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	20^39131+93	50911	Lelio R Paula	01/2013
9752	(21*27^35567-94921)/26	50910	Curtis Bright	05/2015
9753	(7*2^169124-1)/9549	50909	Lelio R Paula	01/2014
9754	(12433^12433+809)/2/3/11	50907	Makoto Morimoto	07/2016
9755	13693^5212+5212^13693	50897	Hans Havermann	02/2016
9756	7*5^72813+6	50895	Lelio R Paula	09/2014
9757	5*10^50890-81	50891	Robert Price	04/2017
9758	3^106656-12028	50888	Enzo Doria	02/2013
9759	(2^169028+3)/259	50881	Lelio R Paula	01/2012
9760	2^169000-1127	50875	Yves Minet	05/2013
9761	19^39780+16	50869	Lelio R Paula	01/2013
9762	(19*2^168960+1)/5	50863	Lelio R Paula	07/2012
9763	(-lucasV(1,2,337937)-2)/(3^2*11)	50863	Mike Oakes	02/2017
9765	11^48840+46	50862	Lelio R Paula	01/2013
9764	(5*10^50861-107)/3	50862	Robert Price	01/2017
9766	20^39087-4203	50854	Enzo Doria	03/2013
9767	(12421^12421+1339)/2^4/5/43/157	50848	Makoto Morimoto	07/2016
9768	2^168907-544447	50847	Paul Bourdelais	11/2012
9769	19312^429+429^19312	50839	Anatoly F. Selevich	12/2006
9770	5^72716-13226	50827	Enzo Doria	02/2013
9771	2^168823+1025	50821	Lelio R Paula	01/2009
9772	7*10^50818-89	50819	Robert Price	01/2017
9774	2^168811+15015*168811	50818	Henri Lifchitz	02/2005
9773	2^168813-2833	50818	Yves Minet	09/2014
9775	(12413^12413+3221)/2/89	50816	Makoto Morimoto	07/2016
9776	7022^13211-13211^7022	50816	Norbert Schneider	12/2017
9777	2^168795+5385	50813	Lelio R Paula	05/2009
9778	7670^13079-13079^7670	50810	Norbert Schneider	09/2017
9779	4*3^106483+5	50806	Lelio R Paula	03/2014
9780	13^45606+4	50803	Lelio R Paula	01/2013
9781	13^45606-38	50803	Lelio R Paula	01/2013
9782	2^168746+58905	50798	Lelio R Paula	05/2009
9783	(16*10^50795-43)/9	50796	Robert Price	02/2015
9784	gcd(V(615445),5F(123089)(F(123089)-1)+1)	50794	Serge Batalov	04/2015
9785	7*10^50789-47	50790	Robert Price	02/2017
9786	2^168717-729523	50789	Paul Bourdelais	11/2012
9787	(12409^12409+136)/5^2/13/5647/473279	50788	Makoto Morimoto	07/2016
9788	(21*2^168652-1)/215	50769	Lelio R Paula	01/2014
9789	2^168629+12909	50763	Lelio R Paula	01/2011
9790	9328^12787+12787^9328	50762	Norbert Schneider	01/2016
9791	2^168627+73113	50762	Enzo Doria	04/2016
9792	2^168623+47333	50761	Yves Minet	02/2010
9793	(8*10^50750-101)/3	50751	Robert Price	10/2017
9794	(12401^12401+154)/3^2/5/31/59/67/97/761/863/12143	50745	Makoto Morimoto	07/2016
9795	(lucasV(1,2,337126)+2)/(5*11)	50739	Mike Oakes	02/2017
9796	3*10^50727-31	50728	Robert Price	10/2017
9797	6152^13387-13387^6152	50724	Norbert Schneider	03/2018
9798	8544^12901-12901^8544	50723	Norbert Schneider	05/2017
9799	(17^41221+1)/18	50720	Paul Bourdelais	03/2010
9800	10^50711+7	50712	Jason Earls	12/2007
9801	10^50711-317969	50711	Patrick De Geest	04/2009
9802	(17^41213+3^41213)/20	50710	Robert Price	08/2013
9803	(12391^12391+58)/59/211/7823	50710	Makoto Morimoto	07/2016
9804	47779!4+1024	50708	Robert Price	08/2017
9806	2^168431-159	50703	Lelio R Paula	01/2011
9805	(7*10^50702-1)/3	50703	Erik Branger	03/2014
9807	117216#-p(117216)	50700	Henri Lifchitz	03/2007
9808	(1543550^8192+1)/65537	50692	Syoichiro Yamada	06/2008
9809	(13*2^168352-1)/477	50678	Lelio R Paula	01/2014
9810	8*10^50675+39	50676	Robert Price	01/2017
9811	(lucasV(1,2,336840)+2)/(1133372360970589125621*144481)	50676	Mike Oakes	02/2017
9812	14415^3274+3274^14415	50670	Hans Havermann	05/2016
9813	(12379^12379+282)/17	50663	Makoto Morimoto	07/2016
9815	5^72480-17126	50662	Enzo Doria	02/2013
9814	(34*10^50667-7)/9/3^3/136277	50662	Makoto Morimoto	04/2016
9816	3^106143+2	50644	Mike Oakes	11/2009
9817	9178^12777-12777^9178	50633	Norbert Schneider	02/2017
9818	(2*10^50603-41)/3	50603	Robert Price	01/2017
9819	(12^46889-1)/11	50601	Paul Bourdelais	09/2008
9820	2^168068-1893	50594	Yves Minet	09/2012
9821	2^168057+8415	50591	Lelio R Paula	11/2011
9822	4*10^50579+9	50580	Robert Price	05/2015
9823	2^168019-94395	50579	Lelio R Paula	07/2011
9825	2^168019+74213	50579	Enzo Doria	04/2016
9824	(47*10^50578+493)/9	50579	Robert Price	11/2017
9826	5925^13406-13406^5925	50577	Norbert Schneider	03/2018
9827	3^106002+70	50576	Lelio R Paula	07/2012
9828	5*2^167970-9	50565	Lelio R Paula	02/2014
9829	(58*10^50558-13)/9	50559	Robert Price	09/2015
9830	88*10^50547+7	50549	Robert Price	11/2016
9831	2^167910-112625	50546	Enzo Doria	06/2014
9832	(1476500^8192+1)/65537	50534	Syoichiro Yamada	06/2008
9833	2^167866+11715	50533	Lelio R Paula	05/2009
9834	gcd(V(621415),5F(124283)(F(124283)+1)+1)	50528	Serge Batalov	04/2015
9835	2^167847-135	50527	Lelio R Paula	01/2011
9836	-lucasV(-1,2,335684)	50526	Mike Oakes	01/2017
9837	(-lucasV(1,2,335677)+2)/(3*226777)	50519	Mike Oakes	02/2017
9838	(12347^12347+1567)/2/3^2/5	50517	Makoto Morimoto	07/2016
9840	2^167807+75	50515	Lelio R Paula	08/2010
9839	2^167805+76277	50515	Enzo Doria	04/2016
9841	8335^12882+12882^8335	50510	Norbert Schneider	03/2016
9842	7*2^167777+9	50507	Lelio R Paula	02/2014
9843	14162^3681+3681^14162	50502	Hans Havermann	05/2016
9844	(17*10^50495-11)/3	50496	Robert Price	07/2015
9845	2^167682+85	50478	Lelio R Paula	08/2010
9846	2^167667-927427	50473	Paul Bourdelais	11/2012
9847	9737^12654+12654^9737	50470	Norbert Schneider	01/2016
9848	(9179*2^167644-1)/17	50469	Lelio R Paula	03/2015
9849	13386^5891+5891^13386	50468	Hans Havermann	05/2016
9850	(10^50467-97)/3	50467	Robert Kinser	10/2017
9851	(lucasV(1,2,335347)+2)/(3511302287439661)	50462	Mike Oakes	02/2017
9852	152^23124+151	50453	Eric Chen	04/2018
9853	5003^13637-156	50447	Enzo Doria	07/2012
9854	6^64826-26723	50445	Enzo Doria	03/2013
9855	(3^105718+7)/32	50439	Lelio R Paula	03/2012
9856	(1436724^8192+1)/65537	50437	Syoichiro Yamada	06/2008
9857	17^40989+56	50435	Lelio R Paula	01/2013
9858	(12329^12329+1652)/421	50435	Makoto Morimoto	07/2016
9859	2*5^72153+7	50434	Lelio R Paula	09/2014
9860	(3126^14431-1)/3125	50433	Richard Fischer	03/2015
9861	8078^12907-12907^8078	50432	Norbert Schneider	05/2017
9862	39^31694+38	50428	Norbert Schneider	05/2014
9863	(7*10^50414-151)/9	50414	Robert Price	09/2017
9864	2^167460+2187	50411	Lelio R Paula	11/2011
9865	(12323^12323+2709)/2^4	50409	Makoto Morimoto	07/2016
9866	11^48400-7710	50404	Enzo Doria	02/2013
9867	2^167432+54615	50403	Lelio R Paula	05/2009
9868	(23*2^167430-1)/4169	50400	Lelio R Paula	01/2014
9869	68677!6-2	50395	Robert Price	07/2017
9870	19^39404+22	50389	Lelio R Paula	01/2013
9871	(102^25087-1)/101	50388	Richard Fischer	08/2017
9872	35^32629-7834	50382	Enzo Doria	03/2013
9873	6^64744+163	50381	Lelio R Paula	06/2012
9874	116447#+174659	50381	Nicolas PALAU	09/2016
9876	2^167353+129	50379	Lelio R Paula	05/2009
9875	20^38722-1133	50379	Enzo Doria	03/2013
9878	3^105567-16	50369	Lelio R Paula	07/2012
9877	2^167321-112849	50369	Enzo Doria	06/2014
9879	(28*10^50362-43)/3	50363	Robert Price	04/2016
9880	11421^12410-12410^11421	50357	Norbert Schneider	08/2013
9881	2^167278-2063	50356	Yves Minet	03/2013
9882	181^22300+22300^181	50347	Serge Batalov	05/2014
9883	9932^12595-12595^9932	50343	Norbert Schneider	12/2016
9884	8993^12732-12732^8993	50342	Norbert Schneider	02/2017
9885	3*5^72018-4	50339	Lelio R Paula	09/2014
9886	2^167207-112687	50335	Enzo Doria	06/2014
9887	6^64674-37	50327	Lelio R Paula	06/2012
9888	2^167177+74801	50326	Enzo Doria	04/2016
9889	13739^4600+4600^13739	50323	Hans Havermann	10/2015
9890	11508^12391+12391^11508	50320	Norbert Schneider	06/2014
9891	2^167132-2163	50312	Yves Minet	08/2013
9892	7^59527-62	50307	Lelio R Paula	06/2012
9894	(310027^9161+1)/310028	50302	Faysal YAtim	04/2008
9893	(12301^12301+74)/3^2/5^3/11/17/1151	50302	Makoto Morimoto	07/2016
9895	2^167083-112519	50297	Enzo Doria	06/2014
9896	272^20659-20659^272	50296	Norbert Schneider	09/2015
9897	25337!!-16	50290	Robert Price	06/2015
9898	9722^12611-12611^9722	50290	Norbert Schneider	12/2016
9899	(15*2^167013+1)/649	50275	Lelio R Paula	07/2012
9900	19^39315-12	50275	Lelio R Paula	01/2013
9901	5^71925-36	50274	Lelio R Paula	06/2012
9902	2^167002+2799139	50273	Enzo Doria	04/2016
9903	10957^12444-12444^10957	50270	Norbert Schneider	07/2013
9904	8*10^50253-99	50254	Robert Price	02/2017
9906	5^71894-54	50252	Lelio R Paula	06/2012
9905	(127^23887+1)/128	50252	Richard Fischer	04/2017
9907	18^40028-5	50247	Lelio R Paula	01/2013
9908	(3*2^166904+1)/1279	50241	Lelio R Paula	07/2012
9909	2^166888-78557	50239	Jorge Menendez	02/2018
9910	24^36397+23	50236	Norbert Schneider	12/2013
9911	7984*29^34345+21	50230	Curtis Bright	05/2015
9912	3^105248-13528	50217	Enzo Doria	02/2013
9913	6^64532-65	50216	Lelio R Paula	06/2012
9914	5^71834-20616	50210	Enzo Doria	03/2013
9915	(31*2^166778-1)/3651	50204	Lelio R Paula	01/2014
9916	2^166752-112397	50198	Enzo Doria	06/2014
9917	(12277^12277+1746)/17/37/151	50197	Makoto Morimoto	07/2016
9918	11^48199-930	50195	Enzo Doria	11/2012
9919	3*10^50194-7	50195	Erik Branger	11/2013
9920	9992^12549+12549^9992	50192	Norbert Schneider	10/2015
9921	2^166708+157	50185	Lelio R Paula	01/2011
9922	(1338272^8192+1)/65537	50184	Syoichiro Yamada	06/2008
9923	7*2^166685+3	50179	Lelio R Paula	02/2014
9924	(104^24877+1)/105	50176	Richard Fischer	02/2018
9925	7*2^166671-9	50174	Lelio R Paula	02/2014
9926	9*2^166670+7	50174	Lelio R Paula	02/2014
9927	2^166670-112541	50173	Enzo Doria	06/2014
9928	6149^13242-13242^6149	50172	Norbert Schneider	01/2018
9929	2^166657+465	50169	Lelio R Paula	11/2011
9930	17^40768-20	50163	Lelio R Paula	01/2013
9932	2^166596-78795	50151	Lelio R Paula	07/2011
9931	135^23541+134	50151	Norbert Schneider	04/2015
9933	24^36335-673	50150	Enzo Doria	03/2013
9934	(12269^12269+291)/2^8/5/7/19/41/109/10426349	50150	Makoto Morimoto	07/2016
9935	(52*10^50149+119)/9	50150	Robert Price	10/2017
9936	(28*10^50147-97)/3	50148	Robert Price	07/2016
9937	263^20718-20718^263	50137	Norbert Schneider	09/2015
9938	t(167020)	50133	Robert Price	01/2015
9939	(12263^12263+1442)/127/5479	50133	Makoto Morimoto	07/2016
9940	2868(2340(29023#-29527)(2340(29023#-29527)+3)+1)(2868(2340(29023#-29527)(2340*(29023#-29527)	50129	Pierre CAMI	06/2008
9941	12^46445-19	50123	Lelio R Paula	12/2012
9942	2^166501-14593	50122	Enzo Doria	04/2013
9943	(31*2^166509-1)/3684077	50120	Lelio R Paula	01/2014
9944	2^166483-169	50117	Lelio R Paula	01/2011
9945	(188^22037+1)/189	50114	Eric Chen	09/2017
9946	9^52515+2*6^52515-4^52515	50113	Mike Oakes	04/2010
9947	(23*2^166487-1)/33770499	50112	Lelio R Paula	01/2014
9948	2*5^71689-9	50109	Lelio R Paula	09/2014
9949	13495^5154+5154^13495	50096	Hans Havermann	04/2016
9951	6^64369-119	50089	Lelio R Paula	06/2012
9950	9224^12633-12633^9224	50089	Norbert Schneider	12/2016
9952	2^166370-112541	50083	Enzo Doria	06/2014
9953	(12253^12253+1454)/3^3/251/947/292427	50081	Makoto Morimoto	07/2016
9954	2^166339-112321	50074	Enzo Doria	06/2014
9955	5^71637-22	50073	Lelio R Paula	06/2012
9956	Phi(50131,10)/89010999409/9123691040118653/18020045580157867/30621915318063801947	50068	Maksym Voznyy	01/2013
9957	(4*10^50060+137)/3	50061	Robert Price	07/2017
9958	5^71618-13826	50059	Enzo Doria	02/2013
9959	15^42563-2	50058	Lelio R Paula	11/2012
9960	1943^15222+15222^1943	50058	Serge Batalov	05/2014
9961	183^22125-2	50057	Lelio R Paula	10/2017
9962	11641^12310+12310^11641	50053	Norbert Schneider	04/2014
9963	13537!-2^13537+1	50052	Joe McLean	06/2006
9964	2^166227-164467	50040	Gary Barnes	08/2009
9965	12241^12241+4756	50039	Makoto Morimoto	07/2016
9966	(106*10^50035-1)/3	50037	Serge Batalov	12/2014
9967	11^48044-810	50033	Enzo Doria	11/2012
9968	15^42539+88	50030	Lelio R Paula	11/2012
9969	524^18397-523^18397	50028	Jean-Louis Charton	10/2009
9970	2^166159-14497	50019	Enzo Doria	04/2013
9971	2^166155+87855	50018	Lelio R Paula	01/2009
9973	2^166138-11655	50013	Lelio R Paula	07/2011
9972	(L(239313)-1)/5-2^9551	50013	Jorge Menendez	06/2017
9974	6487^13118-13118^6487	50007	Norbert Schneider	10/2017
9975	(16*10^50005+41)/3	50006	Robert Price	10/2017
9980	2^166104-112625	50003	Enzo Doria	06/2014
9976	(L(239265)-1)/5-2^906	50003	Jorge Menendez	03/2017
9977	(L(239265)-1)/5-2^3152	50003	Jorge Menendez	04/2017
9978	(L(239265)-1)/5-2^20155	50003	Jorge Menendez	04/2017
9979	(L(239265)-1)/5-2^78912	50003	Jorge Menendez	04/2017
9981	2^166100+199015	50002	Lelio R Paula	05/2008
9987	10^50000+65859	50001	Milton L. Brown	02/2006
9982	(598*10^49999-31)/9	50001	Robert Price	02/2017
9983	10^50000+5810927216133	50001	Jorge Menendez	09/2017
9984	10^50000+5810927605377	50001	Jorge Menendez	09/2017
9985	10^50000+5810927658379	50001	Jorge Menendez	09/2017
9986	10^50000+5810927672223	50001	Jorge Menendez	09/2017
9988	10^49999+91701	50000	Patrick De Geest	03/2005
9989	10^50000-194303	50000	Patrick De Geest	02/2009
9990	(2^74207281/10^948782)%10^50000	50000	Michael Vang	04/2016
9991	(2^57885161/10^11608093)%10^50000	50000	Michael Vang	05/2016
9992	(2^43112609/10^788658)%10^50000	50000	Michael Vang	05/2016
9993	(2^42643801/10^3670320)%10^50000	50000	Michael Vang	05/2016
9994	(2^37156667/10^412682)%10^50000	50000	Michael Vang	05/2016
9995	(2^32582657/10^7836670)%10^50000	50000	Michael Vang	05/2016
9996	(2^24036583/10^3069021)%10^50000	50000	Michael Vang	05/2016
9997	(2^25964951/10^5214128)%10^50000	50000	Michael Vang	05/2016
9998	(2^13466917/10^157937)%10^50000	50000	Michael Vang	05/2016
9999	(2^20996011/10^6193479)%10^50000	50000	Michael Vang	05/2016
10000	(2^6972593/10^381525)%10^50000	50000	Michael Vang	05/2016

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