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 ?
9751	9818^12919-12919^9818	51573	Norbert Schneider	05/2017
9752	(3^108091+7)/382	51570	Lelio R Paula	03/2012
9754	2^171287-3187	51563	Yves Minet	04/2009
9753	-lucasV(-1,2,342569)	51563	Mike Oakes	02/2017
9755	2^171280-1030709	51561	Paul Bourdelais	11/2012
9756	13300^7527+7527^13300	51560	Hans Havermann	05/2016
9757	2^171268+73711	51557	Enzo Doria	04/2016
9758	(17*2^171266+1)/6963	51554	Lelio R Paula	01/2012
9759	(1964814^8192+1)/65537	51551	Lelio R Paula	06/2013
9760	(26*10^51537-503)/9	51538	Robert Price	12/2017
9761	4*10^51530-63	51531	Robert Price	12/2016
9762	3*6^66216-5	51527	Lelio R Paula	09/2014
9763	12569^12569+540	51525	Makoto Morimoto	07/2016
9764	2^171152-2459	51522	Yves Minet	07/2014
9765	(13*10^51511-1)/3	51512	Robert Price	12/2014
9766	5*10^51508+3	51509	Dmitry Domanov	11/2010
9767	3^107919-46	51491	Lelio R Paula	07/2012
9768	4*10^51489+87	51490	Robert Price	05/2016
9769	(22699*2^171030+1)/3029	51487	Lelio R Paula	05/2014
9770	2^171028-3239	51485	Yves Minet	12/2014
9771	2^170992-954209	51474	Paul Bourdelais	11/2012
9772	76^27367+75	51473	Norbert Schneider	11/2012
9773	6007^13620-102	51466	Enzo Doria	07/2012
9774	gcd(V(923445),5F(184689)(F(184689)-1)+1)	51462	Serge Batalov	04/2015
9775	t(194442)	51459	Robert Price	08/2014
9776	6470^13503-13503^6470	51459	Norbert Schneider	05/2018
9777	(22*10^51457+161)/3	51458	Robert Price	02/2017
9778	9^53921+8^(53921+1)	51454	Robert Price	06/2016
9780	2^170921-16995	51453	Lelio R Paula	08/2011
9779	2^170922-2135	51453	Yves Minet	06/2013
9781	4357^14138-120	51451	Enzo Doria	06/2012
9782	153^23550+2	51450	Lelio R Paula	05/2013
9783	(3^107833+2)/25	51449	Lelio R Paula	03/2012
9784	(159^23369+1)/160	51443	Eric Chen	12/2017
9785	7*10^51440-47	51441	Robert Price	02/2017
9786	(10^51431-3^51431)/7	51431	Robert Price	06/2011
9788	U(250849)	51425	Michael Porter	08/2007
9787	(86*10^51424-41)/9	51425	Robert Price	11/2015
9790	12^47649+7	51422	Lelio R Paula	12/2012
9789	(25*10^51421+11)/9	51422	Robert Price	03/2015
9791	3^107768+2660	51419	Lelio R Paula	07/2012
9793	2^170784-6555	51412	Lelio R Paula	05/2009
9792	(-lucasV(1,2,341584)-2)/79	51412	Mike Oakes	03/2017
9795	51^30106+2	51409	Lelio R Paula	05/2013
9794	2^170777-4159	51409	Yves Minet	02/2018
9796	5^73546-12806	51407	Enzo Doria	02/2013
9797	(12545^12545+12546^12546)/(1584571*19137767639)	51404	Walter Nissen	09/2014
9798	(3^107735-4)/431	51401	Lelio R Paula	03/2012
9799	20^39505-6483	51398	Enzo Doria	03/2013
9800	2^170736-15197	51397	Enzo Doria	04/2013
9801	2^170737-3823	51397	Yves Minet	04/2017
9802	(12541^12541+393)/2/563	51395	Makoto Morimoto	07/2016
9803	9^53857-8^53857	51393	Jean-Louis Charton	11/2004
9804	5^73524-14426	51392	Enzo Doria	02/2013
9805	2^170712+243	51390	Lelio R Paula	10/2011
9806	(15*2^170713+1)/1793	51388	Lelio R Paula	07/2012
9807	(2^170702+9)/1261	51384	Lelio R Paula	01/2012
9808	283^20956+20956^283	51380	Norbert Schneider	08/2014
9809	2^170665-31	51376	Lelio R Paula	01/2011
9810	11^49330-12	51372	Lelio R Paula	01/2013
9811	(25*10^51366-73)/3	51367	Robert Price	09/2016
9812	5^73486-2^73487	51365	Mike Oakes	10/2010
9813	(10^51364+119)/3	51364	Serge Batalov	12/2014
9814	15^43672+68	51363	Lelio R Paula	01/2013
9815	2^170609-113143	51359	Enzo Doria	07/2014
9816	760^17827-759^17827	51357	Jean-Louis Charton	12/2010
9817	(22699*2^170592+1)/4435	51355	Lelio R Paula	05/2014
9818	8*7^60767+3	51355	Lelio R Paula	09/2014
9819	7009^13352-13352^7009	51348	Norbert Schneider	03/2018
9820	5^73452-20646	51341	Enzo Doria	03/2013
9821	2^170531-230407	51335	Gary Barnes	08/2009
9822	35^33243-2112	51330	Enzo Doria	03/2013
9823	(1845768^8192+1)/65537	51328	Lelio R Paula	06/2013
9824	13^46072+42	51322	Lelio R Paula	01/2013
9825	14^44778-95	51322	Lelio R Paula	01/2013
9826	11008^12697+12697^11008	51318	Norbert Schneider	01/2016
9827	(11^49279+7^49279)/18	51318	Eric Chen	05/2018
9828	t(180039)	51312	Robert Price	09/2014
9829	2^170444-443	51309	Yves Minet	05/2013
9830	(-lucasV(1,2,340915)+2)/(34091342201898187163)	51294	Mike Oakes	03/2017
9831	(2*10^51285-71)/3	51285	Robert Price	01/2017
9832	(23*10^51283-47)/3	51284	Robert Price	10/2017
9833	(1819288^8192+1)/65537	51277	Lelio R Paula	06/2013
9834	8907^12982-12982^8907	51276	Norbert Schneider	06/2017
9835	5^73350+28	51270	Lelio R Paula	10/2012
9836	3^107450+2	51267	Mike Oakes	11/2009
9837	2^170296+2533	51265	Henri Lifchitz	07/2004
9838	2^170293+76481	51264	Enzo Doria	05/2016
9839	11835^12584+12584^11835	51257	Norbert Schneider	11/2015
9840	(12511^12511+193)/2^5/39371	51256	Makoto Morimoto	07/2016
9842	12^47489+47489^12	51250	Serge Batalov	02/2012
9841	14637^3172+3172^14637	51250	Hans Havermann	04/2016
9843	(2^170245+7)/9	51248	Lelio R Paula	02/2012
9844	5^73308-19926	51241	Enzo Doria	03/2013
9845	8966^12963-12963^8966	51238	Norbert Schneider	06/2017
9846	3*2^170203+5	51237	Lelio R Paula	02/2014
9847	5^73300+46	51235	Lelio R Paula	10/2012
9848	2^170167+71	51226	Lelio R Paula	01/2011
9849	2^170140-15077	51218	Enzo Doria	04/2013
9850	15^43542-46	51210	Lelio R Paula	01/2013
9852	2^170111-1017	51209	Lelio R Paula	06/2008
9851	4*10^51208-87	51209	Robert Price	03/2017
9853	14^44679+83	51208	Lelio R Paula	01/2013
9854	10^51207+100147	51208	Patrick De Geest	06/2016
9855	10^51207-801	51207	Robert Price	04/2016
9857	t(170300)	51191	Robert Price	03/2015
9856	11966^12553-12553^11966	51191	Norbert Schneider	11/2016
9858	14670^3083+3083^14670	51184	Hans Havermann	04/2016
9859	99^25644-98	51177	Norbert Schneider	07/2013
9860	13211^7468+7468^13211	51169	Hans Havermann	04/2016
9861	(2^169969-1017)/35	51165	Lelio R Paula	01/2012
9862	5*10^51163-7	51164	Dmitry Domanov	11/2010
9863	(73*10^51162-1)/9	51163	Robert Price	01/2015
9864	L(244779)+P(244779)	51156	Robert Price	12/2017
9865	(22*10^51154+383)/9	51155	Robert Price	11/2017
9866	2^169899+63	51145	Lelio R Paula	05/2009
9867	2^169898+513	51145	Lelio R Paula	05/2009
9869	3^107186-12388	51141	Enzo Doria	02/2013
9868	(299*10^51139+1)/3	51141	Robert Price	11/2017
9870	(12487^12487+173)/2^2/3/2917/3463/44483	51140	Makoto Morimoto	07/2016
9871	3*6^65715-7	51137	Lelio R Paula	09/2014
9872	116^24768+115	51133	Norbert Schneider	10/2013
9873	35^33113-4026	51129	Enzo Doria	03/2013
9874	(13*2^169830-1)/84477	51121	Lelio R Paula	01/2014
9875	(46*10^51111-1)/9	51112	Serge Batalov	10/2014
9876	15^43452-34	51104	Lelio R Paula	01/2013
9877	2^169750-137	51100	Lelio R Paula	01/2011
9878	2^169739+94065	51097	Lelio R Paula	10/2011
9879	15^43442-26	51092	Lelio R Paula	01/2013
9880	5^73096-17006	51092	Enzo Doria	02/2013
9881	10^51091+71601	51092	Patrick De Geest	07/2017
9882	10^51091-701	51091	Robert Price	06/2017
9883	(-lucasV(1,2,339439)-2)/(79*83)	51088	Mike Oakes	03/2017
9884	2^169706-270551	51087	Gary Barnes	08/2009
9885	(2^169696+5)/21	51083	Lelio R Paula	01/2012
9886	(1722520^8192+1)/65537	51082	Syoichiro Yamada	01/2009
9887	11^49051-8760	51082	Enzo Doria	02/2013
9888	(24737*2^169672+1)/27	51080	Lelio R Paula	05/2014
9889	(14*10^51079+229)/9	51080	Robert Price	11/2017
9890	2^169677+16095	51078	Lelio R Paula	05/2009
9891	2^169659-135	51073	Lelio R Paula	01/2011
9892	2^169638-113183	51067	Enzo Doria	07/2014
9893	(29*2^169622-1)/2346531185	51054	Lelio R Paula	01/2014
9894	(10^51054+17)/9	51054	Robert Price	10/2014
9895	8329^13022-13022^8329	51054	Norbert Schneider	07/2017
9896	(24737*2^169577+1)/5	51052	Lelio R Paula	05/2014
9897	11^49021-78	51051	Lelio R Paula	01/2013
9898	18^40669+61	51051	Lelio R Paula	01/2013
9899	14038^4327+4327^14038	51045	Hans Havermann	02/2016
9900	2^169555-159	51042	Lelio R Paula	01/2011
9901	91^26054-2	51041	Lelio R Paula	08/2013
9902	Phi(101775,10)/1628401	51034	Makoto Kamada	05/2015
9903	7559^13158-13158^7559	51033	Norbert Schneider	11/2017
9904	97*10^51027-3	51029	Robert Price	01/2017
9905	2^169499-2647	51025	Yves Minet	07/2014
9906	5*6^65567+7	51022	Lelio R Paula	09/2014
9907	14763^2858+2858^14763	51022	Hans Havermann	08/2015
9908	24^36966-1477	51021	Enzo Doria	03/2013
9909	(78557*2^169464+1)/160527	51014	Lelio R Paula	06/2014
9910	(34*10^51008-43)/9	51009	Ray Chandler	09/2010
9911	10^51004+128427	51005	Patrick De Geest	08/2009
9913	10^51004-113	51004	Milton L. Brown	12/2008
9912	10^51003+16951	51004	Patrick De Geest	08/2009
9914	10^51003-79601	51003	Milton L. Brown	12/2008
9915	10^51003-80831	51003	Milton L. Brown	12/2008
9916	10^51002+8877	51003	Patrick De Geest	08/2009
9918	10^51002-10541	51002	Milton L. Brown	11/2008
9917	10^51001+52051	51002	Patrick De Geest	08/2009
9919	10^51001-158687	51001	Milton L. Brown	10/2008
9920	2*10^51000+93	51001	Robert Price	07/2016
9921	10^51000+188251	51001	Patrick De Geest	10/2017
9922	10^51000-31289	51000	Patrick De Geest	10/2017
9924	(2^169416+5)/3	50999	Lelio R Paula	01/2012
9923	(49*10^50998+41)/9	50999	Robert Price	07/2015
9925	13292^6867+6867^13292	50999	Hans Havermann	02/2016
9926	(35*10^50997-71)/9	50998	Robert Price	05/2015
9927	6^65536+2*97878-1	50997	Jiahao He	05/2017
9928	29^34871-28^34871	50996	Robert Price	09/2012
9929	76^27112-75	50993	Norbert Schneider	11/2012
9930	(70^27631-1)/69	50981	Richard Fischer	08/2017
9931	(12451^12451+1345)/2^2/19/89/139/6977	50980	Makoto Morimoto	07/2016
9932	10736^12645-12645^10736	50971	Norbert Schneider	12/2016
9933	(1017*2^169315-1)/9715	50968	Lelio R Paula	03/2015
9934	7^60309-6^(60309+1)	50968	Robert Price	06/2016
9936	2^169267+99	50955	Lelio R Paula	07/2009
9935	5*2^169264+3	50955	Lelio R Paula	02/2014
9937	t(192517)	50950	Robert Price	08/2014
9938	10^50943+624451	50944	Robert Price	03/2015
9939	10^50943+54409	50944	Patrick De Geest	02/2016
9940	10^50943-100559	50943	Patrick De Geest	03/2016
9941	2^169206-3645	50937	Lelio R Paula	05/2009
9942	2^169196-112577	50934	Enzo Doria	06/2014
9943	20^39146-3483	50931	Enzo Doria	03/2013
9944	10^50929+16849	50930	Patrick De Geest	01/2012
9946	10^50929-51	50929	Robert Price	05/2011
9945	7^60264+48	50929	Lelio R Paula	10/2012
9948	2^169167+1299	50925	Lelio R Paula	05/2009
9947	10103^12717-100	50925	Enzo Doria	07/2012
9949	3^106721-130	50919	Lelio R Paula	07/2012
9952	18225^622+622^18225	50917	Anatoly F. Selevich	11/2006
9951	(10223*2^169138+1)/1113	50917	Lelio R Paula	05/2014
9950	6057^13462-13462^6057	50917	Norbert Schneider	04/2018
9953	7*2^169125+9	50913	Lelio R Paula	02/2014
9954	(47*2^169123+1)/29	50912	Lelio R Paula	03/2015
9955	20^39131+93	50911	Lelio R Paula	01/2013
9956	(21*27^35567-94921)/26	50910	Curtis Bright	05/2015
9957	(7*2^169124-1)/9549	50909	Lelio R Paula	01/2014
9958	(12433^12433+809)/2/3/11	50907	Makoto Morimoto	07/2016
9959	13693^5212+5212^13693	50897	Hans Havermann	02/2016
9960	7*5^72813+6	50895	Lelio R Paula	09/2014
9961	5*10^50890-81	50891	Robert Price	04/2017
9962	3^106656-12028	50888	Enzo Doria	02/2013
9963	(2^169028+3)/259	50881	Lelio R Paula	01/2012
9964	2^169000-1127	50875	Yves Minet	05/2013
9965	19^39780+16	50869	Lelio R Paula	01/2013
9966	(19*2^168960+1)/5	50863	Lelio R Paula	07/2012
9967	(-lucasV(1,2,337937)-2)/(3^2*11)	50863	Mike Oakes	02/2017
9969	11^48840+46	50862	Lelio R Paula	01/2013
9968	(5*10^50861-107)/3	50862	Robert Price	01/2017
9970	20^39087-4203	50854	Enzo Doria	03/2013
9971	(12421^12421+1339)/2^4/5/43/157	50848	Makoto Morimoto	07/2016
9972	2^168907-544447	50847	Paul Bourdelais	11/2012
9973	19312^429+429^19312	50839	Anatoly F. Selevich	12/2006
9974	5^72716-13226	50827	Enzo Doria	02/2013
9975	2^168823+1025	50821	Lelio R Paula	01/2009
9976	7*10^50818-89	50819	Robert Price	01/2017
9978	2^168811+15015*168811	50818	Henri Lifchitz	02/2005
9977	2^168813-2833	50818	Yves Minet	09/2014
9979	(12413^12413+3221)/2/89	50816	Makoto Morimoto	07/2016
9980	7022^13211-13211^7022	50816	Norbert Schneider	12/2017
9981	2^168795+5385	50813	Lelio R Paula	05/2009
9982	7670^13079-13079^7670	50810	Norbert Schneider	09/2017
9983	4*3^106483+5	50806	Lelio R Paula	03/2014
9984	13^45606+4	50803	Lelio R Paula	01/2013
9985	13^45606-38	50803	Lelio R Paula	01/2013
9986	2^168746+58905	50798	Lelio R Paula	05/2009
9987	(16*10^50795-43)/9	50796	Robert Price	02/2015
9988	gcd(V(615445),5F(123089)(F(123089)-1)+1)	50794	Serge Batalov	04/2015
9989	7*10^50789-47	50790	Robert Price	02/2017
9990	2^168717-729523	50789	Paul Bourdelais	11/2012
9991	(12409^12409+136)/5^2/13/5647/473279	50788	Makoto Morimoto	07/2016
9992	(21*2^168652-1)/215	50769	Lelio R Paula	01/2014
9993	2^168629+12909	50763	Lelio R Paula	01/2011
9994	9328^12787+12787^9328	50762	Norbert Schneider	01/2016
9995	2^168627+73113	50762	Enzo Doria	04/2016
9996	2^168623+47333	50761	Yves Minet	02/2010
9997	(8*10^50750-101)/3	50751	Robert Price	10/2017
9998	(12401^12401+154)/3^2/5/31/59/67/97/761/863/12143	50745	Makoto Morimoto	07/2016
9999	(lucasV(1,2,337126)+2)/(5*11)	50739	Mike Oakes	02/2017
10000	3*10^50727-31	50728	Robert Price	10/2017

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PRP Records

Probable Primes Top 10000

(218736 PRPs in the top)