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	(2^169969-1017)/35	51165	Lelio R Paula	01/2012
9752	5*10^51163-7	51164	Dmitry Domanov	11/2010
9753	(73*10^51162-1)/9	51163	Robert Price	01/2015
9754	L(244779)+P(244779)	51156	Robert Price	12/2017
9755	(22*10^51154+383)/9	51155	Robert Price	11/2017
9756	2^169899+63	51145	Lelio R Paula	05/2009
9757	2^169898+513	51145	Lelio R Paula	05/2009
9759	3^107186-12388	51141	Enzo Doria	02/2013
9758	(299*10^51139+1)/3	51141	Robert Price	11/2017
9760	(12487^12487+173)/2^2/3/2917/3463/44483	51140	Makoto Morimoto	07/2016
9761	3*6^65715-7	51137	Lelio R Paula	09/2014
9762	116^24768+115	51133	Norbert Schneider	10/2013
9763	35^33113-4026	51129	Enzo Doria	03/2013
9764	(13*2^169830-1)/84477	51121	Lelio R Paula	01/2014
9765	(46*10^51111-1)/9	51112	Serge Batalov	10/2014
9766	15^43452-34	51104	Lelio R Paula	01/2013
9767	2^169750-137	51100	Lelio R Paula	01/2011
9768	2^169739+94065	51097	Lelio R Paula	10/2011
9769	15^43442-26	51092	Lelio R Paula	01/2013
9770	5^73096-17006	51092	Enzo Doria	02/2013
9771	10^51091+71601	51092	Patrick De Geest	07/2017
9772	10^51091-701	51091	Robert Price	06/2017
9773	(-lucasV(1,2,339439)-2)/(79*83)	51088	Mike Oakes	03/2017
9774	2^169706-270551	51087	Gary Barnes	08/2009
9775	(2^169696+5)/21	51083	Lelio R Paula	01/2012
9776	(1722520^8192+1)/65537	51082	Syoichiro Yamada	01/2009
9777	11^49051-8760	51082	Enzo Doria	02/2013
9778	(24737*2^169672+1)/27	51080	Lelio R Paula	05/2014
9779	(14*10^51079+229)/9	51080	Robert Price	11/2017
9780	2^169677+16095	51078	Lelio R Paula	05/2009
9781	2^169659-135	51073	Lelio R Paula	01/2011
9782	2^169638-113183	51067	Enzo Doria	07/2014
9783	(29*2^169622-1)/2346531185	51054	Lelio R Paula	01/2014
9784	(10^51054+17)/9	51054	Robert Price	10/2014
9785	8329^13022-13022^8329	51054	Norbert Schneider	07/2017
9786	(24737*2^169577+1)/5	51052	Lelio R Paula	05/2014
9787	11^49021-78	51051	Lelio R Paula	01/2013
9788	18^40669+61	51051	Lelio R Paula	01/2013
9789	14038^4327+4327^14038	51045	Hans Havermann	02/2016
9790	2^169555-159	51042	Lelio R Paula	01/2011
9791	91^26054-2	51041	Lelio R Paula	08/2013
9792	Phi(101775,10)/1628401	51034	Makoto Kamada	05/2015
9793	7559^13158-13158^7559	51033	Norbert Schneider	11/2017
9794	97*10^51027-3	51029	Robert Price	01/2017
9795	2^169499-2647	51025	Yves Minet	07/2014
9796	5*6^65567+7	51022	Lelio R Paula	09/2014
9797	14763^2858+2858^14763	51022	Hans Havermann	08/2015
9798	24^36966-1477	51021	Enzo Doria	03/2013
9799	(78557*2^169464+1)/160527	51014	Lelio R Paula	06/2014
9800	(34*10^51008-43)/9	51009	Ray Chandler	09/2010
9801	10^51004+128427	51005	Patrick De Geest	08/2009
9803	10^51004-113	51004	Milton L. Brown	12/2008
9802	10^51003+16951	51004	Patrick De Geest	08/2009
9804	10^51003-79601	51003	Milton L. Brown	12/2008
9805	10^51003-80831	51003	Milton L. Brown	12/2008
9806	10^51002+8877	51003	Patrick De Geest	08/2009
9808	10^51002-10541	51002	Milton L. Brown	11/2008
9807	10^51001+52051	51002	Patrick De Geest	08/2009
9809	10^51001-158687	51001	Milton L. Brown	10/2008
9810	2*10^51000+93	51001	Robert Price	07/2016
9811	10^51000+188251	51001	Patrick De Geest	10/2017
9812	10^51000-31289	51000	Patrick De Geest	10/2017
9814	(2^169416+5)/3	50999	Lelio R Paula	01/2012
9813	(49*10^50998+41)/9	50999	Robert Price	07/2015
9815	13292^6867+6867^13292	50999	Hans Havermann	02/2016
9816	(35*10^50997-71)/9	50998	Robert Price	05/2015
9817	6^65536+2*97878-1	50997	Jiahao He	05/2017
9818	29^34871-28^34871	50996	Robert Price	09/2012
9819	76^27112-75	50993	Norbert Schneider	11/2012
9820	(70^27631-1)/69	50981	Richard Fischer	08/2017
9821	(12451^12451+1345)/2^2/19/89/139/6977	50980	Makoto Morimoto	07/2016
9822	10736^12645-12645^10736	50971	Norbert Schneider	12/2016
9823	(1017*2^169315-1)/9715	50968	Lelio R Paula	03/2015
9824	7^60309-6^(60309+1)	50968	Robert Price	06/2016
9826	2^169267+99	50955	Lelio R Paula	07/2009
9825	5*2^169264+3	50955	Lelio R Paula	02/2014
9827	t(192517)	50950	Robert Price	08/2014
9828	10^50943+624451	50944	Robert Price	03/2015
9829	10^50943+54409	50944	Patrick De Geest	02/2016
9830	10^50943-100559	50943	Patrick De Geest	03/2016
9831	2^169206-3645	50937	Lelio R Paula	05/2009
9832	2^169196-112577	50934	Enzo Doria	06/2014
9833	20^39146-3483	50931	Enzo Doria	03/2013
9834	10^50929+16849	50930	Patrick De Geest	01/2012
9836	10^50929-51	50929	Robert Price	05/2011
9835	7^60264+48	50929	Lelio R Paula	10/2012
9837	2^169167+1299	50925	Lelio R Paula	05/2009
9838	10103^12717-100	50925	Enzo Doria	07/2012
9839	3^106721-130	50919	Lelio R Paula	07/2012
9841	18225^622+622^18225	50917	Anatoly F. Selevich	11/2006
9840	(10223*2^169138+1)/1113	50917	Lelio R Paula	05/2014
9842	6057^13462-13462^6057	50917	Norbert Schneider	04/2018
9843	7*2^169125+9	50913	Lelio R Paula	02/2014
9844	(47*2^169123+1)/29	50912	Lelio R Paula	03/2015
9845	20^39131+93	50911	Lelio R Paula	01/2013
9846	(21*27^35567-94921)/26	50910	Curtis Bright	05/2015
9847	(7*2^169124-1)/9549	50909	Lelio R Paula	01/2014
9848	(12433^12433+809)/2/3/11	50907	Makoto Morimoto	07/2016
9849	13693^5212+5212^13693	50897	Hans Havermann	02/2016
9850	7*5^72813+6	50895	Lelio R Paula	09/2014
9851	5*10^50890-81	50891	Robert Price	04/2017
9852	3^106656-12028	50888	Enzo Doria	02/2013
9853	(2^169028+3)/259	50881	Lelio R Paula	01/2012
9854	2^169000-1127	50875	Yves Minet	05/2013
9855	19^39780+16	50869	Lelio R Paula	01/2013
9856	(19*2^168960+1)/5	50863	Lelio R Paula	07/2012
9857	(-lucasV(1,2,337937)-2)/(3^2*11)	50863	Mike Oakes	02/2017
9859	11^48840+46	50862	Lelio R Paula	01/2013
9858	(5*10^50861-107)/3	50862	Robert Price	01/2017
9860	20^39087-4203	50854	Enzo Doria	03/2013
9861	(12421^12421+1339)/2^4/5/43/157	50848	Makoto Morimoto	07/2016
9862	2^168907-544447	50847	Paul Bourdelais	11/2012
9863	19312^429+429^19312	50839	Anatoly F. Selevich	12/2006
9864	5^72716-13226	50827	Enzo Doria	02/2013
9865	2^168823+1025	50821	Lelio R Paula	01/2009
9866	7*10^50818-89	50819	Robert Price	01/2017
9868	2^168811+15015*168811	50818	Henri Lifchitz	02/2005
9867	2^168813-2833	50818	Yves Minet	09/2014
9870	(12413^12413+3221)/2/89	50816	Makoto Morimoto	07/2016
9869	7022^13211-13211^7022	50816	Norbert Schneider	12/2017
9871	2^168795+5385	50813	Lelio R Paula	05/2009
9872	7670^13079-13079^7670	50810	Norbert Schneider	09/2017
9873	4*3^106483+5	50806	Lelio R Paula	03/2014
9874	13^45606+4	50803	Lelio R Paula	01/2013
9875	13^45606-38	50803	Lelio R Paula	01/2013
9876	2^168746+58905	50798	Lelio R Paula	05/2009
9877	(16*10^50795-43)/9	50796	Robert Price	02/2015
9878	gcd(V(615445),5F(123089)(F(123089)-1)+1)	50794	Serge Batalov	04/2015
9879	7*10^50789-47	50790	Robert Price	02/2017
9880	2^168717-729523	50789	Paul Bourdelais	11/2012
9881	(12409^12409+136)/5^2/13/5647/473279	50788	Makoto Morimoto	07/2016
9882	(21*2^168652-1)/215	50769	Lelio R Paula	01/2014
9883	2^168629+12909	50763	Lelio R Paula	01/2011
9884	9328^12787+12787^9328	50762	Norbert Schneider	01/2016
9885	2^168627+73113	50762	Enzo Doria	04/2016
9886	2^168623+47333	50761	Yves Minet	02/2010
9887	(8*10^50750-101)/3	50751	Robert Price	10/2017
9888	(12401^12401+154)/3^2/5/31/59/67/97/761/863/12143	50745	Makoto Morimoto	07/2016
9889	(lucasV(1,2,337126)+2)/(5*11)	50739	Mike Oakes	02/2017
9890	3*10^50727-31	50728	Robert Price	10/2017
9891	6152^13387-13387^6152	50724	Norbert Schneider	03/2018
9892	8544^12901-12901^8544	50723	Norbert Schneider	05/2017
9893	(17^41221+1)/18	50720	Paul Bourdelais	03/2010
9894	10^50711+7	50712	Jason Earls	12/2007
9895	10^50711-317969	50711	Patrick De Geest	04/2009
9897	(17^41213+3^41213)/20	50710	Robert Price	08/2013
9896	(12391^12391+58)/59/211/7823	50710	Makoto Morimoto	07/2016
9898	47779!4+1024	50708	Robert Price	08/2017
9900	2^168431-159	50703	Lelio R Paula	01/2011
9899	(7*10^50702-1)/3	50703	Erik Branger	03/2014
9901	117216#-p(117216)	50700	Henri Lifchitz	03/2007
9902	(1543550^8192+1)/65537	50692	Syoichiro Yamada	06/2008
9903	(13*2^168352-1)/477	50678	Lelio R Paula	01/2014
9904	8*10^50675+39	50676	Robert Price	01/2017
9905	(lucasV(1,2,336840)+2)/(1133372360970589125621*144481)	50676	Mike Oakes	02/2017
9906	14415^3274+3274^14415	50670	Hans Havermann	05/2016
9907	(12379^12379+282)/17	50663	Makoto Morimoto	07/2016
9909	5^72480-17126	50662	Enzo Doria	02/2013
9908	(34*10^50667-7)/9/3^3/136277	50662	Makoto Morimoto	04/2016
9910	3^106143+2	50644	Mike Oakes	11/2009
9911	9178^12777-12777^9178	50633	Norbert Schneider	02/2017
9912	(2*10^50603-41)/3	50603	Robert Price	01/2017
9913	(12^46889-1)/11	50601	Paul Bourdelais	09/2008
9914	2^168068-1893	50594	Yves Minet	09/2012
9915	2^168057+8415	50591	Lelio R Paula	11/2011
9916	4*10^50579+9	50580	Robert Price	05/2015
9917	2^168019-94395	50579	Lelio R Paula	07/2011
9918	2^168019+74213	50579	Enzo Doria	04/2016
9919	(47*10^50578+493)/9	50579	Robert Price	11/2017
9920	5925^13406-13406^5925	50577	Norbert Schneider	03/2018
9921	3^106002+70	50576	Lelio R Paula	07/2012
9922	5*2^167970-9	50565	Lelio R Paula	02/2014
9923	(58*10^50558-13)/9	50559	Robert Price	09/2015
9924	88*10^50547+7	50549	Robert Price	11/2016
9925	2^167910-112625	50546	Enzo Doria	06/2014
9926	(1476500^8192+1)/65537	50534	Syoichiro Yamada	06/2008
9927	2^167866+11715	50533	Lelio R Paula	05/2009
9928	gcd(V(621415),5F(124283)(F(124283)+1)+1)	50528	Serge Batalov	04/2015
9929	2^167847-135	50527	Lelio R Paula	01/2011
9930	-lucasV(-1,2,335684)	50526	Mike Oakes	01/2017
9931	(-lucasV(1,2,335677)+2)/(3*226777)	50519	Mike Oakes	02/2017
9932	(12347^12347+1567)/2/3^2/5	50517	Makoto Morimoto	07/2016
9934	2^167807+75	50515	Lelio R Paula	08/2010
9933	2^167805+76277	50515	Enzo Doria	04/2016
9935	8335^12882+12882^8335	50510	Norbert Schneider	03/2016
9936	7*2^167777+9	50507	Lelio R Paula	02/2014
9937	14162^3681+3681^14162	50502	Hans Havermann	05/2016
9938	(17*10^50495-11)/3	50496	Robert Price	07/2015
9939	2^167682+85	50478	Lelio R Paula	08/2010
9940	2^167667-927427	50473	Paul Bourdelais	11/2012
9941	9737^12654+12654^9737	50470	Norbert Schneider	01/2016
9942	(9179*2^167644-1)/17	50469	Lelio R Paula	03/2015
9943	13386^5891+5891^13386	50468	Hans Havermann	05/2016
9944	(10^50467-97)/3	50467	Robert Kinser	10/2017
9945	(lucasV(1,2,335347)+2)/(3511302287439661)	50462	Mike Oakes	02/2017
9946	152^23124+151	50453	Eric Chen	04/2018
9947	5003^13637-156	50447	Enzo Doria	07/2012
9948	6^64826-26723	50445	Enzo Doria	03/2013
9949	(3^105718+7)/32	50439	Lelio R Paula	03/2012
9950	(1436724^8192+1)/65537	50437	Syoichiro Yamada	06/2008
9951	17^40989+56	50435	Lelio R Paula	01/2013
9952	(12329^12329+1652)/421	50435	Makoto Morimoto	07/2016
9953	2*5^72153+7	50434	Lelio R Paula	09/2014
9954	(3126^14431-1)/3125	50433	Richard Fischer	03/2015
9955	8078^12907-12907^8078	50432	Norbert Schneider	05/2017
9956	39^31694+38	50428	Norbert Schneider	05/2014
9957	(7*10^50414-151)/9	50414	Robert Price	09/2017
9958	2^167460+2187	50411	Lelio R Paula	11/2011
9959	(12323^12323+2709)/2^4	50409	Makoto Morimoto	07/2016
9960	11^48400-7710	50404	Enzo Doria	02/2013
9961	2^167432+54615	50403	Lelio R Paula	05/2009
9962	(23*2^167430-1)/4169	50400	Lelio R Paula	01/2014
9963	68677!6-2	50395	Robert Price	07/2017
9964	19^39404+22	50389	Lelio R Paula	01/2013
9965	(102^25087-1)/101	50388	Richard Fischer	08/2017
9966	35^32629-7834	50382	Enzo Doria	03/2013
9968	6^64744+163	50381	Lelio R Paula	06/2012
9967	116447#+174659	50381	Nicolas PALAU	09/2016
9970	2^167353+129	50379	Lelio R Paula	05/2009
9969	20^38722-1133	50379	Enzo Doria	03/2013
9972	3^105567-16	50369	Lelio R Paula	07/2012
9971	2^167321-112849	50369	Enzo Doria	06/2014
9973	(28*10^50362-43)/3	50363	Robert Price	04/2016
9974	11421^12410-12410^11421	50357	Norbert Schneider	08/2013
9975	2^167278-2063	50356	Yves Minet	03/2013
9976	181^22300+22300^181	50347	Serge Batalov	05/2014
9977	9932^12595-12595^9932	50343	Norbert Schneider	12/2016
9978	8993^12732-12732^8993	50342	Norbert Schneider	02/2017
9979	3*5^72018-4	50339	Lelio R Paula	09/2014
9980	2^167207-112687	50335	Enzo Doria	06/2014
9981	6^64674-37	50327	Lelio R Paula	06/2012
9982	2^167177+74801	50326	Enzo Doria	04/2016
9983	13739^4600+4600^13739	50323	Hans Havermann	10/2015
9984	11508^12391+12391^11508	50320	Norbert Schneider	06/2014
9985	2^167132-2163	50312	Yves Minet	08/2013
9986	7^59527-62	50307	Lelio R Paula	06/2012
9987	(310027^9161+1)/310028	50302	Faysal YAtim	04/2008
9988	(12301^12301+74)/3^2/5^3/11/17/1151	50302	Makoto Morimoto	07/2016
9989	2^167083-112519	50297	Enzo Doria	06/2014
9990	272^20659-20659^272	50296	Norbert Schneider	09/2015
9991	25337!!-16	50290	Robert Price	06/2015
9992	9722^12611-12611^9722	50290	Norbert Schneider	12/2016
9993	(15*2^167013+1)/649	50275	Lelio R Paula	07/2012
9994	19^39315-12	50275	Lelio R Paula	01/2013
9995	5^71925-36	50274	Lelio R Paula	06/2012
9996	2^167002+2799139	50273	Enzo Doria	04/2016
9997	10957^12444-12444^10957	50270	Norbert Schneider	07/2013
9998	8*10^50253-99	50254	Robert Price	02/2017
10000	5^71894-54	50252	Lelio R Paula	06/2012
9999	(127^23887+1)/128	50252	Richard Fischer	04/2017

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PRP Records

Probable Primes Top 10000

(212140 PRPs in the top)