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 ?
5751	655^37342+37342^655	105165	Norbert Schneider	08/2018
5752	13^94403+94	105160	Lelio R Paula	12/2016
5753	2^349301-112309	105151	Enzo Doria	06/2014
5754	30291^2960+2960^30291	105149	Hans Havermann	09/2020
5755	27350^6981+6981^27350	105132	Hans Havermann	09/2020
5757	9*2^349220+5	105127	Lelio R Paula	09/2014
5756	(2^349225+3122)/2	105127	Stefano Morozzi	09/2020
5758	7*3^220317+8	105119	Lelio R Paula	09/2014
5759	7^124386+88	105119	Lelio R Paula	11/2016
5760	(2^349197+570)/2	105119	Stefano Morozzi	09/2020
5761	2^349171-19657	105111	Enzo Doria	06/2013
5762	(2^349115+590)/2	105094	Stefano Morozzi	09/2020
5763	(2^(6*58185+1)-5)/3	105093	Kevin Acres	11/2013
5764	(2^349111-5)/3	105093	Lelio R Paula	12/2013
5765	675^37142+37142^675	105087	Norbert Schneider	08/2018
5766	2^348981-2797573	105054	Enzo Doria	04/2016
5767	2^348869-6555	105021	Lelio R Paula	01/2017
5768	5^150217+78	104998	Lelio R Paula	11/2016
5769	(88*10^104989-1)/3	104991	Robert Price	04/2020
5770	(28*10^104972+149)/3	104973	Robert Price	12/2019
5771	24927^16262+16262^24927	104972	Hans Havermann	10/2020
5772	2^348703-113005	104971	Enzo Doria	06/2014
5773	(191*10^104956-17)/3	104958	Robert Price	11/2021
5775	2^348612-809	104943	Yves Minet	05/2013
5774	(73*10^104942-1)/9	104943	Robert Price	01/2015
5776	2^348583-350407	104934	Enzo Doria	06/2015
5777	2^348531-949	104919	Yves Minet	05/2012
5778	20^80636-59	104910	Lelio R Paula	12/2016
5779	8*10^104893-13	104894	Robert Price	08/2019
5781	2^348437+35	104890	Lelio R Paula	09/2011
5780	25208^14487+14487^25208	104890	Hans Havermann	09/2020
5782	2^348348+135	104864	Lelio R Paula	09/2011
5783	(29*10^104858+349)/9	104859	Robert Price	06/2021
5784	6*10^104852-31	104853	Robert Price	07/2020
5786	(2^348284+9)/25	104843	Lelio R Paula	12/2013
5785	75^55914-74	104843	Norbert Schneider	01/2015
5787	2^348268+255255	104840	Lelio R Paula	01/2017
5788	35540^891+891^35540	104839	Hans Havermann	09/2020
5789	5^149985-52	104836	Lelio R Paula	11/2016
5790	2^348224-20249	104826	Enzo Doria	06/2013
5791	(2^348217+2522)/2	104824	Stefano Morozzi	09/2020
5792	2^348212-20105	104823	Enzo Doria	06/2013
5793	24647^17898+17898^24647	104819	Hans Havermann	10/2020
5794	20^80562+19	104814	Lelio R Paula	12/2016
5795	2*10^104811-87	104812	Robert Price	04/2018
5796	2^348149-20053	104804	Enzo Doria	06/2013
5797	2^348095-171	104788	Lelio R Paula	09/2011
5798	25383^13412+13412^25383	104769	Hans Havermann	09/2020
5799	2^348003-20377	104760	Enzo Doria	06/2013
5800	2^347994-741	104757	Lelio R Paula	12/2016
5801	(2^347993+2234)/2	104757	Stefano Morozzi	01/2021
5802	(2^347990+790)/2	104756	Stefano Morozzi	09/2020
5803	25137^14702+14702^25137	104756	Hans Havermann	09/2020
5804	(13*2^347972-1)/282309	104746	Lelio R Paula	03/2014
5805	12883^25484-25484^12883	104740	Norbert Schneider	08/2022
5806	2^347910-109937	104732	Enzo Doria	04/2014
5807	(88*10^104709-637)/9	104710	Robert Price	11/2020
5808	(13*10^104702+71)/3	104703	Robert Price	06/2021
5809	5^149794+28	104702	Lelio R Paula	11/2016
5810	105^51800-2	104698	Lelio R Paula	10/2017
5811	(16^86939+3^86939)/19	104684	Robert Price	06/2013
5812	(15^89009-1)/14	104682	Paul Bourdelais	03/2010
5813	2^347731-18609	104678	Enzo Doria	05/2013
5814	4*6^134519+7	104677	Lelio R Paula	11/2014
5815	(34*10^104672-259)/9	104673	Robert Price	12/2021
5816	25321^13588+13588^25321	104656	Hans Havermann	09/2020
5817	2^347612-18545	104642	Enzo Doria	05/2013
5820	6^134465+95	104635	Lelio R Paula	11/2016
5818	(2^347588+3718)/2	104635	Stefano Morozzi	09/2020
5819	(166*10^104633-7)/3	104635	Robert Price	11/2020
5821	2^347517-17301	104614	Enzo Doria	05/2013
5822	(2^347493+3186)/2	104606	Stefano Morozzi	09/2020
5823	(2^347490+2574)/2	104605	Stefano Morozzi	09/2020
5824	3^219222-310	104596	Lelio R Paula	11/2016
5825	25993^10554+10554^25993	104581	Hans Havermann	09/2020
5826	(15*2^347399-1)/13	104578	Lelio R Paula	03/2014
5827	2^347372-17853	104570	Enzo Doria	05/2013
5828	2^347314+99	104552	Lelio R Paula	09/2011
5829	2^347300-22233	104548	Enzo Doria	06/2013
5830	2^347287-19845	104544	Enzo Doria	06/2013
5831	2^347258-231191	104536	Harrison Mesh	06/2022
5832	(31*2^347254-1)/891	104533	Lelio R Paula	03/2014
5833	5F(250091)(F(250091)-1)+1	104532	Serge Batalov	04/2015
5834	7*2^347239-3	104531	Lelio R Paula	09/2014
5835	(3^219098-8)/514147439969	104525	Lelio R Paula	12/2013
5836	5*3^219047+8	104513	Lelio R Paula	09/2014
5837	2^347148-109073	104502	Enzo Doria	04/2014
5838	2^347129-20145	104497	Enzo Doria	06/2013
5839	4*10^104461-57	104462	Robert Price	10/2018
5840	(2^346989+590)/2	104454	Stefano Morozzi	09/2020
5841	2^346923-19585	104435	Enzo Doria	05/2013
5842	(11*2^346864-1)/175	104416	Lelio R Paula	03/2014
5843	2^346854+346854^2+1	104414	Robert Price	06/2014
5844	2^346834+11715	104408	Lelio R Paula	04/2015
5845	24276^19961+19961^24276	104392	Hans Havermann	09/2020
5846	79^55009+78	104387	Norbert Schneider	02/2015
5847	3^218744+58	104368	Lelio R Paula	11/2016
5848	9*10^104361+89	104362	Robert Price	11/2019
5849	25048^14665+14665^25048	104358	Hans Havermann	09/2020
5850	2^346649+65	104352	Lelio R Paula	09/2011
5851	2^346638-17265	104349	Enzo Doria	05/2013
5852	(2^346606+2082)/2	104339	Stefano Morozzi	09/2020
5853	(2^346607+2070)/2	104339	Stefano Morozzi	09/2020
5854	(2^346582+3202)/2	104332	Stefano Morozzi	09/2020
5855	26092^9967+9967^26092	104331	Hans Havermann	09/2020
5856	5*10^104326+77	104327	Robert Price	12/2018
5857	(2^346564+2026)/2	104326	Stefano Morozzi	09/2020
5859	2^346527-111817	104316	Enzo Doria	05/2014
5858	6^134055+101	104316	Lelio R Paula	11/2016
5860	92105!4+8	104312	Robert Price	09/2019
5861	6^134013+163	104283	Lelio R Paula	11/2016
5862	(22*10^104272-61)/3	104273	Robert Price	03/2022
5863	(2^346318+862)/2	104252	Stefano Morozzi	02/2021
5865	18^83049-89	104250	Lelio R Paula	01/2017
5864	(2^346311+606)/2	104250	Stefano Morozzi	09/2020
5866	(166*10^104230+11)/3	104232	Robert Price	03/2021
5867	2^346213+484049	104221	Enzo Doria	04/2017
5868	18^83021-91	104214	Lelio R Paula	01/2017
5869	10^104212+128779	104213	Patrick De Geest	05/2016
5870	10^104212+237447	104213	Patrick De Geest	05/2016
5871	10^104212+242139	104213	Patrick De Geest	05/2016
5872	10^104212+269199	104213	Patrick De Geest	05/2016
5873	24254^19803+19803^24254	104213	Hans Havermann	09/2020
5874	(10^104212-71)/1	104212	Serge Batalov	12/2014
5875	23678^23821-23821^23678	104202	Norbert Schneider	01/2020
5876	2^346078+7695	104180	Lelio R Paula	12/2016
5877	2^346055-19537	104173	Enzo Doria	05/2013
5878	(3*2^346057+1)/77	104173	Lelio R Paula	12/2013
5879	2^346037-20125	104168	Enzo Doria	06/2013
5880	(34*10^104168-7)/9/13/551179	104162	Makoto Morimoto	05/2016
5881	6^133854-17993	104159	Enzo Doria	03/2013
5882	2^345990+1874239	104154	Enzo Doria	06/2016
5883	2^345988-20373	104153	Enzo Doria	06/2013
5884	(2^345965+2214)/2	104146	Stefano Morozzi	09/2020
5885	(26*10^104132-503)/9	104133	Robert Price	07/2018
5886	3*5^148968+8	104125	Lelio R Paula	11/2014
5887	(7*10^104113+53)/3	104114	Robert Price	05/2018
5888	p(21253)#/2+8	104113	Robert Price	01/2017
5889	33582^1259+1259^33582	104106	Hans Havermann	09/2020
5890	32958^1441+1441^32958	104104	Hans Havermann	09/2020
5891	29127^3748+3748^29127	104095	Hans Havermann	09/2020
5892	322^41507+41507^322	104094	Norbert Schneider	12/2014
5893	6^133768-17423	104092	Enzo Doria	03/2013
5894	2^345786-19557	104092	Enzo Doria	05/2013
5895	171^46606-2	104072	Lelio R Paula	10/2017
5896	(29*10^104071+91)/3	104072	Robert Price	04/2020
5897	norm(Mod(x,x^3-x-1)^852167-1)	104070	Paul Vanderveen	09/2022
5898	2^345704-149	104068	Lelio R Paula	09/2011
5899	25821^10712+10712^25821	104056	Hans Havermann	09/2020
5900	(2^345662+2038)/2	104055	Stefano Morozzi	09/2020
5901	6^133704-17273	104042	Enzo Doria	02/2013
5902	(3*2^345590-1)/23	104033	Lelio R Paula	03/2014
5903	(19*2^345590+1)/33859	104030	Lelio R Paula	12/2013
5904	2^345547+11	104021	Lelio R Paula	09/2011
5905	(19*10^104014-49)/3	104015	Robert Price	05/2019
5906	(2^345519+1794)/2	104012	Stefano Morozzi	01/2021
5907	2^345504+723	104008	Lelio R Paula	09/2011
5908	2^345498-20037	104006	Enzo Doria	06/2013
5910	18^82854-37	104005	Lelio R Paula	01/2017
5909	(2^345497+2070)/2	104005	Stefano Morozzi	09/2020
5911	2^345486-109065	104002	Enzo Doria	04/2014
5912	2^345487-1851507	104002	Enzo Doria	08/2015
5913	2^345476+777	103999	Lelio R Paula	09/2011
5914	(2^345477+1554)/2	103999	Stefano Morozzi	09/2020
5915	4*10^103981-83	103982	Robert Price	10/2018
5916	(2^345327+3206)/2	103954	Stefano Morozzi	09/2020
5917	(5*2^345321-1)/3	103953	Lelio R Paula	03/2014
5918	(2^345267-9)/539049127	103927	Lelio R Paula	12/2013
5919	(19*10^103907+77)/3	103908	Robert Price	05/2019
5920	(78557*2^345163+1)/78589	103905	Lelio R Paula	07/2014
5921	2^345106-112181	103888	Enzo Doria	06/2014
5922	(2^345105+1326)/2	103887	Stefano Morozzi	02/2021
5923	2^345079+99	103880	Lelio R Paula	09/2011
5924	(2^345034+1198)/2	103866	Stefano Morozzi	09/2020
5925	11^99736-1500	103865	Enzo Doria	12/2012
5926	(569^37699-1)/568	103863	Serge Batalov	06/2022
5927	(2^345010+2082)/2	103859	Stefano Morozzi	09/2020
5928	23263^23784-23784^23263	103857	Norbert Schneider	01/2020
5929	3*10^103844+31	103845	Robert Price	06/2021
5930	23927^21814+21814^23927	103813	Hans Havermann	09/2020
5931	2^344842-20157	103808	Enzo Doria	06/2013
5932	(47*2^344822+1)/1071	103801	Lelio R Paula	05/2015
5933	2^344802-20765	103796	Enzo Doria	06/2013
5934	2^344794-3821	103794	Yves Minet	05/2011
5935	2^344782-109103	103790	Enzo Doria	04/2014
5936	3^217521-112292	103784	Enzo Doria	06/2014
5937	2^344759-3505	103783	Lelio R Paula	11/2016
5938	2^344735-147	103776	Lelio R Paula	09/2011
5939	L(496533)-p(496533)	103770	Robert Price	02/2018
5940	2*10^103749-69	103750	Robert Price	03/2018
5941	(55459*2^344617+1)/3	103745	Lelio R Paula	07/2014
5942	2^344607-108891	103738	Enzo Doria	03/2014
5944	(2^344608+3798)/2	103738	Stefano Morozzi	02/2021
5943	(1097^34123-1)/1096	103738	Serge Batalov	06/2022
5945	(148*10^103718-1)/3	103720	Robert Price	03/2020
5946	2^344541-19561	103718	Enzo Doria	05/2013
5947	(1017*2^344529-1)/569	103714	Lelio R Paula	05/2015
5948	(8896^26263-1)/8895	103714	Serge Batalov	06/2022
5949	(2^344503+1758)/2	103706	Stefano Morozzi	09/2020
5950	(4*10^103703-1)/3	103704	Serge Batalov	08/2009
5951	2^344444-455	103688	Yves Minet	03/2012
5952	(4*10^103678-43)/3	103679	Robert Price	01/2022
5953	(1353^238539617^9)/10^307661	103673	Hans Havermann	06/2017
5954	(2^344367+2738)/2	103665	Stefano Morozzi	01/2021
5956	2^344317-109933	103650	Enzo Doria	04/2014
5955	26055^9508+9508^26055	103650	Hans Havermann	09/2020
5957	2^344309-1852033	103648	Enzo Doria	08/2015
5958	25729^10672+10672^25729	103643	Hans Havermann	09/2020
5959	(2^344289+1166)/2	103642	Stefano Morozzi	09/2020
5960	3*10^103637+61	103638	Robert Price	09/2020
5961	(2^344246+1614)/2	103629	Stefano Morozzi	09/2020
5962	2^344213-21253	103619	Enzo Doria	06/2013
5963	2^344196-465	103614	Lelio R Paula	11/2016
5964	2^344187-20001	103611	Enzo Doria	06/2013
5965	(117191#+(355573#)/(117191#))/(200233679)	103602	Makoto Morimoto	10/2017
5966	(237^43627-1)/236	103601	Serge Batalov	06/2022
5967	20^79621-19^79621	103590	Jean-Louis Charton	03/2011
5968	Phi(155391,10)/1243129	103586	Maksym Voznyy	09/2015
5969	2^344085-20365	103580	Enzo Doria	06/2013
5970	5^148169+54	103566	Lelio R Paula	11/2016
5971	2^344017-108795	103560	Enzo Doria	03/2014
5972	(2^343974+2670)/2	103547	Stefano Morozzi	09/2020
5973	2^343971-5077	103546	Lelio R Paula	09/2011
5974	(7*10^103531+71)/3	103532	Robert Price	05/2018
5975	2^343899+141	103524	Lelio R Paula	08/2011
5976	(2^343933+1)/(3*98294339989393)	103520	Gord Palameta	08/2018
5977	6^133029-67	103517	Lelio R Paula	11/2016
5978	(17*2^343877+1)/13625	103515	Lelio R Paula	12/2013
5979	66*10^103507+7	103509	Robert Price	07/2020
5980	26297^8614+8614^26297	103485	Hans Havermann	09/2020
5981	(2^343764+2658)/2	103483	Stefano Morozzi	09/2020
5982	26499^8036+8036^26499	103480	Hans Havermann	09/2020
5983	(136*10^103474-1)/9	103476	Serge Batalov	12/2014
5984	5^148014-24	103458	Lelio R Paula	11/2016
5985	28316^4503+4503^28316	103453	Hans Havermann	09/2020
5986	(22*10^103450+53)/3	103451	Robert Price	07/2019
5987	2^343604+9931	103436	Yves Minet	01/2011
5988	2^343601-21189	103435	Enzo Doria	06/2013
5989	(10^103423+173)/3	103423	Robert Price	05/2021
5990	2^343508-115229	103407	Enzo Doria	06/2015
5991	(8766^26227-1)/8765	103404	Serge Batalov	06/2022
5992	(509203*2^343491-1)/16147	103403	Lelio R Paula	05/2015
5993	3^216685-113056	103386	Enzo Doria	07/2014
5994	24829^14580+14580^24829	103382	Hans Havermann	08/2020
5995	91355!4+1024	103381	Robert Price	09/2019
5996	44^62903-43^62903	103379	Jean-Louis Charton	08/2012
5997	11^99262-20	103371	Lelio R Paula	12/2016
5998	(509203*2^343357-1)/5	103366	Lelio R Paula	05/2015
5999	(2^343363+3570)/2	103363	Stefano Morozzi	09/2020
6000	2^343356-2791889	103361	Enzo Doria	03/2016

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