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	(2^285882+2830)/2	86059	Stefano Morozzi	01/2020
7752	2^285836+65835	86046	Lelio R Paula	09/2013
7753	21587^9670+9670^21587	86034	Hans Havermann	08/2020
7754	(2^285766+78557)/3	86024	Lelio R Paula	01/2013
7755	(2^285732+2682)/2	86014	Stefano Morozzi	01/2020
7756	(5*10^86011-107)/3	86012	Robert Price	01/2017
7757	6^110522+163	86003	Lelio R Paula	12/2015
7758	41^53323-40^53323	85999	Robert Price	07/2012
7759	2^285678-109617	85998	Enzo Doria	04/2014
7760	6^110506-16673	85991	Enzo Doria	02/2013
7761	2^285569-741	85965	Lelio R Paula	09/2013
7762	(32*10^85964+31)/9	85965	Robert Price	05/2015
7763	133^40466+132	85944	Norbert Schneider	02/2019
7764	23378^4743+4743^23378	85939	Hans Havermann	08/2020
7765	6*10^85910-7	85911	Dmitry Domanov	11/2010
7766	(412*10^85897-7)/9	85899	Robert Price	10/2017
7767	4*10^85881+63	85882	Robert Price	06/2016
7768	(2^285257+1514)/2	85871	Stefano Morozzi	01/2020
7769	(2^285248+3738)/2	85868	Stefano Morozzi	01/2020
7770	(10^85864+53)/9	85864	Robert Price	01/2015
7772	2^285230+345	85863	Lelio R Paula	09/2013
7771	21774^8777+8777^21774	85863	Hans Havermann	08/2020
7773	(5*10^85855-473)/9	85855	Robert Price	12/2017
7774	2^285199+75683	85854	Enzo Doria	04/2016
7775	(76*10^85847-211)/9	85848	Robert Price	10/2017
7776	p(17832)#/2+512	85845	Robert Price	05/2017
7777	(16*10^85839+167)/3	85840	Robert Price	10/2017
7778	11^82426-1230	85838	Enzo Doria	11/2012
7779	(14727^20593-1)/14726	85830	Serge Batalov	08/2020
7780	2^285113-109881	85828	Enzo Doria	04/2014
7781	(2^285033+1670)/2	85804	Stefano Morozzi	01/2020
7782	(2^285033+3854)/2	85804	Stefano Morozzi	01/2020
7783	(2^285035+3194)/2	85804	Stefano Morozzi	01/2020
7784	5^122746-92	85796	Lelio R Paula	10/2015
7785	2^285001-113461	85794	Enzo Doria	08/2014
7787	(11*10^85782-131)/3	85783	Robert Price	02/2017
7786	(2^284963+2778)/2	85783	Stefano Morozzi	01/2020
7788	(2^284960+3570)/2	85782	Stefano Morozzi	01/2020
7789	(2^284937+1706)/2	85775	Stefano Morozzi	01/2020
7790	2^284913-110491	85768	Enzo Doria	05/2014
7791	6^110220+47	85768	Lelio R Paula	12/2015
7792	(1966^26041-1)/1965	85765	Serge Batalov	08/2020
7793	20698^13909+13909^20698	85758	Hans Havermann	07/2020
7794	3*6^110202-5	85755	Lelio R Paula	10/2014
7795	9*10^85746+37	85747	Robert Price	12/2020
7796	(157^39047-1)/156	85742	Alexander Zhirkov	06/2016
7797	(3^179705+7)/250	85739	Lelio R Paula	12/2012
7798	(9127^21649-1)/9126	85734	Serge Batalov	08/2020
7799	2^284734-6555	85714	Lelio R Paula	09/2013
7800	(10^85712+53)/9	85712	Robert Price	01/2015
7801	3*10^85703+11	85704	Robert Price	11/2017
7802	(6883*2^284668-1)/3	85697	Lelio R Paula	04/2015
7803	20728^13621+13621^20728	85694	Hans Havermann	07/2020
7804	22126^7459+7459^22126	85687	Hans Havermann	07/2020
7805	(9311^21589-1)/9310	85683	Serge Batalov	08/2020
7806	20^65855+83	85680	Lelio R Paula	01/2016
7807	6^110105+53	85679	Lelio R Paula	12/2015
7808	3*10^85672-73	85673	Robert Price	02/2021
7809	(10^85666-97)/3	85666	Robert Kinser	10/2017
7811	2^284567-7605	85664	Lelio R Paula	09/2013
7810	9*5^122555-2	85664	Lelio R Paula	10/2014
7812	5^122554-14	85662	Lelio R Paula	10/2015
7813	9*5^122543+4	85655	Lelio R Paula	10/2014
7814	3^179489-2^(179489-1)	85639	Robert Price	01/2016
7815	(2^284487+1970)/2	85639	Stefano Morozzi	01/2020
7816	(2^284477+1614)/2	85636	Stefano Morozzi	01/2020
7817	23693^4114+4114^23693	85633	Hans Havermann	07/2020
7818	19690^19941+19941^19690	85632	Norbert Schneider	03/2020
7819	2^284429+177	85622	Lelio R Paula	08/2012
7820	2*3^179452+5	85621	Lelio R Paula	07/2014
7821	21036^11711+11711^21036	85587	Hans Havermann	07/2020
7823	(19^66919+3^66919)/22	85572	Robert Price	07/2013
7822	(2^284265+602)/2	85572	Stefano Morozzi	01/2020
7826	66^47023-65	85561	Norbert Schneider	11/2014
7824	(2^284226+3802)/2	85561	Stefano Morozzi	01/2020
7825	(2^284228+2170)/2	85561	Stefano Morozzi	01/2020
7827	6^109943+13	85553	Lelio R Paula	12/2015
7828	2^284183-4747	85548	Yves Minet	05/2019
7829	(5637^22807-1)/5636	85547	Serge Batalov	08/2020
7830	20782^13071+13071^20782	85546	Hans Havermann	08/2020
7831	(2^284167-509203)/34564775	85536	Lelio R Paula	01/2013
7832	(2^284136+2262)/2	85534	Stefano Morozzi	01/2020
7833	2^284133-3	85533	M. Frind & P. Underwood	07/2002
7834	2^284113+315	85527	Lelio R Paula	09/2013
7835	(2^284098+3082)/2	85522	Stefano Morozzi	01/2020
7836	(2^284070+1482)/2	85514	Stefano Morozzi	01/2020
7837	(2^284068+2866)/2	85513	Stefano Morozzi	01/2020
7838	(8721^21701-1)/8720	85511	Serge Batalov	08/2020
7839	22085^7438+7438^22085	85502	Hans Havermann	07/2020
7840	(28*10^85500+149)/3	85501	Robert Price	10/2017
7841	(16*10^85495-19)/3	85496	Robert Price	03/2016
7842	2^284004+177	85494	Lelio R Paula	08/2012
7843	(16*10^85473-91)/3	85474	Robert Price	06/2016
7844	66*10^85468+7	85470	Robert Price	07/2020
7845	3^179120+22	85462	Robert Price	12/2013
7846	2^283872-2792249	85454	Enzo Doria	03/2016
7847	(4703^23269-1)/4702	85449	Serge Batalov	08/2020
7848	(29*10^85438+259)/9	85439	Robert Price	04/2017
7849	2^283817+82875	85438	Lelio R Paula	09/2013
7850	(2^283815-5)/201	85435	Lelio R Paula	01/2013
7851	2^283796-125	85432	Lelio R Paula	08/2012
7852	(10174^21319-1)/10173	85432	Serge Batalov	08/2020
7853	(29*2^283784-1)/13	85428	Lelio R Paula	02/2014
7854	15^72592-28	85375	Lelio R Paula	11/2015
7856	2^283604-58695	85374	Lelio R Paula	09/2013
7855	21863^8034+8034^21863	85374	Hans Havermann	08/2020
7858	(44*10^85370-503)/9	85371	Robert Price	10/2017
7857	(2^283597+1854)/2	85371	Stefano Morozzi	01/2020
7859	496^31671+31671^496	85369	Norbert Schneider	07/2017
7860	(2^283578+478)/2	85366	Stefano Morozzi	01/2020
7861	(15*2^283583-1)/103051	85364	Lelio R Paula	02/2014
7862	15^72572+92	85352	Lelio R Paula	11/2015
7863	2^283473-1615	85334	Lelio R Paula	09/2013
7864	(2^283469+2934)/2	85333	Stefano Morozzi	01/2020
7865	2^283466-15	85332	Lelio R Paula	08/2012
7866	(2^283437+3446)/2	85323	Stefano Morozzi	01/2020
7867	19966^18761+18761^19966	85320	Hans Havermann	07/2020
7868	(2^283411+3894)/2	85315	Stefano Morozzi	01/2020
7869	11^81916-7020	85307	Enzo Doria	02/2013
7870	6^109626-7	85306	Lelio R Paula	11/2014
7871	2^283374-110327	85305	Enzo Doria	05/2014
7872	33*10^85297+7	85299	Robert Price	07/2016
7873	(6010^22573-1)/6009	85297	Serge Batalov	08/2020
7874	1137^27908+27908^1137	85281	Norbert Schneider	04/2020
7875	18^67933+41	85275	Lelio R Paula	11/2015
7876	2^283271-109341	85274	Enzo Doria	04/2014
7877	(2^283266+3678)/2	85272	Stefano Morozzi	01/2020
7878	19688^19855-19855^19688	85262	Norbert Schneider	03/2020
7879	(2^283216+1926)/2	85257	Stefano Morozzi	01/2020
7880	(25*10^85249-73)/3	85250	Robert Price	09/2016
7881	2*5^121959+3	85246	Lelio R Paula	10/2014
7882	19834^19834+8947	85235	Henri Lifchitz	11/2004
7883	2^283140+1915	85234	Lelio R Paula	09/2013
7884	3*10^85227-97	85228	Robert Price	08/2017
7885	(16*10^85221-31)/3	85222	Robert Price	03/2016
7886	(2^283096+3186)/2	85221	Stefano Morozzi	01/2020
7887	2^283083+1869383	85217	Enzo Doria	05/2016
7888	(24737*2^283051+1)/17	85211	Lelio R Paula	06/2014
7889	(2^283032+78557)/3	85201	Lelio R Paula	01/2013
7890	2^283026-109893	85200	Enzo Doria	04/2014
7891	(2^283012+78557)/129	85193	Lelio R Paula	01/2013
7892	(10^(242589+1)+7210^42589-1)/9	85179	Robert Price	09/2017
7893	2^282860-109727	85150	Enzo Doria	04/2014
7894	(2^282847+13)/3	85145	Stefano Morozzi	03/2020
7895	2^282819+1869413	85138	Enzo Doria	05/2016
7896	3^178428+2	85132	Ray Chandler	07/2011
7897	19985^18162+18162^19985	85120	Hans Havermann	07/2020
7898	(22699*2^282742+1)/73	85117	Lelio R Paula	06/2014
7899	(16^70687+5^70687)/21	85115	Robert Price	07/2013
7900	(2^282732+738)/2	85111	Stefano Morozzi	01/2020
7901	(2^282720+1590)/2	85107	Stefano Morozzi	01/2020
7902	(3^178352-2)/7	85095	Lelio R Paula	12/2012
7903	22150^6939+6939^22150	85085	Hans Havermann	07/2020
7904	11^81699-2790	85081	Enzo Doria	12/2012
7905	2^282612-95	85075	Lelio R Paula	08/2012
7906	2^282609-4069	85074	Yves Minet	02/2018
7907	75^45366-2	85065	Lelio R Paula	08/2013
7908	(2^282550+1918)/2	85056	Stefano Morozzi	01/2020
7909	(2^282515+3786)/2	85046	Stefano Morozzi	01/2020
7910	2^282511+69	85045	Lelio R Paula	08/2012
7911	69^46249+2	85045	Lelio R Paula	06/2013
7912	(2^282488+2382)/2	85038	Stefano Morozzi	01/2020
7913	(2^282489+1862)/2	85038	Stefano Morozzi	01/2020
7914	3^178226+10	85036	Robert Price	10/2013
7915	(2^282475+1050)/2	85034	Stefano Morozzi	01/2020
7916	(182*10^85017+43)/9	85019	Robert Price	11/2017
7917	(14*10^85010+73)/3	85011	Robert Price	04/2016
7918	9*2^282338-7	84994	Lelio R Paula	08/2014
7919	(9913*2^282330-1)/1578003	84988	Lelio R Paula	04/2015
7920	20025^17504+17504^20025	84969	Hans Havermann	07/2020
7921	2^282203+5	84952	Lelio R Paula	08/2012
7922	2^282184+13	84946	Lelio R Paula	08/2012
7923	11^81568-2400	84945	Enzo Doria	12/2012
7924	11^81562-2340	84939	Enzo Doria	12/2012
7925	(41*10^84927+31)/9	84928	Robert Price	05/2015
7926	(3923^23629-1)/3922	84911	Serge Batalov	08/2020
7927	(2^282053+1406)/2	84907	Stefano Morozzi	01/2020
7928	(2*10^84904-17)/3	84904	Robert Price	08/2014
7929	(4^141017+23)/3	84901	Robert Price	02/2017
7930	6^109100-18653	84897	Enzo Doria	03/2013
7931	2^281973+1025	84883	Lelio R Paula	09/2013
7932	2^281951-109651	84876	Enzo Doria	04/2014
7933	21618^8431+8431^21618	84870	Hans Havermann	07/2020
7934	11^81491-5430	84865	Enzo Doria	01/2013
7935	10^84863+141057	84864	Patrick De Geest	02/2021
7936	10^84863-40001	84863	Robert Price	01/2021
7937	((1+sqrt(3)+sqrt(2))^79357-1)((1+sqrt(3)-sqrt(2))^79357-1)((1-sqrt(3)+sqrt(2))^79357-1)*((1-sqrt(3	84849	Mike Oakes	04/2009
7938	(2^281827+650)/2	84839	Stefano Morozzi	01/2020
7939	2^281825-1861483	84838	Enzo Doria	03/2016
7940	2^281809-97305	84833	Lelio R Paula	09/2013
7942	2^281780-114893	84825	Enzo Doria	05/2015
7941	(7654^21841-1)/7653	84825	Serge Batalov	08/2020
7943	3^177719+64	84794	Lelio R Paula	12/2015
7945	2^281675-199	84793	Lelio R Paula	08/2012
7944	2^281673-111223	84793	Enzo Doria	05/2014
7946	(4*10^84779+149)/9	84779	Robert Price	03/2017
7948	129^40167-128	84777	Norbert Schneider	01/2019
7947	(2^281622+3970)/2	84777	Stefano Morozzi	01/2020
7949	(72*10^84772-27)/9	84773	Ray Chandler	01/2011
7950	11^81398-630	84768	Enzo Doria	11/2012
7951	(25*2^281577-1)/23	84764	Lelio R Paula	02/2014
7952	20320^14819+14819^20320	84752	Hans Havermann	07/2020
7953	2^281500-455	84740	Yves Minet	03/2012
7954	10^84725+1145141919	84726	Marisa Kirisame	03/2015
7955	10^84725+142041	84726	Patrick De Geest	10/2015
7956	10^84725-138677	84725	Patrick De Geest	02/2016
7957	76^45044+75	84720	Norbert Schneider	02/2015
7958	54^48897-53	84709	Norbert Schneider	08/2014
7959	(9913*2^281377-1)/65	84706	Lelio R Paula	04/2015
7960	Phi(171124,10)/29946701/7761329021/58560344041	84700	Maksym Voznyy	11/2015
7961	2^281337-111223	84691	Enzo Doria	05/2014
7962	2^281308+54615	84683	Lelio R Paula	09/2013
7963	7*5^121144-6	84677	Lelio R Paula	10/2014
7964	(2^281270+3858)/2	84671	Stefano Morozzi	01/2020
7965	(2^281252+47)/3	84665	Lelio R Paula	01/2013
7966	11^81297-3150	84663	Enzo Doria	12/2012
7967	2^281208-303	84653	Yves Minet	02/2012
7968	197^36892-2	84648	Lelio R Paula	10/2017
7969	(21*2^281187+1)/2483	84644	Lelio R Paula	01/2013
7970	11^81247-84	84611	Lelio R Paula	10/2015
7971	(10876^20959-1)/10875	84597	Serge Batalov	08/2020
7972	2067^25516+25516^2067	84595	Norbert Schneider	11/2019
7974	17^68747-64	84590	Lelio R Paula	11/2015
7973	(2^281002+3718)/2	84590	Stefano Morozzi	01/2020
7975	5^121018-15596	84588	Enzo Doria	02/2013
7976	6^108702+7	84587	Lelio R Paula	11/2014
7977	10^84582+100677	84583	Patrick De Geest	05/2016
7978	10^84582-8001	84582	Robert Price	03/2016
7979	1828^25929+25929^1828	84580	Norbert Schneider	12/2019
7980	(2^280968+1446)/2	84580	Stefano Morozzi	01/2020
7981	3*5^121004-8	84579	Lelio R Paula	10/2014
7982	5^120996-84	84573	Lelio R Paula	10/2015
7983	(2^280896+1522)/2	84558	Stefano Morozzi	01/2020
7984	(10223*2^280881+1)/68419	84553	Lelio R Paula	06/2014
7985	2^280852+97681	84545	Yves Minet	08/2004
7986	2^280848-1203	84544	Lelio R Paula	09/2013
7987	5^120946-24	84538	Lelio R Paula	10/2015
7988	2^280810-2111	84533	Yves Minet	08/2013
7989	11^81161-5160	84521	Enzo Doria	01/2013
7990	2^280737-93	84511	Lelio R Paula	08/2012
7991	(2^280737+494)/2	84510	Stefano Morozzi	01/2020
7992	(2^280717+1166)/2	84504	Stefano Morozzi	01/2020
7993	2^280698+315	84499	Lelio R Paula	09/2013
7994	3^177099-340	84498	Lelio R Paula	12/2015
7995	(8201^21589-1)/8200	84493	Serge Batalov	08/2020
7996	(5*10^84469-107)/3	84470	Robert Price	01/2017
7997	(3^177002+7)/6696022272161744	84436	Lelio R Paula	12/2012
7998	(2^280500-1017)/823	84436	Lelio R Paula	01/2013
7999	24677^2640+2640^24677	84435	Hans Havermann	07/2020
8000	14^73660-5	84424	Lelio R Paula	11/2015

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