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 ?
9751	(2^212131-3)/485	63856	Lelio R Paula	04/2012
9752	2^212112-459995	63853	Enzo Doria	06/2015
9753	15^54290+58	63850	Lelio R Paula	05/2013
9754	3*2^212097-7	63849	Lelio R Paula	04/2014
9755	55^36683-54	63842	Norbert Schneider	08/2014
9756	(509203*2^212056-1)/3	63841	Lelio R Paula	04/2015
9757	(3^133805-7)/172	63839	Lelio R Paula	04/2012
9758	(2^212053+2414)/2	63835	Stefano Morozzi	12/2019
9759	2^212049+149	63834	Lelio R Paula	08/2011
9760	5^91318-18	63829	Lelio R Paula	04/2013
9761	18468^2857+2857^18468	63824	Hans Havermann	03/2017
9762	(2^212024-5)/1111	63823	Lelio R Paula	04/2012
9763	2^211961+12915	63807	Lelio R Paula	02/2013
9764	13046^15503-15503^13046	63803	Norbert Schneider	09/2019
9766	(3^133707-7)/5780	63791	Lelio R Paula	04/2012
9765	(44*10^63790-161)/9	63791	Robert Price	11/2017
9767	(2^211902+2490)/2	63789	Stefano Morozzi	12/2019
9768	747^22198+22198^747	63782	Norbert Schneider	07/2016
9769	11820^15659-15659^11820	63774	Norbert Schneider	01/2020
9771	2^211800-17169	63759	Enzo Doria	05/2013
9770	(85*10^63757-1)/3	63759	Robert Price	07/2017
9772	85089!6-8	63757	Robert Price	08/2018
9773	(14*10^63747-11)/3	63748	Erik Branger	09/2014
9774	91*19^49848+6	63746	Curtis Bright	05/2015
9775	18855^2402+2402^18855	63741	Hans Havermann	03/2017
9776	(142*10^63734-7)/9	63736	Robert Price	02/2017
9777	2^211699-111	63728	Lelio R Paula	08/2011
9778	11^61192-5550	63725	Enzo Doria	01/2013
9779	(11*10^63718+7)/9	63719	Serge Batalov	06/2011
9780	6^81872-13	63709	Lelio R Paula	04/2013
9781	3^133522+98	63707	Lelio R Paula	05/2013
9783	2^211607-61	63701	Lelio R Paula	08/2011
9782	5^91135+8	63701	Lelio R Paula	04/2013
9784	11^61157-270	63689	Enzo Doria	07/2012
9785	10^63685+1145141919	63686	Marisa Kirisame	03/2015
9786	10^63685+103837	63686	Patrick De Geest	03/2016
9787	10^63685-130797	63685	Patrick De Geest	03/2016
9788	2^211547+1155*211547	63682	Henri Lifchitz	02/2005
9789	2^211543+45	63681	Lelio R Paula	08/2011
9790	2^211534+43	63679	Lelio R Paula	08/2011
9791	11^61140-60	63671	Enzo Doria	07/2012
9792	2^211491-112321	63666	Enzo Doria	06/2014
9793	(2^211459+2130)/2	63656	Stefano Morozzi	12/2019
9795	19085^2164+2164^19085	63654	Hans Havermann	03/2017
9794	(2^211454+3474)/2	63654	Stefano Morozzi	12/2019
9796	(2^211451+2910)/2	63653	Stefano Morozzi	12/2019
9797	(2^211430-5)/859	63644	Lelio R Paula	04/2012
9798	2^211401-91	63639	Lelio R Paula	08/2011
9799	(2^211403+1050)/2	63639	Stefano Morozzi	12/2019
9800	(6883*2^211378-1)/69	63634	Lelio R Paula	04/2015
9801	(F(152232)^3-F(152231)^3)/F(152230)	63629	Wayne Halsdorf	03/2012
9802	(29*2^211384-1)/50122621	63627	Lelio R Paula	01/2014
9803	(2^211344+3946)/2	63621	Stefano Morozzi	12/2019
9804	2^211333+15015	63618	Lelio R Paula	01/2013
9805	(2^211321+842)/2	63614	Stefano Morozzi	12/2019
9806	33^41889-32	63610	Norbert Schneider	03/2014
9807	(2^211275+3354)/2	63600	Stefano Morozzi	12/2019
9808	13^57093+18	63599	Lelio R Paula	05/2013
9809	(2^211267+3006)/2	63598	Stefano Morozzi	12/2019
9810	(5*2^211219-1)/9	63583	Lelio R Paula	01/2014
9811	(107*10^63576-17)/9	63578	Robert Price	02/2017
9812	23^46687-1020	63575	Enzo Doria	08/2012
9813	(67607*2^211188+1)/5234319	63573	Lelio R Paula	06/2014
9814	(3^133243+7)/10726	63570	Lelio R Paula	04/2012
9815	(7*2^211181+1)/2745	63570	Lelio R Paula	06/2012
9816	(20^48859-1)/19	63566	Paul Bourdelais	03/2010
9817	2*3^133227+5	63566	Lelio R Paula	04/2014
9818	(2^211160+3822)/2	63566	Stefano Morozzi	12/2019
9819	2^211155+113	63564	Lelio R Paula	08/2011
9820	2^211134+345	63558	Lelio R Paula	09/2011
9821	2^211121+16385	63554	Lelio R Paula	09/2011
9822	16996^5483+5483^16996	63549	Hans Havermann	02/2017
9823	(2^211083+2958)/2	63543	Stefano Morozzi	12/2019
9824	(2^211079+9)/364283	63536	Lelio R Paula	03/2012
9825	(2^211043+3806)/2	63530	Stefano Morozzi	12/2019
9826	3*10^63522+13	63523	Robert Price	08/2017
9827	15852^10157+10157^15852	63516	Hans Havermann	02/2017
9828	(2^210996+3150)/2	63516	Stefano Morozzi	12/2019
9829	(2^210962+2854)/2	63506	Stefano Morozzi	12/2019
9830	2^210948-15873	63502	Enzo Doria	04/2013
9831	7^75136+6	63498	Lelio R Paula	04/2013
9832	2^210928+12915	63496	Lelio R Paula	02/2013
9833	7*10^63493+39	63494	Robert Price	07/2016
9835	2^210909+135	63490	Lelio R Paula	08/2011
9834	(2^210909+422)/2	63490	Stefano Morozzi	12/2019
9836	11457^15638-15638^11457	63476	Norbert Schneider	01/2020
9839	(3*2^210832+1)/7	63467	Lelio R Paula	07/2012
9838	8*7^75098-3	63467	Lelio R Paula	09/2014
9837	(2^210832+2458)/2	63467	Stefano Morozzi	12/2019
9840	17683^3882+3882^17683	63466	Hans Havermann	03/2017
9842	Pell-LucasQ(165799)/2	63464	Eric W. Weisstein	11/2006
9841	2^210820-16905	63464	Enzo Doria	05/2013
9843	5^90795-36	63463	Lelio R Paula	04/2013
9844	84731!6-48	63463	Robert Price	08/2018
9845	2^210816-13197	63462	Enzo Doria	10/2012
9846	2^210750+133	63443	Lelio R Paula	08/2011
9847	(2^210743+1106)/2	63440	Stefano Morozzi	12/2019
9848	291^25742+25742^291	63426	Norbert Schneider	09/2014
9849	(2^210641+1742)/2	63409	Stefano Morozzi	12/2019
9850	(3^132908+8)/279859	63408	Lelio R Paula	04/2012
9851	6^81480-139	63404	Lelio R Paula	04/2013
9852	2^210576-173	63390	Lelio R Paula	08/2011
9853	18^50497+55	63388	Lelio R Paula	05/2013
9854	2^210545+11	63381	Lelio R Paula	08/2011
9855	2^210543+63	63380	Lelio R Paula	08/2011
9856	155^28929-154	63365	Norbert Schneider	12/2018
9858	83^33016+82	63361	Norbert Schneider	04/2015
9857	(2^210480+1690)/2	63361	Stefano Morozzi	12/2019
9859	2^210464+98765331	63356	Jason Earls	12/2008
9860	7*10^63351+9	63352	Dmitry Domanov	11/2010
9861	58483!4+4	63351	Robert Price	09/2019
9862	p(13534)#/2+512	63348	Robert Price	05/2017
9863	1741^19546+19546^1741	63345	Serge Batalov	05/2014
9864	10^63336+19819	63337	Patrick De Geest	12/2013
9865	10^63336-122883	63336	Patrick De Geest	12/2013
9866	(19^49523-2^49523)/17	63327	Robert Price	09/2013
9867	(2^210378+47)/95516931	63323	Lelio R Paula	03/2012
9868	31191!2+256	63316	Robert Price	01/2015
9869	16458^7031+7031^16458	63315	Hans Havermann	01/2017
9870	(lucasV(1,2,420636)-2)/(731^2210319)	63303	Mike Oakes	03/2017
9871	156^28864+155	63303	Norbert Schneider	12/2018
9872	(2^210269+3542)/2	63297	Stefano Morozzi	12/2019
9873	(2^210283+7)/1691145	63296	Lelio R Paula	03/2012
9874	(2^210256+1842)/2	63294	Stefano Morozzi	12/2019
9876	2^210217+1299	63282	Lelio R Paula	09/2011
9875	(2^210218+2598)/2	63282	Stefano Morozzi	12/2019
9877	(2^210221-3)/269	63281	Lelio R Paula	04/2012
9878	Phi(193404,10)/386809/8122969	63268	Maksym Voznyy	10/2011
9879	(2^210153+2402)/2	63263	Stefano Morozzi	12/2019
9880	96^31913-95	63261	Norbert Schneider	04/2016
9881	3^132572+280	63253	Lelio R Paula	04/2013
9882	3^132570-2^(132570-1)	63252	Robert Price	01/2016
9883	11^60734-4920	63248	Enzo Doria	01/2013
9884	(2^210075+2070)/2	63239	Stefano Morozzi	12/2019
9886	2^210061+21	63235	Donovan Johnson	06/2006
9885	18^50375+95	63235	Lelio R Paula	05/2013
9887	85^32773-2	63233	Lelio R Paula	08/2013
9888	(-lucasV(1,2,420115)-2)/(3*5^3)	63232	Mike Oakes	02/2017
9889	(2^210054-1017)/671	63230	Lelio R Paula	04/2012
9890	3*2^210022+5	63224	Lelio R Paula	04/2014
9891	15^53756+32	63222	Lelio R Paula	05/2013
9892	17^51380+22	63221	Lelio R Paula	05/2013
9893	(lucasV(1,2,420045)+2)/257	63221	Mike Oakes	02/2017
9894	43^38700+42	63216	Norbert Schneider	06/2014
9895	5^90431-96	63209	Lelio R Paula	04/2013
9896	(172*10^63202-1)/9	63204	Serge Batalov	12/2014
9897	(43*10^63200+83)/9	63201	Robert Price	08/2017
9898	(2^209928+1146)/2	63195	Stefano Morozzi	12/2019
9899	2^209914-16005	63191	Enzo Doria	04/2013
9900	(2^209913+3642)/2	63190	Stefano Morozzi	12/2019
9901	3*6^81190-5	63179	Lelio R Paula	09/2014
9902	11424^15569-15569^11424	63177	Norbert Schneider	11/2019
9903	2^209820+4257	63163	Lelio R Paula	10/2011
9904	99^31648+2	63158	Lelio R Paula	05/2013
9905	16976^5253+5253^16976	63158	Hans Havermann	01/2017
9906	2^209790+67	63154	Lelio R Paula	08/2011
9907	145878#-p(145878)	63152	Henri Lifchitz	12/2018
9908	(2^209771+2486)/2	63148	Stefano Morozzi	12/2019
9909	2^209759+90195	63144	Lelio R Paula	02/2013
9910	145823#+211507	63142	Arkadiusz Wesolowski	03/2013
9911	2^209707+513	63129	Lelio R Paula	10/2011
9912	(3^132314-8)/17	63129	Lelio R Paula	04/2012
9913	(2*10^63117+7)/9	63117	Erik Branger	03/2011
9914	9*2^209654-7	63114	Lelio R Paula	04/2014
9915	84304!6-9	63112	Robert Price	08/2018
9916	11^60598-14	63107	Lelio R Paula	05/2013
9917	15103^15078+15078^15103	63106	Hans Havermann	01/2017
9918	15346^12941+12941^15346	63103	Hans Havermann	01/2017
9920	3^132253+76	63101	Lelio R Paula	04/2013
9919	(56*10^63100+403)/9	63101	Robert Price	10/2017
9921	17549^3936+3936^17549	63090	Hans Havermann	01/2017
9923	(55459*2^209553+1)/423	63084	Lelio R Paula	06/2014
9922	(2^209560+1602)/2	63084	Stefano Morozzi	12/2019
9924	(331^25033-1)/330	63077	Eric Chen	09/2017
9926	20^48480+31	63074	Lelio R Paula	06/2013
9925	(26*10^63073-23)/3	63074	Robert Price	08/2016
9927	2^209499+76253	63066	Enzo Doria	04/2016
9928	(2^209462+1618)/2	63055	Stefano Morozzi	12/2019
9929	11^60546-11340	63053	Enzo Doria	12/2012
9930	2^209426+57889	63044	Yves Minet	02/2010
9931	(2^209419+2486)/2	63042	Stefano Morozzi	12/2019
9932	(22699*2^209405+1)/21	63041	Lelio R Paula	06/2014
9933	5^90189+54	63040	Lelio R Paula	04/2013
9934	(22*10^63034-73)/3	63035	Robert Price	09/2017
9935	(314021^11467+1)/314022	63029	Faysal YAtim	05/2008
9936	(2^209306+450)/2	63008	Stefano Morozzi	12/2019
9937	V(301486)	63007	Henri Lifchitz	05/2003
9938	(2^209302+3258)/2	63006	Stefano Morozzi	12/2019
9939	(31*2^209298+1)/95	63005	Lelio R Paula	08/2012
9940	(2^209289+3290)/2	63002	Stefano Morozzi	12/2019
9941	(27*2^209245+1)/5	62990	Lelio R Paula	08/2012
9942	6^80946-5^(80946-1)	62989	Robert Price	05/2016
9943	467^23596+23596^467	62986	Norbert Schneider	08/2016
9944	(7*2^209212-1)/3	62980	Lelio R Paula	01/2014
9945	(27*2^209206-1)/11	62978	Lelio R Paula	01/2014
9946	1456^19909+19909^1456	62976	Serge Batalov	05/2014
9947	(5^90107-1)/(4*2162569)	62976	Gord Palameta	07/2019
9948	(3^131964-5)/185212396	62955	Lelio R Paula	04/2012
9949	35^40772-1466	62955	Enzo Doria	03/2013
9950	5^90064-13706	62953	Enzo Doria	02/2013
9951	(2^209070+2658)/2	62937	Stefano Morozzi	12/2019
9952	(22*10^62926+257)/9	62927	Robert Price	11/2017
9953	(13*10^62914+401)/9	62915	Robert Price	10/2017
9954	2^208993+107	62914	Lelio R Paula	08/2011
9955	2^208993+77	62914	Lelio R Paula	08/2011
9956	189^27636-2	62913	Lelio R Paula	10/2017
9957	(2^208948-7)/261	62898	Lelio R Paula	03/2012
9958	15804^9545+9545^15804	62897	Hans Havermann	06/2019
9959	(151*10^62879-1)/3	62881	Robert Price	04/2017
9960	15^53464-82	62879	Lelio R Paula	05/2013
9961	11018^15555-15555^11018	62875	Norbert Schneider	11/2019
9962	2^208843-112921	62869	Enzo Doria	06/2014
9963	(2^208841+2274)/2	62868	Stefano Morozzi	12/2019
9964	14005^15162-15162^14005	62866	Norbert Schneider	03/2020
9965	(2^208794+3594)/2	62853	Stefano Morozzi	12/2019
9966	2^208779+81	62849	Henri Lifchitz	01/2007
9967	159^28548+158	62846	Norbert Schneider	12/2018
9968	(21181*2^208780+1)/8993838841	62844	Lelio R Paula	06/2014
9969	(73*10^62824+17)/9	62825	Robert Price	10/2015
9970	3^131670-82	62823	Lelio R Paula	04/2013
9971	19^49128-90	62823	Lelio R Paula	05/2013
9972	(2^208684+2190)/2	62820	Stefano Morozzi	12/2019
9973	(2^208684+3942)/2	62820	Stefano Morozzi	12/2019
9974	17687^3562+3562^17687	62819	Hans Havermann	06/2019
9975	11^60314-4410	62811	Enzo Doria	01/2013
9976	(17*2^208614-1)/53	62799	Lelio R Paula	01/2014
9977	2^208594+93	62794	Donovan Johnson	06/2008
9978	(-lucasV(1,2,417184)+2)/(3*104297)	62788	Mike Oakes	02/2017
9979	(2^208544+3466)/2	62778	Stefano Morozzi	12/2019
9980	(2^208534+7)/9059	62772	Lelio R Paula	03/2012
9981	(2^208505+2570)/2	62766	Stefano Morozzi	12/2019
9982	14168^15119-15119^14168	62764	Norbert Schneider	02/2020
9984	(13^56333+1)/14	62751	Paul Bourdelais	03/2010
9983	10^62750+57	62751	Robert Price	01/2011
9985	10^62750-267429	62750	Patrick De Geest	01/2013
9986	2^208427-69	62743	Lelio R Paula	08/2011
9987	2^208421-111775	62741	Enzo Doria	05/2014
9988	(2^208406+3802)/2	62737	Stefano Morozzi	12/2019
9989	2^208404-112079	62736	Enzo Doria	06/2014
9990	(2^208381+2930)/2	62729	Stefano Morozzi	12/2019
9991	15242^13041+13041^15242	62726	Hans Havermann	06/2019
9992	2^208343-2221	62718	Yves Minet	08/2013
9993	2^208335+513	62716	Lelio R Paula	10/2011
9994	(2^208328+47)/3	62713	Lelio R Paula	03/2012
9995	11^60220-2040	62713	Enzo Doria	12/2012
9996	2^208292+81	62703	Henri Lifchitz	10/2005
9997	(2^208293+162)/2	62703	Stefano Morozzi	12/2019
9998	15013^15012-15012	62698	Henri Lifchitz	10/2014
9999	2^208271-112747	62696	Enzo Doria	06/2014
10000	11^60202-4380	62694	Enzo Doria	01/2013

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PRP Records

Probable Primes Top 10000

(259919 PRPs in the top)