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	2^342966-16995	103244	Lelio R Paula	11/2016
5752	23797^21774+21774^23797	103230	Hans Havermann	09/2020
5753	25388^11637+11637^25388	103224	Hans Havermann	09/2020
5754	(2^342876+2086)/2	103216	Stefano Morozzi	09/2020
5755	(16*10^103214-31)/3	103215	Robert Price	03/2019
5757	(37*10^103211+611)/9	103212	Robert Price	11/2018
5756	(238*10^103210-1)/3	103212	Robert Price	04/2020
5758	5^147650+16	103203	Lelio R Paula	11/2016
5759	gcd(Phi(852060,10),(10^42603+1)^3(10^42603+1-10^21302)+(10^85206+10^42603)(10^21302+1)+10^127809)	103201	Serge Batalov	04/2015
5760	2^342817+2707067	103199	Enzo Doria	03/2016
5761	43^63177-42	103198	Theodore Burton	02/2007
5762	2^342805-21025	103195	Enzo Doria	06/2013
5763	24129^18890+18890^24129	103182	Hans Havermann	09/2020
5764	(622*10^103171-1)/9	103173	Robert Price	11/2021
5765	2^342714+12285	103168	Lelio R Paula	11/2016
5766	18^82178-4481	103156	Enzo Doria	03/2013
5767	2^342665-17349	103153	Enzo Doria	05/2013
5768	30408^2467+2467^30408	103150	Hans Havermann	09/2020
5769	(5^147571-3^147571)/2	103148	Kellen Shenton	05/2022
5770	(2^342615+3090)/2	103138	Stefano Morozzi	09/2020
5771	2^342612+175	103137	Lelio R Paula	08/2011
5772	5*2^342585-3	103130	Lelio R Paula	09/2014
5773	(16*10^103127+77)/3	103128	Robert Price	03/2019
5774	(2^342527+3774)/2	103111	Stefano Morozzi	02/2021
5775	2^342503-19209	103104	Enzo Doria	05/2013
5776	(2^342484+2586)/2	103098	Stefano Morozzi	09/2020
5777	2^342476+51	103096	Lelio R Paula	08/2011
5778	2^342460-18885	103091	Enzo Doria	05/2013
5779	(2^342442+862)/2	103086	Stefano Morozzi	02/2021
5780	(194*10^103074-17)/3	103076	Robert Price	09/2020
5781	7^121968+82	103075	Lelio R Paula	10/2016
5782	2^342392-108863	103071	Enzo Doria	03/2014
5783	(2^342389+806)/2	103070	Stefano Morozzi	01/2021
5784	3^216014+28	103065	Lelio R Paula	11/2016
5785	2^342353-108879	103059	Enzo Doria	03/2014
5786	10^103055+276081	103056	Patrick De Geest	12/2016
5787	10^103055-53	103055	Lelio R Paula	11/2016
5788	(58*10^103046+419)/9	103047	Robert Price	05/2019
5789	7^121933+4	103046	Lelio R Paula	11/2014
5790	(71*10^103028-143)/9	103029	Robert Price	10/2021
5791	(2^342235+3618)/2	103023	Stefano Morozzi	09/2020
5792	19^80560-68	103017	Lelio R Paula	10/2016
5793	2^342209+76607	103016	Enzo Doria	05/2016
5795	328^40945+40945^328	103013	Norbert Schneider	12/2014
5794	12^95454-91	103013	Lelio R Paula	10/2016
5796	25833^9716+9716^25833	103009	Hans Havermann	01/2019
5797	(893*10^103004+7)/9	103006	Robert Price	06/2021
5798	(1475^32503-1)/1474	102993	Serge Batalov	06/2022
5799	65^56809-64^56809	102990	Robert Price	08/2013
5800	5^147338-6	102985	Lelio R Paula	11/2014
5801	2^342084-112739	102978	Enzo Doria	06/2014
5802	9*6^132330+7	102974	Lelio R Paula	11/2014
5803	2^342034-16737	102963	Enzo Doria	05/2013
5804	(9787*2^342011-1)/25	102959	Lelio R Paula	05/2015
5805	(3^215802-5)/124343756	102956	Lelio R Paula	12/2013
5806	2^341991-17421	102950	Enzo Doria	05/2013
5807	2^341969-112225	102943	Enzo Doria	06/2014
5808	(9787*2^341864-1)/3	102915	Lelio R Paula	05/2015
5809	2^341859+1869413	102910	Enzo Doria	05/2016
5810	10^102909+61	102910	Lelio R Paula	11/2016
5811	10^102909-67049	102909	Patrick De Geest	12/2016
5812	23814^20935+20935^23814	102898	Hans Havermann	02/2019
5813	28345^4264+4264^28345	102888	Hans Havermann	02/2019
5814	25665^10204+10204^25665	102886	Hans Havermann	02/2019
5815	26288^8181+8181^26288	102860	Hans Havermann	02/2019
5816	2^341659+1836773	102850	Enzo Doria	03/2016
5817	2^341608-110639	102835	Enzo Doria	05/2014
5818	10^102824+49	102825	Lelio R Paula	11/2016
5819	10^102824-168011	102824	Patrick De Geest	12/2016
5820	11^98708-8	102794	Lelio R Paula	10/2016
5821	2^341466+4429	102792	Lelio R Paula	09/2011
5822	2^341460-107	102790	Lelio R Paula	08/2011
5823	(2^341388+47)/21014943	102761	Lelio R Paula	12/2013
5824	2^341355+21	102759	Lelio R Paula	08/2011
5825	(6496^26947-1)/6495	102736	Serge Batalov	06/2022
5826	2^341246+40755	102726	Lelio R Paula	11/2016
5827	(2^341256-5)/991699	102723	Lelio R Paula	12/2013
5828	7^121547+78	102720	Lelio R Paula	10/2016
5829	2^341223-461197	102719	Enzo Doria	06/2015
5830	27838^4893+4893^27838	102711	Hans Havermann	03/2019
5832	2^341190-20577	102709	Enzo Doria	06/2013
5831	(27*2^341212+1)/84674449	102709	Lelio R Paula	12/2013
5833	6^131976-65	102698	Lelio R Paula	10/2016
5834	2^341134+2533	102692	Henri Lifchitz	09/2005
5835	13^92184-54	102688	Lelio R Paula	10/2016
5836	2^341116-20873	102687	Enzo Doria	06/2013
5837	2^341094-19953	102680	Enzo Doria	06/2013
5838	23761^20950+20950^23761	102676	Hans Havermann	03/2019
5840	2^341053+129	102668	Lelio R Paula	08/2011
5839	(4724^27943-1)/4723	102668	Serge Batalov	06/2022
5842	(31*2^341006-1)/3	102655	Lelio R Paula	03/2014
5841	7^121471+94	102655	Lelio R Paula	10/2016
5844	2^341004-173	102653	Lelio R Paula	08/2011
5843	20^78901+3	102653	Lelio R Paula	10/2016
5845	(2^341001+1674)/2	102652	Stefano Morozzi	09/2020
5846	5^146853-52	102646	Lelio R Paula	10/2016
5847	2^340969-216931	102642	Enzo Doria	05/2014
5848	122^49196+121	102641	Norbert Schneider	10/2018
5849	2^340952+1870021	102637	Enzo Doria	05/2016
5850	5*2^340940-3	102634	Lelio R Paula	08/2014
5851	(6^131891+1)/7	102631	Paul Bourdelais	01/2010
5852	(11*10^102629-23)/3	102630	Robert Price	09/2021
5853	25876^9239+9239^25876	102615	Hans Havermann	02/2019
5854	(4*10^102612+83)/3	102613	Robert Price	02/2018
5855	75^54717+74	102598	Norbert Schneider	01/2015
5856	(17*10^102597+13)/3	102598	Robert Price	01/2019
5857	2^340806-20393	102593	Enzo Doria	06/2013
5858	(2^340790+5)/138267	102583	Lelio R Paula	12/2013
5859	6^131821+77	102577	Lelio R Paula	10/2016
5860	(203*10^102561-11)/3	102563	Robert Price	12/2020
5861	2^340688-29	102558	Henri Lifchitz	05/2005
5862	2^340685-109101	102557	Enzo Doria	04/2014
5863	65^56567-64	102552	Norbert Schneider	11/2014
5864	26230^8121+8121^26230	102550	Hans Havermann	03/2019
5865	(8*10^102541+49)/3	102542	Robert Price	05/2020
5866	(536*10^102533-23)/9	102535	Robert Price	02/2020
5867	2^340547-108897	102515	Enzo Doria	03/2014
5868	(2^340536+778)/2	102512	Stefano Morozzi	09/2020
5869	25592^10119+10119^25592	102500	Hans Havermann	02/2019
5870	7^121268+82	102484	Lelio R Paula	10/2016
5871	(6883*2^340443-1)/162401	102483	Lelio R Paula	05/2015
5872	2^340434-5955	102481	Lelio R Paula	11/2016
5873	(7*10^102480-19)/3	102481	Robert Price	10/2020
5874	(2^340381+47)/7	102465	Lelio R Paula	12/2013
5875	111^50095+110	102461	Norbert Schneider	04/2017
5876	2^340291-20301	102438	Enzo Doria	06/2013
5877	12^94915+89	102431	Lelio R Paula	10/2016
5878	(106*10^102422+17)/3	102424	Robert Price	04/2021
5879	24466^15349+15349^24466	102417	Hans Havermann	03/2019
5880	2^340212+111546435	102415	Paul Bourdelais	10/2021
5881	2^340208-20373	102413	Enzo Doria	06/2013
5882	6^131598-17273	102404	Enzo Doria	02/2013
5883	(2^340132+1182)/2	102390	Stefano Morozzi	09/2020
5884	(2^340133+1166)/2	102390	Stefano Morozzi	09/2020
5885	2^340115-21181	102385	Enzo Doria	06/2013
5886	(55459*2^340090+1)/1591	102379	Lelio R Paula	07/2014
5887	(2^340064+3630)/2	102370	Stefano Morozzi	09/2020
5888	89^52511-88^52511	102365	Robert Price	06/2015
5889	3^214539-112756	102362	Enzo Doria	07/2014
5890	23159^23450-23450^23159	102353	Norbert Schneider	12/2019
5891	2^340000-19877	102351	Enzo Doria	06/2013
5892	2^339990-114845	102348	Enzo Doria	05/2015
5893	(3^214516-2)/51383	102346	Lelio R Paula	12/2013
5894	20^78661-99	102341	Lelio R Paula	09/2016
5895	2^339951-19585	102336	Enzo Doria	05/2013
5896	(17*10^102335-167)/3	102336	Robert Price	05/2022
5897	(13*2^339943+1)/45	102333	Lelio R Paula	12/2013
5898	(236282#+121441)/(121441*25499429)	102332	Makoto Morimoto	08/2020
5899	5*10^102323-91	102324	Robert Price	03/2021
5901	2^339889+29327	102317	Yves Minet	06/2010
5900	(167*10^102315-17)/3	102317	Robert Price	03/2020
5902	26348^7641+7641^26348	102314	Hans Havermann	03/2019
5903	Phi(239414,10)/6333218543	102303	Makoto Kamada	08/2019
5904	2^339834-109493	102301	Enzo Doria	04/2014
5905	(16*10^102299-19)/3	102300	Robert Price	02/2019
5906	(11^98221-5^98221)/6	102286	Robert Price	01/2013
5907	3^214365+1820	102279	Lelio R Paula	10/2016
5908	31978^1579+1579^31978	102278	Hans Havermann	03/2019
5909	(89*10^102262-467)/9	102263	Robert Price	04/2022
5910	(11*2^339705-1)/183	102261	Lelio R Paula	03/2014
5911	2^339694-16995	102259	Lelio R Paula	09/2016
5912	(56*10^102255+691)/9	102256	Robert Price	05/2019
5913	122^49008+121	102249	Norbert Schneider	10/2018
5914	(2^339652+3178)/2	102246	Stefano Morozzi	09/2020
5915	7^120985-38	102245	Lelio R Paula	10/2016
5916	10^102244+122961	102245	Patrick De Geest	12/2016
5917	10^102244-27	102244	Lelio R Paula	09/2016
5918	7^120982-62	102242	Lelio R Paula	10/2016
5919	(2^339640+2670)/2	102242	Stefano Morozzi	09/2020
5920	4*6^131382-5	102236	Lelio R Paula	11/2014
5921	(2^339607+3290)/2	102232	Stefano Morozzi	02/2021
5922	2^339586-1091	102226	Yves Minet	11/2012
5923	11^98161-3072000	102225	Enzo Doria	12/2012
5924	9*7^120961-4	102225	Lelio R Paula	11/2014
5925	5*3^214250+2	102224	Serge Batalov	10/2010
5926	12^94713-59	102213	Lelio R Paula	10/2016
5927	12^94705+89	102204	Lelio R Paula	10/2016
5928	2^339407-177	102172	Lelio R Paula	08/2011
5929	4*10^102163-57	102164	Robert Price	10/2018
5930	2^339355+65	102157	Lelio R Paula	07/2011
5931	(28*10^102142-31)/3	102143	Robert Price	12/2019
5932	(2^339323+47)/880715	102141	Lelio R Paula	12/2013
5933	(2^339268+1758)/2	102130	Stefano Morozzi	09/2020
5934	s(178551)	102122	Robert Price	05/2020
5935	(797*10^102112-23)/9	102114	Robert Price	01/2022
5936	(2^339175+2790)/2	102102	Stefano Morozzi	02/2021
5938	2^339168+21	102100	Lelio R Paula	07/2011
5939	2^339167-108807	102100	Enzo Doria	03/2014
5937	(2^339169+42)/2	102100	Stefano Morozzi	09/2020
5940	2^339156+163	102097	Lelio R Paula	08/2011
5941	(2^339149+746)/2	102094	Stefano Morozzi	09/2020
5942	(25*10^102076-67)/3	102077	Robert Price	06/2019
5943	2^339081-4543	102074	Yves Minet	03/2019
5944	(3435^28867-1)/3434	102069	Serge Batalov	06/2022
5945	2*10^102062+77	102063	Robert Price	08/2020
5946	24327^15668+15668^24327	102053	Hans Havermann	02/2019
5947	10^102052-7000001	102052	Robert Price	06/2021
5948	2^339000-175635	102050	Stefano Morozzi	12/2021
5949	2^339000-151667	102050	Stefano Morozzi	12/2021
5950	2^338999+79289	102049	Stefano Morozzi	01/2022
5951	2^338994+188757	102048	Stefano Morozzi	05/2022
5952	2^338992+181591	102047	Stefano Morozzi	01/2022
5953	2^338992+136171	102047	Stefano Morozzi	03/2022
5954	2^338991-109435	102047	Stefano Morozzi	04/2022
5955	2^338988-134619	102046	Stefano Morozzi	04/2022
5956	2^338981+106391	102044	Stefano Morozzi	01/2022
5957	2^338982+34069	102044	Stefano Morozzi	03/2022
5958	2^338982-58781	102044	Stefano Morozzi	04/2022
5959	2^338977+83007	102043	Stefano Morozzi	02/2022
5960	2^338979-83601	102043	Stefano Morozzi	04/2022
5961	2^338975+28355	102042	Stefano Morozzi	01/2022
5962	2^338973+134619	102042	Stefano Morozzi	03/2022
5963	2^338974+183777	102042	Stefano Morozzi	03/2022
5968	25080^11711+11711^25080	102041	Hans Havermann	02/2019
5964	2^338972+152343	102041	Stefano Morozzi	12/2021
5965	2^338972-180623	102041	Stefano Morozzi	02/2022
5966	2^338972+84441	102041	Stefano Morozzi	03/2022
5967	2^338971+64875	102041	Stefano Morozzi	05/2022
5969	2^338968+53461	102040	Stefano Morozzi	01/2022
5970	2^338969+160175	102040	Stefano Morozzi	03/2022
5971	2^338967+13409	102040	Stefano Morozzi	04/2022
5972	2^338963-127455	102039	Stefano Morozzi	12/2021
5973	2^338963+132195	102039	Stefano Morozzi	02/2022
5974	2^338966+137919	102039	Stefano Morozzi	04/2022
5979	(2^338982-7)/1754517	102038	Lelio R Paula	12/2013
5975	2^338960+53935	102038	Stefano Morozzi	01/2022
5976	2^338962+83157	102038	Stefano Morozzi	02/2022
5977	2^338961+12341	102038	Stefano Morozzi	04/2022
5978	2^338960+63933	102038	Stefano Morozzi	05/2022
5980	2^338959-30919	102037	Stefano Morozzi	02/2022
5981	2^338959+164769	102037	Stefano Morozzi	05/2022
5982	2^338954-177003	102036	Stefano Morozzi	12/2021
5983	2^338954+154207	102036	Stefano Morozzi	01/2022
5984	2^338956+182493	102036	Stefano Morozzi	02/2022
5985	2^338954+162715	102036	Stefano Morozzi	04/2022
5986	2^338955-158241	102036	Stefano Morozzi	04/2022
5987	2^338956-33395	102036	Stefano Morozzi	04/2022
5988	2^338950+175077	102035	Stefano Morozzi	12/2021
5989	2^338951-51687	102035	Stefano Morozzi	12/2021
5990	2^338949+85449	102034	Stefano Morozzi	03/2022
5991	2^338949-184585	102034	Stefano Morozzi	04/2022
5992	2^338943+127103	102033	Stefano Morozzi	12/2021
5993	2^338944-84003	102033	Stefano Morozzi	04/2022
5994	2^338945+138605	102033	Stefano Morozzi	05/2022
5995	2^338940+78607	102032	Stefano Morozzi	01/2022
5996	2^338939+151569	102031	Stefano Morozzi	12/2021
5997	2^338938+183975	102031	Stefano Morozzi	03/2022
5998	2^338937-33429	102031	Stefano Morozzi	04/2022
5999	2^338939-183259	102031	Stefano Morozzi	04/2022
6000	2^338935+179999	102030	Stefano Morozzi	01/2022

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Probable Primes Top 10000

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