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	7^116240-116240^7	98235	Norbert Schneider	05/2017
5752	17^79826-78	98222	Lelio R Paula	08/2016
5753	2^326268-809	98217	Yves Minet	04/2011
5754	22659^21590+21590^22659	98210	Hans Havermann	10/2019
5755	22268^22587-22587^22268	98202	Norbert Schneider	08/2020
5756	(418*10^98199+23)/9	98201	Robert Price	08/2017
5757	12*10^98198-7	98200	Robert Price	11/2017
5758	15^83496-76	98199	Lelio R Paula	08/2016
5759	(10223*2^326179+1)/6125	98190	Lelio R Paula	07/2014
5760	9*5^140471-4	98186	Lelio R Paula	11/2014
5761	22774^20455+20455^22774	98175	Hans Havermann	07/2020
5762	2^326069-2383	98157	Yves Minet	10/2013
5763	2^325973+1185	98128	Lelio R Paula	07/2016
5764	(25*2^325949-1)/17	98121	Lelio R Paula	02/2014
5765	2^325945-1847269	98120	Enzo Doria	07/2015
5766	8*10^98111-67	98112	Robert Price	10/2017
5767	(2^325902+1138)/2	98106	Stefano Morozzi	09/2020
5768	2^325866+15	98096	Lelio R Paula	12/2012
5769	22591^21952+21952^22591	98079	Hans Havermann	02/2020
5770	2^325765+1974305	98066	Enzo Doria	06/2016
5771	2^325733-58695	98056	Lelio R Paula	07/2016
5772	2^325717-3645	98051	Lelio R Paula	07/2016
5773	(2^325704+718)/2	98047	Stefano Morozzi	09/2020
5774	23968^12293+12293^23968	98021	Hans Havermann	11/2019
5775	(23*2^325583-1)/21	98011	Lelio R Paula	02/2014
5776	(7*10^98007-13)/3	98008	Robert Price	06/2016
5777	(2^325544+1110)/2	97999	Stefano Morozzi	09/2020
5778	2^325512-459959	97989	Enzo Doria	05/2015
5779	(2^325492+682)/2	97983	Stefano Morozzi	09/2020
5780	(3^205354-8)/17	97978	Lelio R Paula	09/2013
5781	2^325433+76817	97966	Enzo Doria	05/2016
5782	5*10^97963+81	97964	Robert Price	08/2017
5783	2^325390-109061	97953	Enzo Doria	04/2014
5784	13^87921+24	97940	Lelio R Paula	08/2016
5785	961^32831-960^32831	97926	Jean-Louis Charton	02/2011
5786	22600^21499+21499^22600	97913	Hans Havermann	05/2020
5787	2^325215+12909	97900	Lelio R Paula	07/2016
5788	22619^21286+21286^22619	97898	Hans Havermann	04/2020
5789	(85*10^97876-49)/9	97877	Robert Price	12/2020
5790	7*10^97874-69	97875	Robert Price	01/2017
5791	5*10^97869-63	97870	Robert Price	04/2021
5793	(17^79537+5^79537)/22	97865	Robert Price	06/2013
5792	15^83212+22	97865	Lelio R Paula	08/2016
5794	2^325087-109057	97861	Enzo Doria	04/2014
5795	2^325074+1870657	97858	Enzo Doria	05/2016
5797	2^325066-2111	97855	Yves Minet	08/2013
5796	CopelandErdos(97855)	97855	Eric W. Weisstein	10/2015
5798	26660^4677+4677^26660	97842	Hans Havermann	12/2019
5799	18^77944-89	97841	Lelio R Paula	07/2016
5800	119^47136+118	97833	Norbert Schneider	09/2018
5801	6^125720-17663	97830	Enzo Doria	02/2013
5802	2^324972-2069	97827	Yves Minet	05/2013
5803	2^324958-4691	97823	Yves Minet	05/2019
5804	2^324944-2788319	97818	Enzo Doria	03/2016
5805	22845^19112+19112^22845	97807	Hans Havermann	10/2019
5806	(2^324898+1270)/2	97804	Stefano Morozzi	09/2020
5808	4*10^97799-9	97800	Erik Branger	11/2013
5807	2^324882+577294575	97800	Lelio R Paula	09/2016
5809	2^324863-1867921	97794	Enzo Doria	04/2016
5810	6^125662-18473	97785	Enzo Doria	03/2013
5811	12^90604+11	97779	Lelio R Paula	07/2016
5812	5^139830+24	97737	Lelio R Paula	04/2016
5813	(2^324672+1198)/2	97736	Stefano Morozzi	09/2020
5814	2^324612+1155	97718	Lelio R Paula	07/2016
5815	(2^324597+3542)/2	97714	Stefano Morozzi	09/2020
5816	19^76404-44	97702	Lelio R Paula	07/2016
5817	2^324505-2983	97686	Yves Minet	04/2011
5818	(144^45259+1)/145	97684	Paul Bourdelais	08/2019
5819	(31*2^324496-1)/45	97683	Lelio R Paula	02/2014
5820	6^125488-17843	97649	Enzo Doria	02/2013
5821	(2^324350+3198)/2	97639	Stefano Morozzi	09/2020
5822	7^115515-2	97622	Lelio R Paula	09/2013
5823	(89^50069-1)/88	97603	Paul Bourdelais	08/2017
5824	6^125418-5	97595	Lelio R Paula	11/2014
5825	(2^324193+3522)/2	97592	Stefano Morozzi	09/2020
5826	(2^324172+666)/2	97586	Stefano Morozzi	09/2020
5827	2^324076+1155	97557	Lelio R Paula	07/2016
5828	(2^324074+9)/13	97555	Lelio R Paula	10/2013
5829	(55459*2^323993+1)/21	97536	Lelio R Paula	07/2014
5830	13^87557-12^87557	97534	Jean-Louis Charton	12/2008
5831	2^323946+73939	97518	Enzo Doria	04/2016
5832	2^323937+1866947	97515	Enzo Doria	03/2016
5834	6^125290-18533	97495	Enzo Doria	03/2013
5833	(2^323870+1650)/2	97495	Stefano Morozzi	09/2020
5835	2^323845+101	97488	Lelio R Paula	12/2012
5836	18^77662+65	97487	Lelio R Paula	07/2016
5837	22634^20265+20265^22634	97479	Hans Havermann	04/2020
5838	2^323772+76771	97466	Enzo Doria	05/2016
5839	2^323765-112213	97463	Enzo Doria	06/2014
5840	22730^19389+19389^22730	97457	Hans Havermann	02/2020
5841	2^323720-6555	97450	Lelio R Paula	07/2016
5842	2^323694-1860401	97442	Enzo Doria	03/2016
5843	20^74886+3	97429	Lelio R Paula	06/2016
5844	24476^9561+9561^24476	97427	Hans Havermann	01/2020
5845	(2^323623+1766)/2	97420	Stefano Morozzi	09/2020
5847	3*10^97399+73	97400	Robert Price	04/2016
5846	7^115252-50	97400	Lelio R Paula	07/2016
5848	224737#+393581	97389	Nicolas PALAU	12/2016
5849	(2^323468+3186)/2	97374	Stefano Morozzi	09/2020
5850	(2^323456+538)/2	97370	Stefano Morozzi	09/2020
5851	23277^15236+15236^23277	97365	Hans Havermann	07/2020
5853	(26*10^97353+31)/3	97354	Robert Price	07/2016
5852	(2^323403+3510)/2	97354	Stefano Morozzi	09/2020
5854	23756^12519+12519^23756	97342	Hans Havermann	07/2020
5855	23991^11402+11402^23991	97332	Hans Havermann	07/2020
5856	61^54517-60^54517	97331	Jean-Louis Charton	09/2005
5857	(38*10^97329+187)/9	97330	Robert Price	11/2017
5858	86455!4+8	97319	Robert Price	09/2019
5859	22591^20310+20310^22591	97316	Hans Havermann	06/2020
5860	25101^7520+7520^25101	97297	Hans Havermann	05/2020
5861	p(19982)#/2-1024	97293	Robert Price	09/2017
5862	6^125021-85	97286	Lelio R Paula	08/2016
5863	2^323164-47355	97283	Lelio R Paula	07/2016
5864	(3^203902+4)/36051015157	97276	Lelio R Paula	09/2013
5865	2^323054-6555	97249	Lelio R Paula	07/2016
5866	22822^18247+18247^22822	97249	Hans Havermann	02/2020
5867	9*10^97247-29	97248	Robert Price	05/2017
5868	24382^9735+9735^24382	97244	Hans Havermann	02/2020
5869	(31*10^97242+41)/9	97243	Robert Price	04/2015
5870	GoldenRatioPrime[97241]	97241	Eric W. Weisstein	06/2009
5871	12^90098-41	97233	Lelio R Paula	07/2016
5872	2^322928-216929	97212	Enzo Doria	05/2014
5873	(7*2^322896-1)/57	97201	Lelio R Paula	02/2014
5874	(2^322897+5)/3146107489	97193	Lelio R Paula	10/2013
5875	(2^322789+2214)/2	97169	Stefano Morozzi	09/2020
5876	2^322725+75761	97150	Enzo Doria	04/2016
5877	(13*2^322686+1)/119	97138	Lelio R Paula	11/2013
5878	22402^21639+21639^22402	97118	Hans Havermann	07/2020
5879	23399^14128+14128^23399	97108	Hans Havermann	06/2020
5880	(2^322525+2606)/2	97090	Stefano Morozzi	09/2020
5881	(41*10^97085+373)/9	97086	Robert Price	04/2017
5882	(2^322473+854)/2	97074	Stefano Morozzi	02/2021
5883	2^322413+77	97056	Lelio R Paula	12/2012
5884	2^322406+177	97054	Lelio R Paula	12/2012
5885	(14*10^97044+31)/9	97045	Robert Price	02/2015
5886	2^322302+255255	97023	Lelio R Paula	07/2016
5887	2^322196-113093	96991	Enzo Doria	07/2014
5888	(2^322169+2690)/2	96983	Stefano Morozzi	09/2020
5889	23109^15668+15668^23109	96943	Hans Havermann	07/2020
5890	2^322000-1861469	96932	Enzo Doria	03/2016
5891	2^321971-112747	96923	Enzo Doria	06/2014
5892	23754^12023+12023^23754	96917	Hans Havermann	07/2020
5893	11^93062-92	96915	Lelio R Paula	06/2016
5894	(2^321922+2214)/2	96908	Stefano Morozzi	09/2020
5895	(2^321900+2086)/2	96902	Stefano Morozzi	09/2020
5896	(11*2^321841-7)/15	96884	Renaud Lifchitz	03/2011
5897	3^203051+34	96880	Lelio R Paula	05/2016
5898	2*10^96867-51	96868	Robert Price	11/2017
5899	(2^321779+2618)/2	96865	Stefano Morozzi	09/2020
5900	(64*10^96863-1)/27	96864	Serge Batalov	05/2010
5901	2^321716-2786939	96847	Enzo Doria	03/2016
5902	22496^20181+20181^22496	96844	Hans Havermann	03/2020
5904	2^321701-113053	96842	Enzo Doria	07/2014
5903	2^321700-28635	96842	Lelio R Paula	06/2016
5905	(5*2^321691-1)/27	96838	Lelio R Paula	02/2014
5906	6^124433-124433	96828	Robert Price	01/2014
5907	2^321631+69	96821	Lelio R Paula	12/2012
5908	(13*2^321606+1)/119	96813	Lelio R Paula	11/2013
5909	(46*10^96798-1)/9	96799	Serge Batalov	10/2014
5910	(59*10^96798+31)/9	96799	Robert Price	09/2015
5911	(2^321536+2062)/2	96792	Stefano Morozzi	09/2020
5912	223319#+231223	96790	Makoto Morimoto	02/2016
5913	2^321519-28635	96787	Lelio R Paula	06/2016
5914	2^321487-1867237	96778	Enzo Doria	03/2016
5915	2^321461-63	96770	Lelio R Paula	12/2012
5916	2^321439+123	96763	Lelio R Paula	12/2012
5917	2^321434+709	96762	Lelio R Paula	02/2013
5918	(2^321415+554)/2	96756	Stefano Morozzi	09/2020
5919	14^84413+89	96749	Lelio R Paula	07/2016
5920	(28*10^96743+71)/9	96744	Serge Batalov	12/2008
5921	13^86847+96	96743	Lelio R Paula	06/2016
5922	9*2^321336-7	96733	Lelio R Paula	08/2014
5923	(209*10^96722-17)/3	96724	Robert Price	05/2017
5924	2^321237-4615	96702	Yves Minet	05/2019
5925	2^321187-1159	96687	Yves Minet	11/2012
5926	2^321182-1850081	96686	Enzo Doria	08/2015
5927	23359^13768+13768^23359	96680	Hans Havermann	06/2020
5928	2^321116-112829	96666	Enzo Doria	06/2014
5929	2^321108-109499	96664	Enzo Doria	04/2014
5931	2^321098+2793859	96661	Enzo Doria	03/2016
5930	(2^321100+1170)/2	96661	Stefano Morozzi	09/2020
5932	2^321057+4097	96648	Lelio R Paula	06/2016
5933	(4435*29^66081-4)/7	96640	Curtis Bright	05/2015
5934	22743^17750+17750^22743	96640	Hans Havermann	04/2020
5935	22882^16679+16679^22882	96612	Hans Havermann	02/2020
5936	23452^13163+13163^23452	96608	Hans Havermann	02/2020
5937	(2^320863+666)/2	96590	Stefano Morozzi	09/2020
5938	p(19849)#/2-64	96581	Robert Price	04/2017
5940	2^320817+189	96576	Lelio R Paula	12/2012
5939	2^320816-4685	96576	Yves Minet	05/2019
5941	(361*10^96567-163)/9	96569	Robert Price	10/2017
5942	2^320788-110327	96567	Enzo Doria	05/2014
5943	2^320764+793	96560	Lelio R Paula	02/2013
5944	(2^320752+1842)/2	96556	Stefano Morozzi	02/2021
5945	(9179*2^320652-1)/221	96528	Lelio R Paula	05/2015
5946	23288^13947+13947^23288	96517	Hans Havermann	07/2020
5947	2^320616-78795	96516	Lelio R Paula	03/2016
5948	2^320612-461939	96514	Enzo Doria	07/2015
5949	10^96504+987654321	96505	Robert Price	12/2019
5950	10^96504+71887	96505	Patrick De Geest	02/2020
5951	22654^18195+18195^22654	96505	Hans Havermann	07/2020
5952	10^96504-139277	96504	Patrick De Geest	02/2020
5953	5*2^320431+7	96461	Lelio R Paula	08/2014
5954	19^75431-90	96458	Lelio R Paula	06/2016
5955	(2^320386+2814)/2	96446	Stefano Morozzi	02/2021
5956	(2^320370+3)/67	96440	Lelio R Paula	10/2013
5957	3*10^96431-17	96432	Robert Price	03/2021
5958	2^320309+1871477	96423	Enzo Doria	05/2016
5959	tau(809^6028)	96410	Nik Lygeros / Olivier Rozier / LR team	10/2013
5960	(21*2^320252-1)/1895	96404	Lelio R Paula	02/2014
5961	2^320232-173	96400	Lelio R Paula	12/2012
5962	175^42975-2	96395	Lelio R Paula	10/2017
5963	(2^320170+2718)/2	96381	Stefano Morozzi	09/2020
5964	10^96377+199911	96378	Patrick De Geest	12/2016
5965	10^96377-20001	96377	Robert Price	11/2016
5966	2^320124-2790449	96367	Enzo Doria	03/2016
5967	22488^19255+19255^22488	96351	Hans Havermann	11/2019
5968	23248^13939+13939^23248	96346	Hans Havermann	11/2019
5970	2^320043-108775	96343	Enzo Doria	04/2014
5969	24989^7168+7168^24989	96343	Hans Havermann	11/2019
5971	10^96338+424939	96339	Patrick De Geest	03/2016
5972	10^96338-9281	96338	Robert Price	09/2015
5973	(3*2^320008+1)/7	96332	Lelio R Paula	09/2013
5974	25699^5596+5596^25699	96317	Hans Havermann	07/2020
5975	26502^4297+4297^26502	96287	Hans Havermann	07/2020
5976	2^319838+4257	96281	Lelio R Paula	03/2016
5977	2^319830-16995	96279	Lelio R Paula	03/2016
5978	6^123713+143	96268	Lelio R Paula	05/2016
5979	(28*10^96265-97)/3	96266	Robert Price	07/2016
5980	103^47825-102	96264	Norbert Schneider	10/2016
5981	(2^319777+2082)/2	96263	Stefano Morozzi	09/2020
5982	(2^319771+3686)/2	96261	Stefano Morozzi	09/2020
5983	2^319713-81	96244	Lelio R Paula	11/2012
5984	(55459*2^319706+1)/20167	96242	Lelio R Paula	07/2014
5985	22834^16393+16393^22834	96238	Hans Havermann	05/2020
5986	12^89153-43	96213	Lelio R Paula	06/2016
5988	(2*10^96195-59)/3	96195	Robert Price	05/2017
5987	9*10^96194-77	96195	Robert Price	08/2020
5989	2^319545+147	96193	Lelio R Paula	11/2012
5990	23357^13128+13128^23357	96189	Hans Havermann	02/2020
5991	25952^5073+5073^25952	96160	Hans Havermann	12/2019
5992	(50^56597+1)/51	96155	Robert Price	03/2014
5993	22313^20374+20374^22313	96149	Hans Havermann	12/2019
5994	22279^20668+20668^22279	96141	Hans Havermann	11/2019
5995	(41*10^96137-59)/9	96138	Robert Price	10/2017
5996	2^319353-110343	96135	Enzo Doria	05/2014
5997	11^92309-42	96130	Lelio R Paula	05/2016
5998	14^83869-13^83869	96125	Jean-Louis Charton	01/2009
5999	(7*10^96112+143)/3	96113	Robert Price	04/2016
6000	26731^3940+3940^26731	96112	Hans Havermann	07/2020

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Probable Primes Top 10000

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