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 ?
8751	(2^287172+658)/2	86448	Stefano Morozzi	01/2020
8752	(2^287146+2542)/2	86440	Stefano Morozzi	01/2020
8753	(2^287136+1726)/2	86437	Stefano Morozzi	01/2020
8754	(2^287128+958)/2	86434	Stefano Morozzi	01/2020
8755	87^44563-86^44563	86431	Robert Price	05/2015
8756	6^111057+61	86420	Lelio R Paula	12/2015
8757	2^287057-109909	86413	Enzo Doria	04/2014
8758	5^123608+22	86399	Lelio R Paula	10/2015
8759	(2^286970+618)/2	86387	Stefano Morozzi	01/2020
8760	(2^286916+2646)/2	86371	Stefano Morozzi	01/2020
8761	(2^286907+3690)/2	86368	Stefano Morozzi	01/2020
8762	(31*10^86364-121)/9	86365	Robert Price	06/2016
8763	(2^286868+2686)/2	86356	Stefano Morozzi	01/2020
8764	2^286859+71663	86354	Enzo Doria	04/2016
8765	(2^286845+1866)/2	86349	Stefano Morozzi	01/2020
8766	2^286740+29835	86318	Lelio R Paula	10/2013
8767	2*10^86310+9^86310	86311	Mike Oakes	05/2011
8768	11^82878-1860	86309	Enzo Doria	12/2012
8769	2223^25780+25780^2223	86285	Norbert Schneider	12/2019
8770	2^286547+16095	86260	Lelio R Paula	10/2013
8771	(58*10^86242+329)/9	86243	Robert Price	11/2017
8772	2^286455-110427	86232	Enzo Doria	05/2014
8773	(37*10^86230+53)/9	86231	Robert Price	05/2015
8774	8*3^180700+5	86217	Lelio R Paula	08/2014
8775	3^180697-40	86215	Lelio R Paula	12/2015
8776	(2^286383+3386)/2	86210	Stefano Morozzi	01/2020
8777	(13*2^286318-1)/13257	86188	Lelio R Paula	02/2014
8778	(2^286295+1934)/2	86184	Stefano Morozzi	01/2020
8779	(2^286251+3974)/2	86170	Stefano Morozzi	01/2020
8780	2^286165+77	86145	Lelio R Paula	08/2012
8781	9*2^286140+7	86138	Lelio R Paula	08/2014
8782	(2^286128+1762)/2	86133	Stefano Morozzi	01/2020
8783	(118*10^86131+71)/9	86133	Robert Price	11/2021
8784	(29*2^286108-1)/2002367	86123	Lelio R Paula	02/2014
8785	(2^286077+1122)/2	86118	Stefano Morozzi	01/2020
8786	10^86110+161113	86111	Patrick De Geest	07/2013
8787	10^86110-69	86110	Robert Price	05/2011
8788	2^286036-869688105	86106	Lelio R Paula	07/2016
8789	(2^285946+2358)/2	86079	Stefano Morozzi	01/2020
8790	5*10^86076-21	86077	Robert Price	12/2021
8792	(77*10^86072+31)/9	86073	Robert Price	10/2015
8791	(2^285926+3382)/2	86073	Stefano Morozzi	01/2020
8793	2^285923+345	86072	Lelio R Paula	09/2013
8794	13^77266-90	86070	Lelio R Paula	11/2015
8795	2^285910-458903	86068	Enzo Doria	04/2015
8796	2^285904-125	86066	Lelio R Paula	08/2012
8797	(2^285882+2830)/2	86059	Stefano Morozzi	01/2020
8798	2^285836+65835	86046	Lelio R Paula	09/2013
8799	21587^9670+9670^21587	86034	Hans Havermann	08/2020
8800	(2^285766+78557)/3	86024	Lelio R Paula	01/2013
8801	(2^285732+2682)/2	86014	Stefano Morozzi	01/2020
8802	(5*10^86011-107)/3	86012	Robert Price	01/2017
8803	6^110522+163	86003	Lelio R Paula	12/2015
8804	41^53323-40^53323	85999	Robert Price	07/2012
8805	2^285678-109617	85998	Enzo Doria	04/2014
8806	6^110506-16673	85991	Enzo Doria	02/2013
8807	2^285569-741	85965	Lelio R Paula	09/2013
8808	(32*10^85964+31)/9	85965	Robert Price	05/2015
8809	133^40466+132	85944	Norbert Schneider	02/2019
8810	23378^4743+4743^23378	85939	Hans Havermann	08/2020
8811	6*10^85910-7	85911	Dmitry Domanov	11/2010
8812	(412*10^85897-7)/9	85899	Robert Price	10/2017
8813	4*10^85881+63	85882	Robert Price	06/2016
8814	(2^285257+1514)/2	85871	Stefano Morozzi	01/2020
8815	(2^285248+3738)/2	85868	Stefano Morozzi	01/2020
8816	(10^85864+53)/9	85864	Robert Price	01/2015
8817	2^285230+345	85863	Lelio R Paula	09/2013
8818	21774^8777+8777^21774	85863	Hans Havermann	08/2020
8819	(5*10^85855-473)/9	85855	Robert Price	12/2017
8820	2^285199+75683	85854	Enzo Doria	04/2016
8821	(76*10^85847-211)/9	85848	Robert Price	10/2017
8822	p(17832)#/2+512	85845	Robert Price	05/2017
8823	(16*10^85839+167)/3	85840	Robert Price	10/2017
8824	11^82426-1230	85838	Enzo Doria	11/2012
8825	(14727^20593-1)/14726	85830	Serge Batalov	08/2020
8826	2^285113-109881	85828	Enzo Doria	04/2014
8827	(2^285033+1670)/2	85804	Stefano Morozzi	01/2020
8828	(2^285033+3854)/2	85804	Stefano Morozzi	01/2020
8829	(2^285035+3194)/2	85804	Stefano Morozzi	01/2020
8830	5^122746-92	85796	Lelio R Paula	10/2015
8831	2^285001-113461	85794	Enzo Doria	08/2014
8832	(11*10^85782-131)/3	85783	Robert Price	02/2017
8833	(2^284963+2778)/2	85783	Stefano Morozzi	01/2020
8834	(2^284960+3570)/2	85782	Stefano Morozzi	01/2020
8835	(2^284937+1706)/2	85775	Stefano Morozzi	01/2020
8837	2^284913-110491	85768	Enzo Doria	05/2014
8836	6^110220+47	85768	Lelio R Paula	12/2015
8838	(1966^26041-1)/1965	85765	Serge Batalov	08/2020
8839	20698^13909+13909^20698	85758	Hans Havermann	07/2020
8840	3*6^110202-5	85755	Lelio R Paula	10/2014
8841	9*10^85746+37	85747	Robert Price	12/2020
8842	(157^39047-1)/156	85742	Alexander Zhirkov	06/2016
8843	(3^179705+7)/250	85739	Lelio R Paula	12/2012
8844	(9127^21649-1)/9126	85734	Serge Batalov	08/2020
8845	2^284734-6555	85714	Lelio R Paula	09/2013
8846	(10^85712+53)/9	85712	Robert Price	01/2015
8847	3*10^85703+11	85704	Robert Price	11/2017
8848	(6883*2^284668-1)/3	85697	Lelio R Paula	04/2015
8849	20728^13621+13621^20728	85694	Hans Havermann	07/2020
8850	22126^7459+7459^22126	85687	Hans Havermann	07/2020
8851	(9311^21589-1)/9310	85683	Serge Batalov	08/2020
8852	20^65855+83	85680	Lelio R Paula	01/2016
8853	6^110105+53	85679	Lelio R Paula	12/2015
8854	3*10^85672-73	85673	Robert Price	02/2021
8855	(10^85666-97)/3	85666	Robert Kinser	10/2017
8857	2^284567-7605	85664	Lelio R Paula	09/2013
8856	9*5^122555-2	85664	Lelio R Paula	10/2014
8858	5^122554-14	85662	Lelio R Paula	10/2015
8859	9*5^122543+4	85655	Lelio R Paula	10/2014
8860	(7*10^85647+173)/9	85647	Robert Price	01/2022
8862	3^179489-2^(179489-1)	85639	Robert Price	01/2016
8861	(2^284487+1970)/2	85639	Stefano Morozzi	01/2020
8863	(2^284477+1614)/2	85636	Stefano Morozzi	01/2020
8864	23693^4114+4114^23693	85633	Hans Havermann	07/2020
8865	19690^19941+19941^19690	85632	Norbert Schneider	03/2020
8866	2^284429+177	85622	Lelio R Paula	08/2012
8867	2*3^179452+5	85621	Lelio R Paula	07/2014
8868	21036^11711+11711^21036	85587	Hans Havermann	07/2020
8870	(19^66919+3^66919)/22	85572	Robert Price	07/2013
8869	(2^284265+602)/2	85572	Stefano Morozzi	01/2020
8871	66^47023-65	85561	Norbert Schneider	11/2014
8872	(2^284226+3802)/2	85561	Stefano Morozzi	01/2020
8873	(2^284228+2170)/2	85561	Stefano Morozzi	01/2020
8874	6^109943+13	85553	Lelio R Paula	12/2015
8875	2^284183-4747	85548	Yves Minet	05/2019
8876	(5637^22807-1)/5636	85547	Serge Batalov	08/2020
8877	20782^13071+13071^20782	85546	Hans Havermann	08/2020
8878	(2^284167-509203)/34564775	85536	Lelio R Paula	01/2013
8879	(2^284136+2262)/2	85534	Stefano Morozzi	01/2020
8880	2^284133-3	85533	M. Frind & P. Underwood	07/2002
8881	2^284113+315	85527	Lelio R Paula	09/2013
8882	(2^284098+3082)/2	85522	Stefano Morozzi	01/2020
8883	(2^284070+1482)/2	85514	Stefano Morozzi	01/2020
8884	(2^284068+2866)/2	85513	Stefano Morozzi	01/2020
8885	(8721^21701-1)/8720	85511	Serge Batalov	08/2020
8886	22085^7438+7438^22085	85502	Hans Havermann	07/2020
8887	(28*10^85500+149)/3	85501	Robert Price	10/2017
8888	(16*10^85495-19)/3	85496	Robert Price	03/2016
8889	2^284004+177	85494	Lelio R Paula	08/2012
8890	(16*10^85473-91)/3	85474	Robert Price	06/2016
8891	66*10^85468+7	85470	Robert Price	07/2020
8892	3^179120+22	85462	Robert Price	12/2013
8893	2^283872-2792249	85454	Enzo Doria	03/2016
8894	(4703^23269-1)/4702	85449	Serge Batalov	08/2020
8895	(29*10^85438+259)/9	85439	Robert Price	04/2017
8896	2^283817+82875	85438	Lelio R Paula	09/2013
8897	(2^283815-5)/201	85435	Lelio R Paula	01/2013
8898	2^283796-125	85432	Lelio R Paula	08/2012
8899	(10174^21319-1)/10173	85432	Serge Batalov	08/2020
8900	(29*2^283784-1)/13	85428	Lelio R Paula	02/2014
8901	15^72592-28	85375	Lelio R Paula	11/2015
8902	2^283604-58695	85374	Lelio R Paula	09/2013
8903	21863^8034+8034^21863	85374	Hans Havermann	08/2020
8905	(44*10^85370-503)/9	85371	Robert Price	10/2017
8904	(2^283597+1854)/2	85371	Stefano Morozzi	01/2020
8906	496^31671+31671^496	85369	Norbert Schneider	07/2017
8907	(2^283578+478)/2	85366	Stefano Morozzi	01/2020
8908	(15*2^283583-1)/103051	85364	Lelio R Paula	02/2014
8909	15^72572+92	85352	Lelio R Paula	11/2015
8910	2^283473-1615	85334	Lelio R Paula	09/2013
8911	(2^283469+2934)/2	85333	Stefano Morozzi	01/2020
8912	2^283466-15	85332	Lelio R Paula	08/2012
8913	(2^283437+3446)/2	85323	Stefano Morozzi	01/2020
8914	19966^18761+18761^19966	85320	Hans Havermann	07/2020
8915	(2^283411+3894)/2	85315	Stefano Morozzi	01/2020
8916	11^81916-7020	85307	Enzo Doria	02/2013
8917	6^109626-7	85306	Lelio R Paula	11/2014
8918	2^283374-110327	85305	Enzo Doria	05/2014
8919	33*10^85297+7	85299	Robert Price	07/2016
8920	(6010^22573-1)/6009	85297	Serge Batalov	08/2020
8921	1137^27908+27908^1137	85281	Norbert Schneider	04/2020
8922	18^67933+41	85275	Lelio R Paula	11/2015
8923	2^283271-109341	85274	Enzo Doria	04/2014
8924	(2^283266+3678)/2	85272	Stefano Morozzi	01/2020
8925	19688^19855-19855^19688	85262	Norbert Schneider	03/2020
8926	(2^283216+1926)/2	85257	Stefano Morozzi	01/2020
8927	(5*10^85254-191)/3	85255	Robert Price	05/2021
8928	(25*10^85249-73)/3	85250	Robert Price	09/2016
8929	2*5^121959+3	85246	Lelio R Paula	10/2014
8930	19834^19834+8947	85235	Henri Lifchitz	11/2004
8931	2^283140+1915	85234	Lelio R Paula	09/2013
8932	3*10^85227-97	85228	Robert Price	08/2017
8933	(16*10^85221-31)/3	85222	Robert Price	03/2016
8934	(2^283096+3186)/2	85221	Stefano Morozzi	01/2020
8935	2^283083+1869383	85217	Enzo Doria	05/2016
8936	(24737*2^283051+1)/17	85211	Lelio R Paula	06/2014
8937	(2^283032+78557)/3	85201	Lelio R Paula	01/2013
8938	2^283026-109893	85200	Enzo Doria	04/2014
8939	(2^283012+78557)/129	85193	Lelio R Paula	01/2013
8940	(10^(242589+1)+7210^42589-1)/9	85179	Robert Price	09/2017
8941	2^282860-109727	85150	Enzo Doria	04/2014
8942	(2^282847+13)/3	85145	Stefano Morozzi	03/2020
8943	2^282819+1869413	85138	Enzo Doria	05/2016
8944	3^178428+2	85132	Ray Chandler	07/2011
8945	19985^18162+18162^19985	85120	Hans Havermann	07/2020
8946	(22699*2^282742+1)/73	85117	Lelio R Paula	06/2014
8947	(16^70687+5^70687)/21	85115	Robert Price	07/2013
8948	(2^282732+738)/2	85111	Stefano Morozzi	01/2020
8949	(2^282720+1590)/2	85107	Stefano Morozzi	01/2020
8950	(3^178352-2)/7	85095	Lelio R Paula	12/2012
8951	22150^6939+6939^22150	85085	Hans Havermann	07/2020
8952	11^81699-2790	85081	Enzo Doria	12/2012
8953	2^282612-95	85075	Lelio R Paula	08/2012
8954	2^282609-4069	85074	Yves Minet	02/2018
8955	75^45366-2	85065	Lelio R Paula	08/2013
8956	(2^282550+1918)/2	85056	Stefano Morozzi	01/2020
8957	(2^282515+3786)/2	85046	Stefano Morozzi	01/2020
8958	2^282511+69	85045	Lelio R Paula	08/2012
8959	69^46249+2	85045	Lelio R Paula	06/2013
8960	(2^282488+2382)/2	85038	Stefano Morozzi	01/2020
8961	(2^282489+1862)/2	85038	Stefano Morozzi	01/2020
8962	3^178226+10	85036	Robert Price	10/2013
8963	(2^282475+1050)/2	85034	Stefano Morozzi	01/2020
8964	(182*10^85017+43)/9	85019	Robert Price	11/2017
8965	(14*10^85010+73)/3	85011	Robert Price	04/2016
8966	9*2^282338-7	84994	Lelio R Paula	08/2014
8967	(9913*2^282330-1)/1578003	84988	Lelio R Paula	04/2015
8968	5*10^84985-31	84986	Robert Price	12/2021
8969	20025^17504+17504^20025	84969	Hans Havermann	07/2020
8970	2^282203+5	84952	Lelio R Paula	08/2012
8971	2^282184+13	84946	Lelio R Paula	08/2012
8972	11^81568-2400	84945	Enzo Doria	12/2012
8973	11^81562-2340	84939	Enzo Doria	12/2012
8974	(41*10^84927+31)/9	84928	Robert Price	05/2015
8975	(3923^23629-1)/3922	84911	Serge Batalov	08/2020
8976	(2^282053+1406)/2	84907	Stefano Morozzi	01/2020
8977	(2*10^84904-17)/3	84904	Robert Price	08/2014
8978	(4^141017+23)/3	84901	Robert Price	02/2017
8979	6^109100-18653	84897	Enzo Doria	03/2013
8980	2^281973+1025	84883	Lelio R Paula	09/2013
8981	2^281951-109651	84876	Enzo Doria	04/2014
8982	21618^8431+8431^21618	84870	Hans Havermann	07/2020
8983	11^81491-5430	84865	Enzo Doria	01/2013
8984	10^84863+141057	84864	Patrick De Geest	02/2021
8985	10^84863-40001	84863	Robert Price	01/2021
8986	((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
8987	(2^281827+650)/2	84839	Stefano Morozzi	01/2020
8988	2^281825-1861483	84838	Enzo Doria	03/2016
8989	2^281809-97305	84833	Lelio R Paula	09/2013
8990	2^281780-114893	84825	Enzo Doria	05/2015
8991	(7654^21841-1)/7653	84825	Serge Batalov	08/2020
8992	3^177719+64	84794	Lelio R Paula	12/2015
8994	2^281675-199	84793	Lelio R Paula	08/2012
8993	2^281673-111223	84793	Enzo Doria	05/2014
8995	(4*10^84779+149)/9	84779	Robert Price	03/2017
8997	129^40167-128	84777	Norbert Schneider	01/2019
8996	(2^281622+3970)/2	84777	Stefano Morozzi	01/2020
8998	9*10^84775-47	84776	Robert Price	11/2021
8999	(72*10^84772-27)/9	84773	Ray Chandler	01/2011
9000	11^81398-630	84768	Enzo Doria	11/2012

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Probable Primes Top 10000

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