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 ?
7751	2^247311-1017	74449	Lelio R Paula	05/2013
7752	(2^247288+1938)/2	74441	Stefano Morozzi	01/2020
7753	2^247280+7	74439	Lelio R Paula	03/2012
7754	(68*10^74434+13)/9	74435	Ray Chandler	11/2010
7755	3^156004-62	74433	Lelio R Paula	01/2015
7756	21865^2536+2536^21865	74432	Hans Havermann	11/2019
7757	(2^247223+1050)/2	74422	Stefano Morozzi	01/2020
7758	36095!2-64	74416	Robert Price	06/2015
7759	67699!4+16	74409	Robert Price	09/2019
7760	2^247165-3	74405	M. Frind & P. Underwood	07/2002
7761	2^247150+32769	74400	Lelio R Paula	05/2013
7762	(2^247130+3858)/2	74394	Stefano Morozzi	01/2020
7763	(2^247055+2426)/2	74371	Stefano Morozzi	01/2020
7764	12^68911+73	74368	Lelio R Paula	01/2015
7765	2^246999+74903	74355	Enzo Doria	04/2016
7766	2^246989-110643	74352	Enzo Doria	05/2014
7767	10^74350+279439	74351	Patrick De Geest	07/2017
7770	(10^74350+11)/3	74350	Robert Price	11/2014
7768	10^74350-400000001	74350	Robert Price	07/2017
7769	10^74350-716241	74350	Patrick De Geest	07/2017
7771	67647!4-512	74346	Robert Price	11/2019
7772	10^74335+13659	74336	Patrick De Geest	05/2013
7773	10^74335-53	74335	Robert Price	05/2011
7774	23360^1521+1521^23360	74335	Hans Havermann	11/2019
7775	(2^246914+3418)/2	74329	Stefano Morozzi	01/2020
7776	2^246906-1215	74327	Lelio R Paula	05/2013
7777	(2^246879+1494)/2	74318	Stefano Morozzi	01/2020
7778	2^246848+111	74309	Lelio R Paula	03/2012
7779	(2^246842+2490)/2	74307	Stefano Morozzi	01/2020
7781	6^95490-18443	74306	Enzo Doria	03/2013
7780	(2^246840+2902)/2	74306	Stefano Morozzi	01/2020
7782	18^59188-2369	74298	Enzo Doria	03/2013
7783	(13632^246767+1)/(35713^2*743)	74281	Jens K. Andersen	09/2007
7784	2^246744+40755	74278	Lelio R Paula	05/2013
7785	(29*10^74276+91)/3	74277	Robert Price	03/2016
7786	17222^17533-17533^17222	74272	Norbert Schneider	11/2019
7787	(2^246720+3606)/2	74270	Stefano Morozzi	01/2020
7788	6^95441+163	74268	Lelio R Paula	01/2015
7789	V(390863)	74258	Serge Batalov	03/2015
7790	10^74254+91	74255	Robert Price	03/2011
7792	(19*10^74253-1)/9	74254	Ray Chandler	02/2012
7791	10^74254-130569	74254	Patrick De Geest	05/2013
7793	771^25718+25718^771	74250	Norbert Schneider	10/2016
7794	2^246618+427	74240	Henri Lifchitz	02/2005
7795	88*10^74234+3	74236	Robert Price	11/2016
7796	8*10^74234-49	74235	Robert Price	04/2016
7797	2^246578+12285	74228	Lelio R Paula	05/2013
7798	(3^155569-5)/2	74225	Lelio R Paula	06/2012
7799	13^66628+46	74220	Lelio R Paula	01/2015
7800	(2^246534+3034)/2	74214	Stefano Morozzi	01/2020
7801	(2^246486+798)/2	74200	Stefano Morozzi	01/2020
7802	2^246476-17295	74197	Lelio R Paula	05/2013
7803	(2^246465+446)/2	74194	Stefano Morozzi	01/2020
7804	(61*10^74189-1)/3	74191	Robert Price	11/2017
7805	(15185*2^246432-1)/13	74187	Lelio R Paula	04/2015
7806	5*2^246413-3	74179	Lelio R Paula	05/2014
7807	2^246386-28635	74170	Lelio R Paula	05/2013
7808	(2^246371+3050)/2	74165	Stefano Morozzi	01/2020
7809	2^246334-111245	74154	Enzo Doria	05/2014
7810	39^77708+7^77708-24^77708-3	74153	Mike Oakes	12/2010
7811	15^63045+82	74147	Lelio R Paula	01/2015
7812	19255!+19255#+1	74140	D. Gazzoni Filho & Lucas Teixeira	06/2005
7813	(2^246277+2114)/2	74137	Stefano Morozzi	01/2020
7814	2^246268-110507	74135	Enzo Doria	05/2014
7815	3^155328+2660	74111	Lelio R Paula	01/2015
7817	2^246148-2786249	74098	Enzo Doria	03/2016
7816	19740^5671+5671^19740	74098	Hans Havermann	01/2020
7818	(2^246135+3386)/2	74094	Stefano Morozzi	01/2020
7819	(16*10^74092-19)/3	74093	Robert Price	03/2016
7820	2^246115-110767	74088	Enzo Doria	05/2014
7821	7^87666-68	74087	Lelio R Paula	08/2014
7822	(2^246091+1938)/2	74081	Stefano Morozzi	01/2020
7823	10^74079+1145141919	74080	Marisa Kirisame	03/2015
7824	10^74079+6219	74080	Patrick De Geest	03/2016
7825	10^74079-282707	74079	Patrick De Geest	03/2016
7826	129^35098+2	74078	Lelio R Paula	05/2013
7827	22193^2176+2176^22193	74073	Hans Havermann	12/2019
7828	17703^15278+15278^17703	74071	Hans Havermann	12/2019
7829	2^246025-112123	74061	Enzo Doria	06/2014
7830	(67*10^74045+17)/3	74047	Robert Price	02/2017
7831	(2^245944+2202)/2	74037	Stefano Morozzi	01/2020
7832	(2^245885+1446)/2	74019	Stefano Morozzi	01/2020
7833	2^245823+66831	74001	Marek Hubal	02/2017
7834	5^105869+42	74000	Lelio R Paula	08/2014
7835	(21*2^245806+1)/634555	73991	Lelio R Paula	08/2012
7836	(22699*2^245762+1)/119	73985	Lelio R Paula	06/2014
7837	(3^155048-7)/262	73975	Lelio R Paula	06/2012
7838	9998*2^245696+3	73966	Donovan Johnson	10/2004
7839	13^66400-80	73966	Lelio R Paula	01/2015
7841	(2^245704+9)/25	73963	Lelio R Paula	07/2012
7842	11^71023-7170	73963	Enzo Doria	01/2013
7840	3*10^73962+13	73963	Robert Price	08/2017
7843	(31*2^245660-1)/114195	73948	Lelio R Paula	01/2014
7844	2^245629-2797813	73942	Eric Chen	03/2016
7845	2^245557-153	73921	Lelio R Paula	03/2012
7846	(77*10^73917-59)/9	73918	Robert Price	11/2017
7847	15010^17699+17699^15010	73918	Norbert Schneider	11/2019
7848	2^245525+1869881	73911	Enzo Doria	06/2016
7849	2^245522+159	73910	Lelio R Paula	03/2012
7850	(2^245507+1986)/2	73905	Stefano Morozzi	01/2020
7851	(13*10^73891-43)/3	73892	Robert Price	08/2017
7852	19^57783-56	73891	Lelio R Paula	01/2015
7853	7*10^73888+79	73889	Robert Price	02/2017
7854	(2^245449+942)/2	73888	Stefano Morozzi	01/2020
7855	6^94948+174281	73884	Mike Oakes	02/2011
7856	(2^245431+3630)/2	73882	Stefano Morozzi	01/2020
7857	11^70939-4860	73876	Enzo Doria	01/2013
7858	18637^9196+9196^18637	73870	Hans Havermann	01/2020
7859	2^245372+54615	73865	Lelio R Paula	05/2013
7860	2^245362-143	73862	Lelio R Paula	03/2012
7861	7^87396+6^(87396-1)	73859	Robert Price	03/2016
7862	(22*10^73853-37)/3	73854	Robert Price	05/2017
7863	5^105646-14246	73844	Enzo Doria	02/2013
7865	2^245290-41	73840	Lelio R Paula	03/2012
7864	2^245290-94395	73840	Lelio R Paula	05/2013
7866	15770^17589+17589^15770	73836	Norbert Schneider	10/2019
7867	12352^18043+18043^12352	73828	Norbert Schneider	11/2019
7868	(2^245240+3598)/2	73825	Stefano Morozzi	01/2020
7869	(2^245242+498)/2	73825	Stefano Morozzi	01/2020
7870	8*5^105600-7	73813	Lelio R Paula	10/2014
7871	7*5^105573-4	73794	Lelio R Paula	10/2014
7872	(2^245112+1122)/2	73786	Stefano Morozzi	01/2020
7873	20151^4570+4570^20151	73751	Hans Havermann	12/2019
7874	(2^244968+1318)/2	73743	Stefano Morozzi	01/2020
7875	18^58742-4805	73738	Enzo Doria	03/2013
7876	13^66179+66	73720	Lelio R Paula	01/2015
7877	(2^244881+942)/2	73717	Stefano Morozzi	01/2020
7878	(2^244883+1946)/2	73717	Stefano Morozzi	01/2020
7879	(82*10^73714-1)/9	73715	Robert Price	12/2014
7880	(2^244862+3682)/2	73711	Stefano Morozzi	01/2020
7881	(29*2^244856-1)/186121	73706	Lelio R Paula	01/2014
7882	(13*2^244840-1)/2799	73702	Lelio R Paula	01/2014
7883	(13*10^73701+17)/3	73702	Robert Price	06/2015
7884	(2^244787-1017)/28411	73684	Lelio R Paula	07/2012
7885	21213^2974+2974^21213	73680	Hans Havermann	01/2020
7886	(3^154421-4)/23	73677	Lelio R Paula	06/2012
7887	14596^17691+17691^14596	73670	Norbert Schneider	11/2019
7888	8*7^87170+5	73669	Lelio R Paula	10/2014
7889	(29*10^73659-113)/3	73660	Robert Price	11/2017
7890	Phi(40100,-40100)	73651	Henri Lifchitz	06/2013
7891	(4*10^73647-19)/3	73648	Robert Price	06/2017
7892	2^244618-2297	73638	Yves Minet	10/2009
7893	3*5^105344+8	73633	Lelio R Paula	10/2014
7894	(2^244588+2562)/2	73629	Stefano Morozzi	01/2020
7895	5^105334-14096	73626	Enzo Doria	02/2013
7896	(2^244562+1534)/2	73621	Stefano Morozzi	01/2020
7897	(2^244584-7)/13237074243033	73614	Lelio R Paula	07/2012
7898	2^244465-110185	73592	Enzo Doria	05/2014
7899	(2^244465+2934)/2	73591	Stefano Morozzi	01/2020
7900	2^244443+40755	73585	Lelio R Paula	05/2013
7901	23155^1506+1506^23155	73583	Hans Havermann	12/2019
7902	10^73579+987654321	73580	Robert Price	12/2019
7903	10^73579+124173	73580	Patrick De Geest	02/2020
7904	10^73579-176379	73579	Patrick De Geest	02/2020
7905	2^244404+3841	73573	Yves Minet	03/2011
7906	19770^5263+5263^19770	73569	Hans Havermann	12/2019
7907	2^244372-110627	73564	Enzo Doria	05/2014
7908	19778^5241+5241^19778	73563	Hans Havermann	12/2019
7909	(2^244349+2186)/2	73557	Stefano Morozzi	01/2020
7910	(2^244309+3710)/2	73545	Stefano Morozzi	01/2020
7911	18428^9783+9783^18428	73537	Hans Havermann	01/2020
7912	(3*2^244255+1)/245	73527	Lelio R Paula	08/2012
7913	(11*2^244245+1)/23	73525	Lelio R Paula	08/2012
7914	18140^11301+11301^18140	73524	Hans Havermann	12/2019
7915	(15185*2^244187-1)/6111	73509	Lelio R Paula	04/2015
7916	(2^244152+2058)/2	73497	Stefano Morozzi	01/2020
7917	(2^244109+1422)/2	73484	Stefano Morozzi	01/2020
7918	17063^17362+17362^17063	73477	Norbert Schneider	04/2019
7919	(91^37507+1)/92	73476	Paul Bourdelais	08/2017
7920	18^58521+65	73460	Lelio R Paula	01/2015
7921	13^65940+36	73454	Lelio R Paula	01/2015
7922	19065^7112+7112^19065	73439	Hans Havermann	12/2019
7923	(625^26267+1)/626	73437	Richard Fischer	12/2017
7924	(2^243935+530)/2	73432	Stefano Morozzi	01/2020
7925	5^105050-14	73427	Lelio R Paula	08/2014
7926	(2^243850+1474)/2	73406	Stefano Morozzi	01/2020
7927	(((((((((((((30201^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2)^2-2	73401	Serge Batalov	07/2016
7928	15^62410-46	73400	Lelio R Paula	01/2015
7929	(2^243806+2494)/2	73393	Stefano Morozzi	01/2020
7930	(2^243790+2530)/2	73388	Stefano Morozzi	01/2020
7931	(2^243766+2362)/2	73381	Stefano Morozzi	01/2020
7932	2^243733+1869707	73371	Enzo Doria	05/2016
7933	11^70439-5430	73355	Enzo Doria	01/2013
7934	2^243676-87	73354	Lelio R Paula	03/2012
7935	(101*10^73346-17)/3	73348	Robert Price	08/2016
7936	21639^2452+2452^21639	73346	Hans Havermann	12/2019
7937	(2^243647+2438)/2	73345	Stefano Morozzi	01/2020
7938	2^243621-113185	73338	Enzo Doria	07/2014
7939	(5*2^243610-1)/1669	73332	Lelio R Paula	01/2014
7940	19857^4928+4928^19857	73326	Hans Havermann	12/2019
7941	2*5^104888-7	73314	Lelio R Paula	10/2014
7942	(58695*2^243516-1)/983	73308	Lelio R Paula	04/2015
7943	(3^153648-2)/33423138097	73299	Lelio R Paula	06/2012
7944	(2^243467+470)/2	73291	Stefano Morozzi	01/2020
7945	(2^243460+2410)/2	73289	Stefano Morozzi	01/2020
7946	18^58376-5255	73278	Enzo Doria	03/2013
7947	11^70363+32	73276	Lelio R Paula	02/2015
7948	2^243413+4257	73275	Lelio R Paula	05/2013
7949	104824^5+5^104824	73269	Andrey Kulsha	07/2010
7950	7^86689-6^86689	73261	Predrag Minovic	09/2004
7951	(2^243355+3846)/2	73257	Stefano Morozzi	01/2020
7952	2^243296+90195	73240	Lelio R Paula	05/2013
7953	2^243281-4843	73235	Yves Minet	05/2019
7955	p(15433)#/2-4	73218	Robert Price	12/2016
7954	(59*10^73217-77)/9	73218	Robert Price	11/2017
7956	2^243127+71355	73189	Lelio R Paula	05/2013
7957	2^243116-249419	73186	Paul Bourdelais	03/2013
7958	(58695*2^243085-1)/11	73180	Lelio R Paula	04/2015
7959	(2^243084+3406)/2	73176	Stefano Morozzi	01/2020
7960	11^70262-98	73171	Lelio R Paula	02/2015
7961	(2^243034+47)/722703303	73152	Lelio R Paula	07/2012
7962	(2^242966+47)/46887	73136	Lelio R Paula	07/2012
7963	(43^44773-1)/42	73134	Robert Price	04/2014
7964	6^93980-158359	73131	Mike Oakes	02/2011
7965	19953^4616+4616^19953	73114	Hans Havermann	11/2019
7966	(2^242855+2546)/2	73107	Stefano Morozzi	01/2020
7967	(2^242845+3926)/2	73104	Stefano Morozzi	01/2020
7968	6^93915+53	73081	Lelio R Paula	01/2015
7969	(5*10^73079+211)/9	73079	Robert Price	12/2017
7970	(74*10^73076+43)/9	73077	Robert Price	10/2015
7971	(3^153125+2)/1144955	73054	Lelio R Paula	06/2012
7972	2^242632-112199	73040	Enzo Doria	06/2014
7973	V(351646)	73029	Serge Batalov	03/2015
7974	(2^242598+1090)/2	73029	Stefano Morozzi	01/2020
7975	18^58175-85	73026	Lelio R Paula	01/2015
7976	p(15395)#/2-4	73019	Robert Price	12/2016
7977	(4^121271+3^121271)/7	73012	Jean-Louis Charton	03/2011
7978	8*6^93825-5	73011	Lelio R Paula	10/2014
7979	19090^6673+6673^19090	73007	Hans Havermann	11/2019
7981	(F(220)^1601-F(219)^1601)/F(218)	73005	Wayne Halsdorf	08/2013
7980	(73^39181+1)/74	73005	Paul Bourdelais	08/2017
7982	6^93815+143	73003	Lelio R Paula	01/2015
7984	6^93812+5	73000	Wojciech Florek	03/2006
7983	17874^12137+12137^17874	73000	Hans Havermann	11/2019
7985	19^57078-62	72989	Lelio R Paula	01/2015
7986	(29*10^72985+91)/3	72986	Robert Price	03/2016
7987	20691^3368+3368^20691	72985	Hans Havermann	10/2019
7988	(2^242451+558)/2	72985	Stefano Morozzi	01/2020
7989	11^70082-2520	72983	Enzo Doria	12/2012
7990	(2^242429+2142)/2	72979	Stefano Morozzi	01/2020
7991	6^93773+133	72970	Lelio R Paula	01/2015
7992	(2^242392+3762)/2	72967	Stefano Morozzi	01/2020
7993	2^242328-59	72948	Lelio R Paula	03/2012
7994	5^104358-13016	72944	Enzo Doria	02/2013
7995	(75*10^72941-57)/99	72941	Ray Chandler	03/2011
7996	12^67585-95	72937	Lelio R Paula	02/2015
7997	(2^242261+3834)/2	72928	Stefano Morozzi	01/2020
7998	2^242230-113285	72919	Enzo Doria	07/2014
7999	(2^242229+2742)/2	72918	Stefano Morozzi	01/2020
8000	(5*10^72916-11)/3	72917	Erik Branger	12/2013

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Probable Primes Top 10000

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