49118	Robert Price	12/2013
9506	(2*10^49117+457)/9	49117	Robert Price	01/2017
9507	(988635^8192+1)/2	49112	Lelio R Paula	12/2014
9508	(26*10^49106-23)/3	49107	Robert Price	08/2016
9509	(986617^8192+1)/2	49104	Lelio R Paula	12/2014
9510	14313^2696+2696^14313	49104	Hans Havermann	08/2015
9511	(89*10^49101-53)/9	49102	Erik Branger	05/2013
9512	9*7^58099-4	49101	Lelio R Paula	09/2014
9513	(-lucasV(1,2,326291)+2)/(5835637935289)	49100	Mike Oakes	02/2017
9514	23^36054-1050	49096	Enzo Doria	08/2012
9515	(984325^8192+1)/131074	49091	Lelio R Paula	12/2014
9516	(3^51443-87)^2-89	49090	Jorge Menendez	02/2017
9517	9286492((10^49081-1)/9)+1	49087	Danilo Nitsche	01/2016
9518	5922712((10^49081-1)/9)+1	49087	Danilo Nitsche	01/2016
9519	5800432((10^49081-1)/9)+1	49087	Danilo Nitsche	01/2016
9520	5555002((10^49081-1)/9)+1	49087	Danilo Nitsche	01/2016
9521	5126512((10^49081-1)/9)+1	49087	Danilo Nitsche	01/2016
9522	1433582((10^49081-1)/9)+1	49086	Danilo Nitsche	01/2016
9523	1074452((10^49081-1)/9)+1	49086	Danilo Nitsche	01/2016
9524	1173602((10^49081-1)/9)+1	49086	Danilo Nitsche	01/2016
9525	281242((10^49081-1)/9)+1	49085	Danilo Nitsche	01/2016
9526	18^39100-29	49082	Lelio R Paula	11/2012
9527	(10^49081-1)/9	49081	Harvey Dubner	09/1999
9528	(978811^8192+1)/2	49076	Lelio R Paula	12/2014
9529	17200^713+713^17200	49074	Anatoly F. Selevich	07/2006
9530	9*2^163006+5	49071	Lelio R Paula	02/2014
9531	11^47113-1710	49064	Enzo Doria	11/2012
9532	11^47106-1410	49056	Enzo Doria	11/2012
9533	2^162954-23	49055	Lelio R Paula	08/2010
9534	2^162924-28635	49046	Lelio R Paula	04/2009
9535	24771!2-8	49045	Robert Price	06/2015
9536	(26*10^49039-77)/3	49040	Robert Price	02/2017
9537	5^70155-4	49037	Theodore Burton	11/2005
9538	3^102763-14	49031	Lelio R Paula	06/2012
9539	(21*2^162876+1)/23	49031	Lelio R Paula	07/2012
9540	5^70146+58	49030	Lelio R Paula	06/2012
9541	2^162864-744389	49027	Paul Bourdelais	11/2012
9542	2^162860-112859	49026	Enzo Doria	06/2014
9543	(10^49025-1)/3-2*10^24512	49025	Patrick De Geest	07/2005
9544	2^162856-229209	49025	Enzo Doria	01/2013
9545	(10^(224512+1)-610^24512-1)/3	49025	Robert Price	02/2016
9546	(965897^8192+1)/327682	49024	Lelio R Paula	12/2014
9547	(5*2^162859-1)/53919	49022	Lelio R Paula	01/2014
9548	6^62990+31	49016	Lelio R Paula	06/2012
9549	46329!4+2	49014	Robert Price	03/2017
9550	2^162816-219209	49013	Enzo Doria	11/2012
9551	(127^23297-1)/126	49011	Alexander Zhirkov	10/2010
9552	(13^43997+12^43997)/25	49009	Robert Price	04/2013
9553	10^49008+66669	49009	Patrick De Geest	01/2016
9554	10^49008-5037	49008	Robert Price	09/2015
9555	5^70110+52	49005	Lelio R Paula	06/2012
9556	10^49000+213037	49001	Patrick De Geest	07/2012
9557	15^41664-94	49001	Lelio R Paula	11/2012
9558	3^102699-340	49000	Lelio R Paula	06/2012
9559	10^49000-621	49000	Patrick De Geest	07/2012
9560	10^48999+268791	49000	Patrick De Geest	07/2012
9561	10^48999-74639	48999	Patrick De Geest	07/2012
9562	(21181*2^162764+1)/65583709	48994	Lelio R Paula	05/2014
9563	1033^16254+16254^1033	48992	Serge Batalov	05/2014
9564	8602^12451+12451^8602	48990	Norbert Schneider	07/2014
9565	12^45385+5	48979	Lelio R Paula	10/2012
9566	(951919^8192+1)/2	48977	Lelio R Paula	12/2014
9567	(12007^12007+2128)/37/11801	48977	Makoto Morimoto	07/2016
9568	2^162669-1795	48969	Lelio R Paula	01/2009
9569	2^162668-112757	48968	Enzo Doria	06/2014
9570	13527^4168+4168^13527	48967	Hans Havermann	04/2016
9571	(6883*2^162649-1)/5	48966	Lelio R Paula	03/2015
9572	(944123^8192+1)/2	48948	Lelio R Paula	12/2014
9573	(229*10^48944-1)/3	48946	Robert Price	12/2016
9574	2003^14821-102	48935	Enzo Doria	06/2012
9575	7^57901+82	48933	Lelio R Paula	06/2012
9576	t(166683)	48933	Robert Price	10/2014
9577	11^46985-18	48930	Lelio R Paula	10/2012
9578	2^162521+98765331	48924	Jason Earls	12/2008
9579	V(380406)	48914	Serge Batalov	03/2015
9580	2^162482+65835	48912	Lelio R Paula	10/2011
9581	12^45317+7	48906	Lelio R Paula	10/2012
9582	(4^81223+3^81223)/7	48901	Jean-Louis Charton	03/2011
9583	(2^162474-5)/1353094831	48901	Lelio R Paula	01/2012
9584	3^102477+2660	48894	Lelio R Paula	07/2012
9585	2^162412+29835	48891	Lelio R Paula	10/2011
9586	9*6^62820+7	48885	Lelio R Paula	09/2014
9587	(169^21943+1)/170	48885	Richard Fischer	11/2015
9588	(11987^11987+3067)/2/3/5^2/11/13/2857	48884	Makoto Morimoto	07/2016
9589	13^43881-50	48881	Lelio R Paula	11/2012
9590	8173^12492-12492^8173	48874	Norbert Schneider	05/2013
9591	20^37563-1363	48871	Enzo Doria	03/2013
9593	(923522^8192+1)/114689	48864	Lelio R Paula	11/2014
9592	13137^5242+5242^13137	48864	Hans Havermann	04/2016
9594	15^41545+92	48861	Lelio R Paula	11/2012
9595	(11981^11981+632)/97/1709	48860	Makoto Morimoto	07/2016
9596	(919695^8192+1)/131074	48850	Lelio R Paula	12/2014
9597	(917697^8192+1)/2	48847	Lelio R Paula	12/2014
9598	(12^45259-5^45259)/7	48842	Robert Price	03/2013
9599	9*5^69862+8	48833	Lelio R Paula	09/2014
9600	12^45244-95	48827	Lelio R Paula	10/2012
9601	(29*2^162182-1)/5	48823	Lelio R Paula	01/2014
9602	(2^162167-3)6+10^4881813803-7	48823	Gilbert Mozzo	11/2016
9603	(2^162167-3)*6-7	48818	Gilbert Mozzo	03/2016
9604	7*10^48816-69	48817	Robert Price	01/2017
9605	(11971^11971+3180)/103/7577	48814	Makoto Morimoto	07/2016
9606	2^162143-51	48810	Lelio R Paula	08/2010
9607	2^162136-284519	48808	Gary Barnes	08/2009
9608	5^69828-15386	48808	Enzo Doria	02/2013
9609	5^69826-3*4^69826	48807	Mike Oakes	02/2010
9610	2^162123+74063	48804	Enzo Doria	04/2016
9611	21001^11289-104	48794	Enzo Doria	07/2012
9612	5^69802-32	48790	Lelio R Paula	05/2012
9613	(902939^8192+1)/2	48789	Lelio R Paula	12/2014
9614	(2^162059+78557)/35	48784	Lelio R Paula	05/2012
9615	(900239^8192+1)/2	48778	Lelio R Paula	12/2014
9616	138^22794-137	48777	Norbert Schneider	10/2015
9617	2^162033+76757	48777	Enzo Doria	05/2016
9618	18^38850-37	48768	Lelio R Paula	11/2012
9619	(898286^8192+1)/786433	48765	Lelio R Paula	11/2014
9620	68^26610+67	48764	Norbert Schneider	10/2012
9621	2^161987+15015	48763	Lelio R Paula	10/2011
9622	(11959^11959+6523)/2/5581	48762	Makoto Morimoto	07/2016
9623	3^102198-86	48761	Lelio R Paula	06/2012
9624	(13224!+1)/221497	48755	Donovan Johnson	04/2006
9625	18^38838-13	48753	Lelio R Paula	11/2012
9626	161923*2^161923+161923+2	48749	Robert Price	05/2016
9627	(892493^8192+1)/131074	48743	Lelio R Paula	12/2014
9628	(11953^11953+133)/2/46861	48734	Makoto Morimoto	06/2016
9629	2^161881-14941	48732	Enzo Doria	04/2013
9631	(888215^8192+1)/2	48730	Lelio R Paula	12/2014
9630	-lucasV(1,2,323749)-2	48730	Mike Oakes	02/2017
9632	10268^12147+12147^10268	48728	Norbert Schneider	11/2013
9634	(26*10^48726-11)/3	48727	Erik Branger	05/2013
9633	3*6^62618-7	48727	Lelio R Paula	09/2014
9636	2^161857-45	48724	Lelio R Paula	08/2010
9635	(889160^8192+1)/73283633153	48724	Lelio R Paula	11/2014
9637	2^161837+467	48718	Lelio R Paula	11/2007
9638	3^102102+10	48716	Lelio R Paula	01/2007
9639	2^161806-8295	48709	Lelio R Paula	04/2009
9640	(25*2^161811-1)/457	48709	Lelio R Paula	01/2014
9641	13311^4558+4558^13311	48702	Hans Havermann	05/2016
9642	24^35284-457	48700	Enzo Doria	03/2013
9643	3^102058+8680	48695	Lelio R Paula	06/2012
9644	13537^3948+3948^13537	48685	Hans Havermann	05/2016
9645	(11941^11941+6414)/5	48684	Makoto Morimoto	07/2016
9646	2^161719-15097	48683	Enzo Doria	04/2013
9647	(41*10^48678+373)/9	48679	Robert Price	04/2017
9648	3*10^48668-7^48668	48669	Mike Oakes	01/2010
9649	13201!+13201!2+13201#-2	48666	Joe McLean	10/2007
9650	2*3^101994-5	48664	Lelio R Paula	03/2014
9651	(11939^11939+2801)/2^2/5/19/307/2210473	48664	Makoto Morimoto	07/2016
9652	11933^11933+1316	48648	Makoto Morimoto	07/2016
9653	(-lucasV(1,2,323096)+2)/(3*193)	48629	Mike Oakes	02/2017
9654	(lucasV(1,2,323208)-2)/(3^3571137173320111660317957*80803)	48622	Mike Oakes	02/2017
9655	95^24584+94	48621	Norbert Schneider	05/2013
9656	(11927^11927+2091)/2/2273/62683	48613	Makoto Morimoto	07/2016
9657	(10^48604-31)/3	48604	Serge Batalov	12/2014
9658	Phi(11923,11925)	48600	Henri Lifchitz	11/2003
9659	(11923^11923+3199)/2/42649	48598	Makoto Morimoto	07/2016
9660	75^25915-2	48593	Lelio R Paula	08/2013
9661	3^101816-104	48579	Lelio R Paula	07/2012
9663	(852175^8192+1)/327682	48578	Lelio R Paula	12/2014
9662	numbpart(61681*61682/2)	48578	Serge Batalov	04/2017
9664	132^22904+131	48570	Norbert Schneider	03/2015
9665	2^161333-114871	48567	Enzo Doria	05/2015
9666	13889^3138+3138^13889	48566	Hans Havermann	05/2016
9667	13174^4857+4857^13174	48565	Hans Havermann	05/2016
9669	2^161326+7969	48564	Yves Minet	02/2010
9668	(2^161330-5)/29	48564	Lelio R Paula	01/2012
9670	(848412^8192+1)/786433	48562	Lelio R Paula	11/2014
9671	(847181^8192+1)/2	48562	Lelio R Paula	12/2014
9672	4*10^48548+79	48549	Robert Price	01/2017
9674	(13*10^48547+11)/3	48548	Erik Branger	05/2013
9673	(9913*2^161263-1)/17	48548	Lelio R Paula	03/2015
9675	2^161258+63439	48544	Yves Minet	11/2010
9676	2^161238-459491	48538	Enzo Doria	05/2015
9677	(11909^11909+305)/2/157771	48535	Makoto Morimoto	07/2016
9678	2^161226+66615	48534	Lelio R Paula	12/2008
9679	2^161205-5955	48528	Lelio R Paula	04/2009
9680	10^48526+13	48527	Jason Earls	02/2008
9681	10^48526-41441	48526	Patrick De Geest	06/2009
9682	2^161199-14569	48526	Enzo Doria	04/2013
9683	9*2^161190-7	48524	Lelio R Paula	02/2014
9684	(3^101708+7)/53384	48523	Lelio R Paula	03/2012
9685	(2^161187+78557)/236155	48517	Lelio R Paula	05/2012
9686	(19*2^161174-1)/5685	48516	Lelio R Paula	01/2014
9687	(835525^8192+1)/2	48513	Lelio R Paula	12/2014
9688	20^37287-61	48512	Lelio R Paula	11/2012
9689	2^161143-14089	48509	Enzo Doria	04/2013
9690	(11903^11903+3950)/7/563	48509	Makoto Morimoto	07/2016
9691	(8*10^48507+49)/3	48508	Robert Price	03/2016
9692	2^161106-246581	48498	Gary Barnes	08/2009
9693	2^161098+18915	48496	Lelio R Paula	10/2011
9694	(832081^8192+1)/1474562	48492	Lelio R Paula	12/2014
9695	8*10^48490+21	48491	Robert Price	02/2017
9696	7^57369+22	48483	Lelio R Paula	06/2012
9697	3^101615+2660	48483	Lelio R Paula	06/2012
9698	(11897^11897+3419)/2^2/593	48483	Makoto Morimoto	07/2016
9699	7337^12542-12542^7337	48482	Norbert Schneider	11/2016
9700	(828754^8192+1)/638977	48478	Lelio R Paula	11/2014
9701	(265*10^48474+11)/3	48476	Robert Price	03/2017
9702	13260^4523+4523^13260	48471	Hans Havermann	05/2016
9703	2^161003-113059	48467	Enzo Doria	07/2014
9704	(73*10^48461+53)/9	48462	Erik Branger	05/2013
9705	(822278^8192+1)/65537	48452	Syoichiro Yamada	05/2008
9706	10^48449+112501	48450	Patrick De Geest	05/2007
9707	10^48449-48449	48449	Henri Lifchitz	07/2002
9708	10^48442+57	48443	Robert Price	01/2011
9709	2^160922-869688105	48443	Lelio R Paula	10/2011
9710	10^48442-33533	48442	Patrick De Geest	01/2012
9711	5101^13065-110	48441	Enzo Doria	07/2012
9712	(818917^8192+1)/2	48441	Lelio R Paula	12/2014
9713	(11887^11887+7018)/19/31/327319	48433	Makoto Morimoto	07/2016
9714	2^160883+76763	48431	Enzo Doria	05/2016
9715	2^160873+18915	48428	Lelio R Paula	10/2011
9716	13206^4645+4645^13206	48427	Hans Havermann	04/2016
9717	10^48420+6139	48421	Patrick De Geest	05/2016
9718	10^48420-2*10^1592-1	48420	Serge Batalov	01/2015
9719	10^48420-29273	48420	Patrick De Geest	03/2016
9721	2^160822-2163	48413	Yves Minet	08/2013
9720	(lucasV(1,2,321685)+2)/(571*911)	48413	Mike Oakes	02/2017
9723	10^48410+9^(48410-1)	48411	Robert Price	03/2016
9722	10^48410+90163	48411	Patrick De Geest	12/2016
9725	(3^101473+4)/264481	48410	Lelio R Paula	03/2012
9726	9*2^160811+7	48410	Lelio R Paula	02/2014
9724	10^48410-3287	48410	Patrick De Geest	12/2016
9727	(22699*2^160806+1)/1573	48409	Lelio R Paula	05/2014
9728	3*7^57278-8	48407	Lelio R Paula	09/2014
9729	2^160789-113215	48403	Enzo Doria	07/2014
9730	6900^12607-12607^6900	48397	Norbert Schneider	12/2016
9731	3^101404+2	48383	Mike Oakes	11/2009
9732	3^101395-110	48378	Lelio R Paula	06/2012
9733	2^160701+191	48376	Lelio R Paula	01/2011
9734	6*F(231436)+1	48368	Gilbert Mozzo	06/2015
9735	2^160654-15	48362	Lelio R Paula	08/2010
9736	20^37167+53	48356	Lelio R Paula	11/2012
9737	(799247^8192+1)/2	48355	Lelio R Paula	12/2014
9738	(238*10^48352-1)/3	48354	Robert Price	05/2016
9739	18661^390+390^18661	48352	Anatoly F. Selevich	01/2007
9740	21^36566+2	48349	Ray Chandler	08/2011
9741	7^57208-92	48347	Lelio R Paula	06/2012
9743	5^69165-2^69166	48345	Mike Oakes	10/2010
9742	(11867^11867+2981)/2^3/111341	48345	Makoto Morimoto	07/2016
9744	(3^101331-4)/4679	48344	Lelio R Paula	03/2012
9745	13^43396-24	48341	Lelio R Paula	10/2012
9747	Phi(85113,10)/170227/340453/2080331947/20239360723/577232068985083	48339	Serge Batalov	06/2011
9746	7*2^160574-9	48339	Lelio R Paula	02/2014
9748	lucasU(42,1,29781)+lucasU(42,1,29780)	48334	Mike Oakes	04/2009
9749	3^101296-19318	48331	Enzo Doria	02/2013
9750	(lucasV(1,2,321119)+2)/(5*53)	48331	Mike Oakes	01/2017

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