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 ?
6751	2^350253-20365	105437	Enzo Doria	06/2013
6752	(3*29^72089-1075)/4	105423	Curtis Bright	05/2015
6753	(2^350187+2658)/2	105417	Stefano Morozzi	09/2020
6754	4*10^105415-69	105416	Robert Price	01/2022
6755	(22*10^105407+179)/3	105408	Robert Price	02/2022
6756	2^350139-109009	105403	Enzo Doria	04/2014
6757	(2^350129+3026)/2	105400	Stefano Morozzi	09/2020
6758	(2^350097+2070)/2	105390	Stefano Morozzi	09/2020
6759	3*5^150763+4	105380	Lelio R Paula	11/2014
6760	12^97643+91	105375	Lelio R Paula	02/2017
6761	6*5^150744-7	105367	Lelio R Paula	11/2014
6762	(2^350018+2074)/2	105366	Stefano Morozzi	09/2020
6763	4*10^105364-39	105365	Robert Price	09/2020
6765	2^349996-112169	105360	Enzo Doria	06/2014
6764	(2^349997+3702)/2	105360	Stefano Morozzi	09/2020
6766	(418*10^105343+23)/9	105345	Robert Price	02/2020
6767	25490^13563+13563^25490	105334	Hans Havermann	10/2020
6768	11^101142-1080	105329	Enzo Doria	12/2012
6769	(68*10^105320-41)/9	105321	Robert Price	10/2013
6770	24800^17649+17649^24800	105319	Hans Havermann	09/2020
6771	3^220712-9934	105307	Enzo Doria	05/2014
6772	7*10^105296+9	105297	Robert Price	09/2015
6773	89*10^105284-7	105286	Robert Price	04/2020
6774	2^349739+1873373	105282	Enzo Doria	06/2016
6775	7^124574+24	105278	Lelio R Paula	11/2016
6776	2^349708-20957	105273	Enzo Doria	06/2013
6777	34115^1218+1218^34115	105267	Hans Havermann	09/2020
6778	2^349649-20469	105255	Enzo Doria	06/2013
6779	2^349607-20109	105243	Enzo Doria	06/2013
6780	(85*10^105242+473)/9	105243	Robert Price	01/2020
6781	2^349594-19085	105239	Enzo Doria	05/2013
6782	2^349530+1874479	105220	Enzo Doria	06/2016
6783	(3^220528+8)/8081	105215	Lelio R Paula	12/2013
6784	(106*10^105199+17)/3	105201	Robert Price	04/2021
6785	(2^349452+3570)/2	105196	Stefano Morozzi	09/2020
6786	3^220464-112852	105189	Enzo Doria	07/2014
6787	2^349419-17349	105186	Enzo Doria	05/2013
6788	2^349400-2579	105180	Yves Minet	07/2014
6789	8*5^150471+3	105176	Lelio R Paula	11/2014
6790	(2^349359+2298)/2	105168	Stefano Morozzi	02/2021
6791	655^37342+37342^655	105165	Norbert Schneider	08/2018
6792	13^94403+94	105160	Lelio R Paula	12/2016
6793	2^349301-112309	105151	Enzo Doria	06/2014
6794	30291^2960+2960^30291	105149	Hans Havermann	09/2020
6795	27350^6981+6981^27350	105132	Hans Havermann	09/2020
6797	9*2^349220+5	105127	Lelio R Paula	09/2014
6796	(2^349225+3122)/2	105127	Stefano Morozzi	09/2020
6798	7*3^220317+8	105119	Lelio R Paula	09/2014
6799	7^124386+88	105119	Lelio R Paula	11/2016
6800	(2^349197+570)/2	105119	Stefano Morozzi	09/2020
6801	2^349171-19657	105111	Enzo Doria	06/2013
6802	(2^349115+590)/2	105094	Stefano Morozzi	09/2020
6803	(2^(6*58185+1)-5)/3	105093	Kevin Acres	11/2013
6804	(2^349111-5)/3	105093	Lelio R Paula	12/2013
6805	675^37142+37142^675	105087	Norbert Schneider	08/2018
6806	2^348981-2797573	105054	Enzo Doria	04/2016
6807	2^348869-6555	105021	Lelio R Paula	01/2017
6808	5^150217+78	104998	Lelio R Paula	11/2016
6809	(88*10^104989-1)/3	104991	Robert Price	04/2020
6810	(28*10^104972+149)/3	104973	Robert Price	12/2019
6811	24927^16262+16262^24927	104972	Hans Havermann	10/2020
6812	2^348703-113005	104971	Enzo Doria	06/2014
6813	(191*10^104956-17)/3	104958	Robert Price	11/2021
6815	2^348612-809	104943	Yves Minet	05/2013
6814	(73*10^104942-1)/9	104943	Robert Price	01/2015
6816	2^348583-350407	104934	Enzo Doria	06/2015
6817	2^348531-949	104919	Yves Minet	05/2012
6818	20^80636-59	104910	Lelio R Paula	12/2016
6819	8*10^104893-13	104894	Robert Price	08/2019
6821	2^348437+35	104890	Lelio R Paula	09/2011
6820	25208^14487+14487^25208	104890	Hans Havermann	09/2020
6822	2^348348+135	104864	Lelio R Paula	09/2011
6823	(29*10^104858+349)/9	104859	Robert Price	06/2021
6824	6*10^104852-31	104853	Robert Price	07/2020
6826	(2^348284+9)/25	104843	Lelio R Paula	12/2013
6825	75^55914-74	104843	Norbert Schneider	01/2015
6827	2^348268+255255	104840	Lelio R Paula	01/2017
6828	35540^891+891^35540	104839	Hans Havermann	09/2020
6829	5^149985-52	104836	Lelio R Paula	11/2016
6830	2^348224-20249	104826	Enzo Doria	06/2013
6831	(2^348217+2522)/2	104824	Stefano Morozzi	09/2020
6832	2^348212-20105	104823	Enzo Doria	06/2013
6833	24647^17898+17898^24647	104819	Hans Havermann	10/2020
6834	20^80562+19	104814	Lelio R Paula	12/2016
6835	2*10^104811-87	104812	Robert Price	04/2018
6836	2^348149-20053	104804	Enzo Doria	06/2013
6837	2^348095-171	104788	Lelio R Paula	09/2011
6838	25383^13412+13412^25383	104769	Hans Havermann	09/2020
6839	2^348003-20377	104760	Enzo Doria	06/2013
6840	2^347994-741	104757	Lelio R Paula	12/2016
6841	(2^347993+2234)/2	104757	Stefano Morozzi	01/2021
6842	(2^347990+790)/2	104756	Stefano Morozzi	09/2020
6843	25137^14702+14702^25137	104756	Hans Havermann	09/2020
6844	(13*2^347972-1)/282309	104746	Lelio R Paula	03/2014
6845	12883^25484-25484^12883	104740	Norbert Schneider	08/2022
6846	2^347910-109937	104732	Enzo Doria	04/2014
6847	(88*10^104709-637)/9	104710	Robert Price	11/2020
6848	(13*10^104702+71)/3	104703	Robert Price	06/2021
6849	5^149794+28	104702	Lelio R Paula	11/2016
6850	105^51800-2	104698	Lelio R Paula	10/2017
6851	(16^86939+3^86939)/19	104684	Robert Price	06/2013
6852	(15^89009-1)/14	104682	Paul Bourdelais	03/2010
6853	2^347731-18609	104678	Enzo Doria	05/2013
6854	4*6^134519+7	104677	Lelio R Paula	11/2014
6855	(34*10^104672-259)/9	104673	Robert Price	12/2021
6856	25321^13588+13588^25321	104656	Hans Havermann	09/2020
6857	2^347625+5367	104646	Riley Fisher	04/2023
6858	2^347612-18545	104642	Enzo Doria	05/2013
6861	6^134465+95	104635	Lelio R Paula	11/2016
6860	(2^347588+3718)/2	104635	Stefano Morozzi	09/2020
6859	(166*10^104633-7)/3	104635	Robert Price	11/2020
6862	2^347517-17301	104614	Enzo Doria	05/2013
6863	(2^347493+3186)/2	104606	Stefano Morozzi	09/2020
6864	(2^347490+2574)/2	104605	Stefano Morozzi	09/2020
6865	3^219222-310	104596	Lelio R Paula	11/2016
6866	25993^10554+10554^25993	104581	Hans Havermann	09/2020
6867	(15*2^347399-1)/13	104578	Lelio R Paula	03/2014
6868	2^347372-17853	104570	Enzo Doria	05/2013
6869	2^347314+99	104552	Lelio R Paula	09/2011
6870	2^347300-22233	104548	Enzo Doria	06/2013
6871	2^347287-19845	104544	Enzo Doria	06/2013
6872	2^347258-231191	104536	Harrison Mesh	06/2022
6873	(31*2^347254-1)/891	104533	Lelio R Paula	03/2014
6874	5F(250091)(F(250091)-1)+1	104532	Serge Batalov	04/2015
6875	7*2^347239-3	104531	Lelio R Paula	09/2014
6876	(3^219098-8)/514147439969	104525	Lelio R Paula	12/2013
6877	5*3^219047+8	104513	Lelio R Paula	09/2014
6878	2^347148-109073	104502	Enzo Doria	04/2014
6879	2^347129-20145	104497	Enzo Doria	06/2013
6880	4*10^104461-57	104462	Robert Price	10/2018
6881	(710^(252227+1)+9*10^52227-7)/9	104455	Robert Price	10/2023
6882	(2^346989+590)/2	104454	Stefano Morozzi	09/2020
6883	2^346923-19585	104435	Enzo Doria	05/2013
6884	(11*2^346864-1)/175	104416	Lelio R Paula	03/2014
6885	2^346854+346854^2+1	104414	Robert Price	06/2014
6886	2^346834+11715	104408	Lelio R Paula	04/2015
6887	24276^19961+19961^24276	104392	Hans Havermann	09/2020
6888	79^55009+78	104387	Norbert Schneider	02/2015
6889	3^218744+58	104368	Lelio R Paula	11/2016
6890	9*10^104361+89	104362	Robert Price	11/2019
6891	25048^14665+14665^25048	104358	Hans Havermann	09/2020
6892	2^346649+65	104352	Lelio R Paula	09/2011
6893	(19*33^68718-600883)/32	104350	Eric Chen	05/2023
6894	2^346638-17265	104349	Enzo Doria	05/2013
6895	(2^346606+2082)/2	104339	Stefano Morozzi	09/2020
6896	(2^346607+2070)/2	104339	Stefano Morozzi	09/2020
6897	(2^346582+3202)/2	104332	Stefano Morozzi	09/2020
6898	26092^9967+9967^26092	104331	Hans Havermann	09/2020
6899	5*10^104326+77	104327	Robert Price	12/2018
6900	(2^346564+2026)/2	104326	Stefano Morozzi	09/2020
6901	(8925^26569-1)/(8925^163-1)	104320	Ryan Propper	11/2023
6904	2^346527-111817	104316	Enzo Doria	05/2014
6903	6^134055+101	104316	Lelio R Paula	11/2016
6902	fibonacci(499147)-4	104316	Jon Grantham	08/2023
6905	92105!4+8	104312	Robert Price	09/2019
6906	(7^123407-5^123407)/2	104291	Jon Grantham	08/2023
6907	6^134013+163	104283	Lelio R Paula	11/2016
6908	10^(2*52140+1)-10^52140-1	104281	Robert Price	07/2023
6909	(22*10^104272-61)/3	104273	Robert Price	03/2022
6910	(2^346318+862)/2	104252	Stefano Morozzi	02/2021
6912	18^83049-89	104250	Lelio R Paula	01/2017
6911	(2^346311+606)/2	104250	Stefano Morozzi	09/2020
6913	(166*10^104230+11)/3	104232	Robert Price	03/2021
6914	2^346213+484049	104221	Enzo Doria	04/2017
6915	18^83021-91	104214	Lelio R Paula	01/2017
6916	10^104212+128779	104213	Patrick De Geest	05/2016
6917	10^104212+237447	104213	Patrick De Geest	05/2016
6918	10^104212+242139	104213	Patrick De Geest	05/2016
6919	10^104212+269199	104213	Patrick De Geest	05/2016
6920	24254^19803+19803^24254	104213	Hans Havermann	09/2020
6921	(10^104212-71)/1	104212	Serge Batalov	12/2014
6922	23678^23821-23821^23678	104202	Norbert Schneider	01/2020
6923	(13*31^69863+12407)/30	104191	Eric Chen	04/2024
6924	2^346078+7695	104180	Lelio R Paula	12/2016
6925	2^346055-19537	104173	Enzo Doria	05/2013
6926	(3*2^346057+1)/77	104173	Lelio R Paula	12/2013
6927	2^346037-20125	104168	Enzo Doria	06/2013
6928	(34*10^104168-7)/9/13/551179	104162	Makoto Morimoto	05/2016
6929	6^133854-17993	104159	Enzo Doria	03/2013
6930	2^345990+1874239	104154	Enzo Doria	06/2016
6931	2^345988-20373	104153	Enzo Doria	06/2013
6932	(2^345965+2214)/2	104146	Stefano Morozzi	09/2020
6933	(26*10^104132-503)/9	104133	Robert Price	07/2018
6934	3*5^148968+8	104125	Lelio R Paula	11/2014
6935	(7*10^104113+53)/3	104114	Robert Price	05/2018
6936	p(21253)#/2+8	104113	Robert Price	01/2017
6937	33582^1259+1259^33582	104106	Hans Havermann	09/2020
6938	32958^1441+1441^32958	104104	Hans Havermann	09/2020
6939	29127^3748+3748^29127	104095	Hans Havermann	09/2020
6940	322^41507+41507^322	104094	Norbert Schneider	12/2014
6941	6^133768-17423	104092	Enzo Doria	03/2013
6942	2^345786-19557	104092	Enzo Doria	05/2013
6943	171^46606-2	104072	Lelio R Paula	10/2017
6944	(29*10^104071+91)/3	104072	Robert Price	04/2020
6945	norm(Mod(x,x^3-x-1)^852167-1)	104070	Paul Vanderveen	09/2022
6946	2^345704-149	104068	Lelio R Paula	09/2011
6947	25821^10712+10712^25821	104056	Hans Havermann	09/2020
6948	(2^345662+2038)/2	104055	Stefano Morozzi	09/2020
6949	6^133704-17273	104042	Enzo Doria	02/2013
6950	(3*2^345590-1)/23	104033	Lelio R Paula	03/2014
6951	(19*2^345590+1)/33859	104030	Lelio R Paula	12/2013
6952	2^345547+11	104021	Lelio R Paula	09/2011
6953	(19*10^104014-49)/3	104015	Robert Price	05/2019
6954	(2^345519+1794)/2	104012	Stefano Morozzi	01/2021
6955	2^345504+723	104008	Lelio R Paula	09/2011
6956	2^345498-20037	104006	Enzo Doria	06/2013
6958	18^82854-37	104005	Lelio R Paula	01/2017
6957	(2^345497+2070)/2	104005	Stefano Morozzi	09/2020
6959	2^345486-109065	104002	Enzo Doria	04/2014
6960	2^345487-1851507	104002	Enzo Doria	08/2015
6961	2^345476+777	103999	Lelio R Paula	09/2011
6962	(2^345477+1554)/2	103999	Stefano Morozzi	09/2020
6963	4*10^103981-83	103982	Robert Price	10/2018
6964	(2^345327+3206)/2	103954	Stefano Morozzi	09/2020
6965	(5*2^345321-1)/3	103953	Lelio R Paula	03/2014
6966	(2^345267-9)/539049127	103927	Lelio R Paula	12/2013
6967	(19*10^103907+77)/3	103908	Robert Price	05/2019
6968	(78557*2^345163+1)/78589	103905	Lelio R Paula	07/2014
6969	2^345106-112181	103888	Enzo Doria	06/2014
6970	(2^345105+1326)/2	103887	Stefano Morozzi	02/2021
6971	2^345079+99	103880	Lelio R Paula	09/2011
6972	(2^345034+1198)/2	103866	Stefano Morozzi	09/2020
6973	11^99736-1500	103865	Enzo Doria	12/2012
6974	(569^37699-1)/568	103863	Serge Batalov	06/2022
6975	(2^345010+2082)/2	103859	Stefano Morozzi	09/2020
6976	23263^23784-23784^23263	103857	Norbert Schneider	01/2020
6977	3*10^103844+31	103845	Robert Price	06/2021
6978	444*33^68368+19	103821	Eric Chen	05/2023
6979	23927^21814+21814^23927	103813	Hans Havermann	09/2020
6980	2^344842-20157	103808	Enzo Doria	06/2013
6981	(47*2^344822+1)/1071	103801	Lelio R Paula	05/2015
6982	2^344802-20765	103796	Enzo Doria	06/2013
6983	2^344794-3821	103794	Yves Minet	05/2011
6984	2^344782-109103	103790	Enzo Doria	04/2014
6985	3^217521-112292	103784	Enzo Doria	06/2014
6986	2^344759-3505	103783	Lelio R Paula	11/2016
6987	2^344735-147	103776	Lelio R Paula	09/2011
6988	L(496533)-p(496533)	103770	Robert Price	02/2018
6989	2*10^103749-69	103750	Robert Price	03/2018
6990	(55459*2^344617+1)/3	103745	Lelio R Paula	07/2014
6991	2^344607-108891	103738	Enzo Doria	03/2014
6993	(2^344608+3798)/2	103738	Stefano Morozzi	02/2021
6992	(1097^34123-1)/1096	103738	Serge Batalov	06/2022
6994	2^344560+22411	103723	Enzo Doria	09/2023
6995	(148*10^103718-1)/3	103720	Robert Price	03/2020
6996	2^344541-19561	103718	Enzo Doria	05/2013
6997	(1017*2^344529-1)/569	103714	Lelio R Paula	05/2015
6998	(8896^26263-1)/8895	103714	Serge Batalov	06/2022
6999	(2^344503+1758)/2	103706	Stefano Morozzi	09/2020
7000	(4*10^103703-1)/3	103704	Serge Batalov	08/2009

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