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	27350^6981+6981^27350	105132	Hans Havermann	09/2020
6753	9*2^349220+5	105127	Lelio R Paula	09/2014
6752	(2^349225+3122)/2	105127	Stefano Morozzi	09/2020
6754	7*3^220317+8	105119	Lelio R Paula	09/2014
6755	7^124386+88	105119	Lelio R Paula	11/2016
6756	(2^349197+570)/2	105119	Stefano Morozzi	09/2020
6757	2^349171-19657	105111	Enzo Doria	06/2013
6758	(2^349115+590)/2	105094	Stefano Morozzi	09/2020
6759	(2^(6*58185+1)-5)/3	105093	Kevin Acres	11/2013
6760	(2^349111-5)/3	105093	Lelio R Paula	12/2013
6761	675^37142+37142^675	105087	Norbert Schneider	08/2018
6762	2^348981-2797573	105054	Enzo Doria	04/2016
6763	2^348869-6555	105021	Lelio R Paula	01/2017
6764	5^150217+78	104998	Lelio R Paula	11/2016
6765	(88*10^104989-1)/3	104991	Robert Price	04/2020
6766	(28*10^104972+149)/3	104973	Robert Price	12/2019
6767	24927^16262+16262^24927	104972	Hans Havermann	10/2020
6768	2^348703-113005	104971	Enzo Doria	06/2014
6769	(191*10^104956-17)/3	104958	Robert Price	11/2021
6771	2^348612-809	104943	Yves Minet	05/2013
6770	(73*10^104942-1)/9	104943	Robert Price	01/2015
6772	2^348583-350407	104934	Enzo Doria	06/2015
6773	2^348531-949	104919	Yves Minet	05/2012
6774	20^80636-59	104910	Lelio R Paula	12/2016
6775	8*10^104893-13	104894	Robert Price	08/2019
6777	2^348437+35	104890	Lelio R Paula	09/2011
6776	25208^14487+14487^25208	104890	Hans Havermann	09/2020
6778	2^348348+135	104864	Lelio R Paula	09/2011
6779	(29*10^104858+349)/9	104859	Robert Price	06/2021
6780	6*10^104852-31	104853	Robert Price	07/2020
6782	(2^348284+9)/25	104843	Lelio R Paula	12/2013
6781	75^55914-74	104843	Norbert Schneider	01/2015
6783	2^348268+255255	104840	Lelio R Paula	01/2017
6784	35540^891+891^35540	104839	Hans Havermann	09/2020
6785	5^149985-52	104836	Lelio R Paula	11/2016
6786	2^348224-20249	104826	Enzo Doria	06/2013
6787	(2^348217+2522)/2	104824	Stefano Morozzi	09/2020
6788	2^348212-20105	104823	Enzo Doria	06/2013
6789	24647^17898+17898^24647	104819	Hans Havermann	10/2020
6790	20^80562+19	104814	Lelio R Paula	12/2016
6791	2*10^104811-87	104812	Robert Price	04/2018
6792	2^348149-20053	104804	Enzo Doria	06/2013
6793	2^348095-171	104788	Lelio R Paula	09/2011
6794	25383^13412+13412^25383	104769	Hans Havermann	09/2020
6795	2^348003-20377	104760	Enzo Doria	06/2013
6796	2^347994-741	104757	Lelio R Paula	12/2016
6797	(2^347993+2234)/2	104757	Stefano Morozzi	01/2021
6798	(2^347990+790)/2	104756	Stefano Morozzi	09/2020
6799	25137^14702+14702^25137	104756	Hans Havermann	09/2020
6800	(13*2^347972-1)/282309	104746	Lelio R Paula	03/2014
6801	12883^25484-25484^12883	104740	Norbert Schneider	08/2022
6802	2^347910-109937	104732	Enzo Doria	04/2014
6803	(88*10^104709-637)/9	104710	Robert Price	11/2020
6804	(13*10^104702+71)/3	104703	Robert Price	06/2021
6805	5^149794+28	104702	Lelio R Paula	11/2016
6806	105^51800-2	104698	Lelio R Paula	10/2017
6807	(16^86939+3^86939)/19	104684	Robert Price	06/2013
6808	(15^89009-1)/14	104682	Paul Bourdelais	03/2010
6809	2^347731-18609	104678	Enzo Doria	05/2013
6810	4*6^134519+7	104677	Lelio R Paula	11/2014
6811	(34*10^104672-259)/9	104673	Robert Price	12/2021
6812	25321^13588+13588^25321	104656	Hans Havermann	09/2020
6813	2^347625+5367	104646	Riley Fisher	04/2023
6814	2^347612-18545	104642	Enzo Doria	05/2013
6817	6^134465+95	104635	Lelio R Paula	11/2016
6816	(2^347588+3718)/2	104635	Stefano Morozzi	09/2020
6815	(166*10^104633-7)/3	104635	Robert Price	11/2020
6818	2^347517-17301	104614	Enzo Doria	05/2013
6819	(2^347493+3186)/2	104606	Stefano Morozzi	09/2020
6820	(2^347490+2574)/2	104605	Stefano Morozzi	09/2020
6821	3^219222-310	104596	Lelio R Paula	11/2016
6822	25993^10554+10554^25993	104581	Hans Havermann	09/2020
6823	(15*2^347399-1)/13	104578	Lelio R Paula	03/2014
6824	2^347372-17853	104570	Enzo Doria	05/2013
6825	2^347314+99	104552	Lelio R Paula	09/2011
6826	2^347300-22233	104548	Enzo Doria	06/2013
6827	2^347287-19845	104544	Enzo Doria	06/2013
6828	2^347258-231191	104536	Harrison Mesh	06/2022
6829	(31*2^347254-1)/891	104533	Lelio R Paula	03/2014
6830	5F(250091)(F(250091)-1)+1	104532	Serge Batalov	04/2015
6831	7*2^347239-3	104531	Lelio R Paula	09/2014
6832	(3^219098-8)/514147439969	104525	Lelio R Paula	12/2013
6833	5*3^219047+8	104513	Lelio R Paula	09/2014
6834	2^347148-109073	104502	Enzo Doria	04/2014
6835	2^347129-20145	104497	Enzo Doria	06/2013
6836	4*10^104461-57	104462	Robert Price	10/2018
6837	(710^(252227+1)+9*10^52227-7)/9	104455	Robert Price	10/2023
6838	(2^346989+590)/2	104454	Stefano Morozzi	09/2020
6839	2^346923-19585	104435	Enzo Doria	05/2013
6840	(11*2^346864-1)/175	104416	Lelio R Paula	03/2014
6841	2^346854+346854^2+1	104414	Robert Price	06/2014
6842	2^346834+11715	104408	Lelio R Paula	04/2015
6843	24276^19961+19961^24276	104392	Hans Havermann	09/2020
6844	79^55009+78	104387	Norbert Schneider	02/2015
6845	3^218744+58	104368	Lelio R Paula	11/2016
6846	9*10^104361+89	104362	Robert Price	11/2019
6847	25048^14665+14665^25048	104358	Hans Havermann	09/2020
6848	2^346649+65	104352	Lelio R Paula	09/2011
6849	(19*33^68718-600883)/32	104350	Eric Chen	05/2023
6850	2^346638-17265	104349	Enzo Doria	05/2013
6851	(2^346606+2082)/2	104339	Stefano Morozzi	09/2020
6852	(2^346607+2070)/2	104339	Stefano Morozzi	09/2020
6853	(2^346582+3202)/2	104332	Stefano Morozzi	09/2020
6854	26092^9967+9967^26092	104331	Hans Havermann	09/2020
6855	5*10^104326+77	104327	Robert Price	12/2018
6856	(2^346564+2026)/2	104326	Stefano Morozzi	09/2020
6857	(8925^26569-1)/(8925^163-1)	104320	Ryan Propper	11/2023
6860	2^346527-111817	104316	Enzo Doria	05/2014
6859	6^134055+101	104316	Lelio R Paula	11/2016
6858	fibonacci(499147)-4	104316	Jon Grantham	08/2023
6861	92105!4+8	104312	Robert Price	09/2019
6862	(7^123407-5^123407)/2	104291	Jon Grantham	08/2023
6863	6^134013+163	104283	Lelio R Paula	11/2016
6864	10^(2*52140+1)-10^52140-1	104281	Robert Price	07/2023
6865	(22*10^104272-61)/3	104273	Robert Price	03/2022
6866	(2^346318+862)/2	104252	Stefano Morozzi	02/2021
6868	18^83049-89	104250	Lelio R Paula	01/2017
6867	(2^346311+606)/2	104250	Stefano Morozzi	09/2020
6869	(166*10^104230+11)/3	104232	Robert Price	03/2021
6870	2^346213+484049	104221	Enzo Doria	04/2017
6871	18^83021-91	104214	Lelio R Paula	01/2017
6872	10^104212+128779	104213	Patrick De Geest	05/2016
6873	10^104212+237447	104213	Patrick De Geest	05/2016
6874	10^104212+242139	104213	Patrick De Geest	05/2016
6875	10^104212+269199	104213	Patrick De Geest	05/2016
6876	24254^19803+19803^24254	104213	Hans Havermann	09/2020
6877	(10^104212-71)/1	104212	Serge Batalov	12/2014
6878	23678^23821-23821^23678	104202	Norbert Schneider	01/2020
6879	(13*31^69863+12407)/30	104191	Eric Chen	04/2024
6880	2^346078+7695	104180	Lelio R Paula	12/2016
6881	2^346055-19537	104173	Enzo Doria	05/2013
6882	(3*2^346057+1)/77	104173	Lelio R Paula	12/2013
6883	2^346037-20125	104168	Enzo Doria	06/2013
6884	(34*10^104168-7)/9/13/551179	104162	Makoto Morimoto	05/2016
6885	6^133854-17993	104159	Enzo Doria	03/2013
6886	2^345990+1874239	104154	Enzo Doria	06/2016
6887	2^345988-20373	104153	Enzo Doria	06/2013
6888	(2^345965+2214)/2	104146	Stefano Morozzi	09/2020
6889	(26*10^104132-503)/9	104133	Robert Price	07/2018
6890	3*5^148968+8	104125	Lelio R Paula	11/2014
6891	(7*10^104113+53)/3	104114	Robert Price	05/2018
6892	p(21253)#/2+8	104113	Robert Price	01/2017
6893	33582^1259+1259^33582	104106	Hans Havermann	09/2020
6894	32958^1441+1441^32958	104104	Hans Havermann	09/2020
6895	29127^3748+3748^29127	104095	Hans Havermann	09/2020
6896	322^41507+41507^322	104094	Norbert Schneider	12/2014
6897	6^133768-17423	104092	Enzo Doria	03/2013
6898	2^345786-19557	104092	Enzo Doria	05/2013
6899	171^46606-2	104072	Lelio R Paula	10/2017
6900	(29*10^104071+91)/3	104072	Robert Price	04/2020
6901	norm(Mod(x,x^3-x-1)^852167-1)	104070	Paul Vanderveen	09/2022
6902	2^345704-149	104068	Lelio R Paula	09/2011
6903	25821^10712+10712^25821	104056	Hans Havermann	09/2020
6904	(2^345662+2038)/2	104055	Stefano Morozzi	09/2020
6905	6^133704-17273	104042	Enzo Doria	02/2013
6906	(3*2^345590-1)/23	104033	Lelio R Paula	03/2014
6907	(19*2^345590+1)/33859	104030	Lelio R Paula	12/2013
6908	2^345547+11	104021	Lelio R Paula	09/2011
6909	(19*10^104014-49)/3	104015	Robert Price	05/2019
6910	(2^345519+1794)/2	104012	Stefano Morozzi	01/2021
6911	2^345504+723	104008	Lelio R Paula	09/2011
6912	2^345498-20037	104006	Enzo Doria	06/2013
6914	18^82854-37	104005	Lelio R Paula	01/2017
6913	(2^345497+2070)/2	104005	Stefano Morozzi	09/2020
6915	2^345486-109065	104002	Enzo Doria	04/2014
6916	2^345487-1851507	104002	Enzo Doria	08/2015
6917	2^345476+777	103999	Lelio R Paula	09/2011
6918	(2^345477+1554)/2	103999	Stefano Morozzi	09/2020
6919	4*10^103981-83	103982	Robert Price	10/2018
6920	(2^345327+3206)/2	103954	Stefano Morozzi	09/2020
6921	(5*2^345321-1)/3	103953	Lelio R Paula	03/2014
6922	(2^345267-9)/539049127	103927	Lelio R Paula	12/2013
6923	(19*10^103907+77)/3	103908	Robert Price	05/2019
6924	(78557*2^345163+1)/78589	103905	Lelio R Paula	07/2014
6925	2^345106-112181	103888	Enzo Doria	06/2014
6926	(2^345105+1326)/2	103887	Stefano Morozzi	02/2021
6927	2^345079+99	103880	Lelio R Paula	09/2011
6928	(2^345034+1198)/2	103866	Stefano Morozzi	09/2020
6929	11^99736-1500	103865	Enzo Doria	12/2012
6930	(569^37699-1)/568	103863	Serge Batalov	06/2022
6931	(2^345010+2082)/2	103859	Stefano Morozzi	09/2020
6932	23263^23784-23784^23263	103857	Norbert Schneider	01/2020
6933	3*10^103844+31	103845	Robert Price	06/2021
6934	444*33^68368+19	103821	Eric Chen	05/2023
6935	23927^21814+21814^23927	103813	Hans Havermann	09/2020
6936	2^344842-20157	103808	Enzo Doria	06/2013
6937	(47*2^344822+1)/1071	103801	Lelio R Paula	05/2015
6938	2^344802-20765	103796	Enzo Doria	06/2013
6939	2^344794-3821	103794	Yves Minet	05/2011
6940	2^344782-109103	103790	Enzo Doria	04/2014
6941	3^217521-112292	103784	Enzo Doria	06/2014
6942	2^344759-3505	103783	Lelio R Paula	11/2016
6943	2^344735-147	103776	Lelio R Paula	09/2011
6944	L(496533)-p(496533)	103770	Robert Price	02/2018
6945	2*10^103749-69	103750	Robert Price	03/2018
6946	(55459*2^344617+1)/3	103745	Lelio R Paula	07/2014
6947	2^344607-108891	103738	Enzo Doria	03/2014
6949	(2^344608+3798)/2	103738	Stefano Morozzi	02/2021
6948	(1097^34123-1)/1096	103738	Serge Batalov	06/2022
6950	2^344560+22411	103723	Enzo Doria	09/2023
6951	(148*10^103718-1)/3	103720	Robert Price	03/2020
6952	2^344541-19561	103718	Enzo Doria	05/2013
6953	(1017*2^344529-1)/569	103714	Lelio R Paula	05/2015
6954	(8896^26263-1)/8895	103714	Serge Batalov	06/2022
6955	(2^344503+1758)/2	103706	Stefano Morozzi	09/2020
6956	(4*10^103703-1)/3	103704	Serge Batalov	08/2009
6957	2^344444-455	103688	Yves Minet	03/2012
6958	(4*10^103678-43)/3	103679	Robert Price	01/2022
6959	(1353^238539617^9)/10^307661	103673	Hans Havermann	06/2017
6960	(2^344367+2738)/2	103665	Stefano Morozzi	01/2021
6962	2^344317-109933	103650	Enzo Doria	04/2014
6961	26055^9508+9508^26055	103650	Hans Havermann	09/2020
6963	2^344309-1852033	103648	Enzo Doria	08/2015
6964	25729^10672+10672^25729	103643	Hans Havermann	09/2020
6965	(2^344289+1166)/2	103642	Stefano Morozzi	09/2020
6966	3*10^103637+61	103638	Robert Price	09/2020
6967	(2^344246+1614)/2	103629	Stefano Morozzi	09/2020
6968	2^344213-21253	103619	Enzo Doria	06/2013
6969	2^344196-465	103614	Lelio R Paula	11/2016
6970	2^344187-20001	103611	Enzo Doria	06/2013
6971	(117191#+(355573#)/(117191#))/(200233679)	103602	Makoto Morimoto	10/2017
6972	(237^43627-1)/236	103601	Serge Batalov	06/2022
6973	20^79621-19^79621	103590	Jean-Louis Charton	03/2011
6974	Phi(155391,10)/1243129	103586	Maksym Voznyy	09/2015
6975	(9^108553-2^108553)/7	103586	Jon Grantham	07/2023
6976	2^344085-20365	103580	Enzo Doria	06/2013
6977	5^148169+54	103566	Lelio R Paula	11/2016
6978	2^344017-108795	103560	Enzo Doria	03/2014
6979	(2^343974+2670)/2	103547	Stefano Morozzi	09/2020
6980	2^343971-5077	103546	Lelio R Paula	09/2011
6981	(7*10^103531+71)/3	103532	Robert Price	05/2018
6982	2^343899+141	103524	Lelio R Paula	08/2011
6983	(2^343933+1)/(3*98294339989393)	103520	Gord Palameta	08/2018
6984	6^133029-67	103517	Lelio R Paula	11/2016
6985	(17*2^343877+1)/13625	103515	Lelio R Paula	12/2013
6986	66*10^103507+7	103509	Robert Price	07/2020
6987	26297^8614+8614^26297	103485	Hans Havermann	09/2020
6988	(2^343764+2658)/2	103483	Stefano Morozzi	09/2020
6989	26499^8036+8036^26499	103480	Hans Havermann	09/2020
6990	(136*10^103474-1)/9	103476	Serge Batalov	12/2014
6991	5^148014-24	103458	Lelio R Paula	11/2016
6992	28316^4503+4503^28316	103453	Hans Havermann	09/2020
6993	(22*10^103450+53)/3	103451	Robert Price	07/2019
6994	2^343604+9931	103436	Yves Minet	01/2011
6995	2^343601-21189	103435	Enzo Doria	06/2013
6996	(10^103423+173)/3	103423	Robert Price	05/2021
6997	2^343508-115229	103407	Enzo Doria	06/2015
6998	(8766^26227-1)/8765	103404	Serge Batalov	06/2022
6999	(509203*2^343491-1)/16147	103403	Lelio R Paula	05/2015
7000	3^216685-113056	103386	Enzo Doria	07/2014

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