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	(13*10^87565+11)/3	87566	Robert Price	05/2015
5752	(2^290881+1022)/2	87564	Stefano Morozzi	01/2020
5753	(2^290857-7)/55	87555	Lelio R Paula	01/2013
5754	(2^290808+1498)/2	87542	Stefano Morozzi	01/2020
5755	2^290802+82875	87541	Lelio R Paula	10/2013
5756	(509203*2^290792-1)/7560987	87536	Lelio R Paula	04/2015
5757	3^183441+236	87524	Lelio R Paula	12/2015
5758	2^290618-33	87485	Lelio R Paula	09/2012
5759	(184*10^87473-1)/3	87475	Robert Price	02/2017
5760	2^290534-115151	87460	Enzo Doria	06/2015
5761	2^290512-109757	87453	Enzo Doria	04/2014
5762	(32*10^87448-41)/9	87449	Robert Price	05/2015
5763	(2^290493+3074)/2	87447	Stefano Morozzi	01/2020
5764	(2^290491+9)/3179	87444	Lelio R Paula	01/2013
5765	(25*2^290489-1)/51809	87443	Lelio R Paula	02/2014
5766	2^290426+82875	87427	Lelio R Paula	11/2013
5767	3*2^290415-7	87425	Lelio R Paula	08/2014
5769	10^87408+57	87409	Robert Price	03/2011
5768	2^290366+74779	87409	Enzo Doria	04/2016
5770	10^87408-123569	87408	Patrick De Geest	07/2013
5771	(2^290268+3882)/2	87380	Stefano Morozzi	01/2020
5772	2^290265+58905	87379	Lelio R Paula	10/2013
5773	7^103391+16	87376	Lelio R Paula	10/2015
5774	(115*10^87368-7)/9	87370	Robert Price	11/2017
5775	(92^44491-1)/91	87369	Paul Bourdelais	08/2017
5776	8*7^103379+3	87367	Lelio R Paula	10/2014
5777	(2^290226+7)/71	87365	Lelio R Paula	01/2013
5778	(2^290160+2686)/2	87347	Stefano Morozzi	01/2020
5779	13^78407-30	87341	Lelio R Paula	11/2015
5780	4*10^87337-99	87338	Robert Price	12/2016
5781	7*10^87319+39	87320	Robert Price	07/2016
5782	3*5^124921+2	87317	Lelio R Paula	10/2014
5783	78315!4-16	87316	Robert Price	11/2019
5784	3^182984+88	87306	Lelio R Paula	12/2015
5785	(10^87323-1)/(9*33909262597306826117)	87303	Alfred Reich	02/2019
5786	(2^290008+958)/2	87301	Stefano Morozzi	01/2020
5787	4*10^87287-99	87288	Robert Price	12/2016
5788	11^83813-1860	87283	Enzo Doria	12/2012
5789	734^30453+30453^734	87270	Norbert Schneider	04/2017
5790	12^80855+29	87258	Lelio R Paula	11/2015
5791	3*6^112119-5	87247	Lelio R Paula	10/2014
5792	12^80806+79	87205	Lelio R Paula	11/2015
5793	91382^9+9^91382	87201	Andrey Kulsha	11/2004
5794	(21181*2^289657+1)/81	87198	Lelio R Paula	06/2014
5795	6^112054-47	87195	Lelio R Paula	12/2015
5796	(55459*2^289632+1)/55	87191	Lelio R Paula	06/2014
5797	15^74131-68	87185	Lelio R Paula	11/2015
5798	2^289583-741	87174	Lelio R Paula	10/2013
5799	7^103146+12	87169	Lelio R Paula	10/2015
5800	(2^289562+2182)/2	87167	Stefano Morozzi	01/2020
5801	5*2^289556-3	87166	Lelio R Paula	08/2014
5802	2^289543-112735	87162	Enzo Doria	06/2014
5803	8*3^182655-7	87150	Lelio R Paula	08/2014
5804	2*10^87144+81	87145	Robert Price	01/2017
5805	7^103106+2*3^103106	87135	Mike Oakes	08/2010
5806	8*3^182614+7	87130	Lelio R Paula	08/2014
5807	(2^289368-509203)/9	87108	Lelio R Paula	01/2013
5808	3^182566+14	87107	Robert Price	09/2013
5809	(3^182385-5)/2	87020	Lelio R Paula	01/2013
5810	11^83534-8	86992	Lelio R Paula	11/2015
5811	4^144479-14267	86986	Mike Oakes	03/2011
5812	(145*10^86982-1)/9	86984	Serge Batalov	12/2014
5813	(151*10^86963-1)/3	86965	Robert Price	04/2017
5814	(2^288892+826)/2	86965	Stefano Morozzi	01/2020
5815	15^73940-58	86961	Lelio R Paula	11/2015
5816	2^288761-113143	86926	Enzo Doria	07/2014
5818	2^288747+3083	86922	Yves Minet	03/2011
5817	(2^288749+3102)/2	86922	Stefano Morozzi	01/2020
5819	30^58842+29	86917	Norbert Schneider	03/2017
5820	(2^288705+2186)/2	86909	Stefano Morozzi	01/2020
5821	(10^86906-13)/3	86906	Robert Price	02/2017
5822	2^288692-110027	86905	Enzo Doria	04/2014
5823	(2^288682+7)/259895449	86894	Lelio R Paula	01/2013
5824	(2^288636+47)/1293	86885	Lelio R Paula	01/2013
5825	3^182089-34	86879	Robert Price	11/2013
5826	(2^288571+1698)/2	86869	Stefano Morozzi	01/2020
5827	2^288543-109801	86861	Enzo Doria	04/2014
5828	60^48847-59	86858	Norbert Schneider	10/2014
5829	(2^288484+3186)/2	86843	Stefano Morozzi	01/2020
5830	2^288470-64875	86839	Lelio R Paula	10/2013
5831	10^86816+32997	86817	Patrick De Geest	07/2013
5832	10^86816-99	86816	Robert Price	05/2011
5833	(89*10^86802-539)/9	86803	Robert Price	11/2017
5834	(2^288316+1530)/2	86792	Stefano Morozzi	01/2020
5835	(2^288316+2218)/2	86792	Stefano Morozzi	01/2020
5836	41487!2+256	86786	Robert Price	01/2015
5837	(5*2^288301-1)/999	86785	Lelio R Paula	02/2014
5838	(2^288278+1750)/2	86781	Stefano Morozzi	01/2020
5839	2^288243+76043	86770	Enzo Doria	04/2016
5840	(29*2^288232+1)/15	86767	Lelio R Paula	01/2013
5841	9*6^111495+5	86761	Lelio R Paula	10/2014
5842	(5*2^288202+1)/81	86757	Lelio R Paula	01/2013
5843	9*7^102654-2	86754	Lelio R Paula	10/2014
5844	(2^288155+1154)/2	86743	Stefano Morozzi	01/2020
5845	2^288122-112841	86734	Enzo Doria	06/2014
5846	5^124062-68	86716	Lelio R Paula	10/2015
5847	(2^288007-3)/125	86697	Lelio R Paula	01/2013
5848	379*10^86691+9	86694	Arkadiusz Wesolowski	10/2011
5849	7^102555+48	86670	Lelio R Paula	10/2015
5850	2^287902-4961	86668	Yves Minet	05/2019
5851	77779!4+2	86660	Robert Price	08/2017
5852	(2^287842+3250)/2	86649	Stefano Morozzi	01/2020
5853	2^287809-111355	86640	Enzo Doria	05/2014
5854	(47*2^287795+1)/7	86636	Lelio R Paula	04/2015
5855	9*7^102504+8	86627	Lelio R Paula	10/2014
5856	3^181551+32	86622	Robert Price	11/2013
5857	2^287735-521347	86617	Paul Bourdelais	05/2013
5858	(1017*2^287600-1)/91	86578	Lelio R Paula	04/2015
5859	(2^287552+1302)/2	86562	Stefano Morozzi	01/2020
5860	2^287540-112967	86559	Enzo Doria	06/2014
5861	3^181407+20	86554	Robert Price	10/2013
5863	(13*10^86546+83)/3	86547	Robert Price	09/2016
5862	(2^287502+2238)/2	86547	Stefano Morozzi	01/2020
5864	2^287482-4715	86541	Yves Minet	05/2019
5865	3^181378-2^(181378-1)	86540	Robert Price	01/2016
5866	83^45080-2	86513	Lelio R Paula	08/2013
5867	(2^287367+2570)/2	86506	Stefano Morozzi	01/2020
5869	(78557*2^287351+1)/611	86504	Lelio R Paula	06/2014
5868	(2^287360+1006)/2	86504	Stefano Morozzi	01/2020
5870	25*29^59147+20936	86498	Curtis Bright	05/2015
5871	2^287298+1871359	86486	Enzo Doria	05/2016
5872	118^41740-117	86481	Norbert Schneider	08/2018
5873	3*10^86478+89	86479	Robert Price	03/2017
5874	2^287272-79049	86478	Paul Bourdelais	02/2012
5875	(2^287259+2846)/2	86474	Stefano Morozzi	01/2020
5876	9067052((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
5877	8118242((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
5878	7790642((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
5879	7683852((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
5880	7008912((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
5881	6523202((10^86453-1)/9)+1	86459	Danilo Nitsche	01/2016
5882	3779202((10^86453-1)/9)+1	86458	Danilo Nitsche	01/2016
5883	2550602((10^86453-1)/9)+1	86458	Danilo Nitsche	01/2016
5884	1871112((10^86453-1)/9)+1	86458	Danilo Nitsche	01/2016
5885	(10^86453-1)/9	86453	Lew Baxter	10/2000
5886	(2^287172+658)/2	86448	Stefano Morozzi	01/2020
5887	(2^287146+2542)/2	86440	Stefano Morozzi	01/2020
5888	(2^287136+1726)/2	86437	Stefano Morozzi	01/2020
5889	(2^287128+958)/2	86434	Stefano Morozzi	01/2020
5890	87^44563-86^44563	86431	Robert Price	05/2015
5891	6^111057+61	86420	Lelio R Paula	12/2015
5892	2^287057-109909	86413	Enzo Doria	04/2014
5893	5^123608+22	86399	Lelio R Paula	10/2015
5894	(2^286970+618)/2	86387	Stefano Morozzi	01/2020
5895	(2^286916+2646)/2	86371	Stefano Morozzi	01/2020
5896	(2^286907+3690)/2	86368	Stefano Morozzi	01/2020
5897	(31*10^86364-121)/9	86365	Robert Price	06/2016
5898	(2^286868+2686)/2	86356	Stefano Morozzi	01/2020
5899	2^286859+71663	86354	Enzo Doria	04/2016
5900	(2^286845+1866)/2	86349	Stefano Morozzi	01/2020
5901	2^286740+29835	86318	Lelio R Paula	10/2013
5902	2*10^86310+9^86310	86311	Mike Oakes	05/2011
5903	11^82878-1860	86309	Enzo Doria	12/2012
5904	2223^25780+25780^2223	86285	Norbert Schneider	12/2019
5905	2^286547+16095	86260	Lelio R Paula	10/2013
5906	(58*10^86242+329)/9	86243	Robert Price	11/2017
5907	2^286455-110427	86232	Enzo Doria	05/2014
5908	(37*10^86230+53)/9	86231	Robert Price	05/2015
5909	8*3^180700+5	86217	Lelio R Paula	08/2014
5910	3^180697-40	86215	Lelio R Paula	12/2015
5911	(2^286383+3386)/2	86210	Stefano Morozzi	01/2020
5912	(13*2^286318-1)/13257	86188	Lelio R Paula	02/2014
5913	(2^286295+1934)/2	86184	Stefano Morozzi	01/2020
5914	(2^286251+3974)/2	86170	Stefano Morozzi	01/2020
5915	2^286165+77	86145	Lelio R Paula	08/2012
5916	9*2^286140+7	86138	Lelio R Paula	08/2014
5917	(2^286128+1762)/2	86133	Stefano Morozzi	01/2020
5918	(29*2^286108-1)/2002367	86123	Lelio R Paula	02/2014
5919	(2^286077+1122)/2	86118	Stefano Morozzi	01/2020
5920	10^86110+161113	86111	Patrick De Geest	07/2013
5921	10^86110-69	86110	Robert Price	05/2011
5922	2^286036-869688105	86106	Lelio R Paula	07/2016
5923	(2^285946+2358)/2	86079	Stefano Morozzi	01/2020
5925	(77*10^86072+31)/9	86073	Robert Price	10/2015
5924	(2^285926+3382)/2	86073	Stefano Morozzi	01/2020
5926	2^285923+345	86072	Lelio R Paula	09/2013
5927	13^77266-90	86070	Lelio R Paula	11/2015
5928	2^285910-458903	86068	Enzo Doria	04/2015
5929	2^285904-125	86066	Lelio R Paula	08/2012
5930	(2^285882+2830)/2	86059	Stefano Morozzi	01/2020
5931	2^285836+65835	86046	Lelio R Paula	09/2013
5932	(2^285766+78557)/3	86024	Lelio R Paula	01/2013
5933	(2^285732+2682)/2	86014	Stefano Morozzi	01/2020
5934	(5*10^86011-107)/3	86012	Robert Price	01/2017
5935	6^110522+163	86003	Lelio R Paula	12/2015
5936	41^53323-40^53323	85999	Robert Price	07/2012
5937	2^285678-109617	85998	Enzo Doria	04/2014
5938	6^110506-16673	85991	Enzo Doria	02/2013
5939	2^285569-741	85965	Lelio R Paula	09/2013
5940	(32*10^85964+31)/9	85965	Robert Price	05/2015
5941	133^40466+132	85944	Norbert Schneider	02/2019
5942	6*10^85910-7	85911	Dmitry Domanov	11/2010
5943	(412*10^85897-7)/9	85899	Robert Price	10/2017
5944	4*10^85881+63	85882	Robert Price	06/2016
5945	(2^285257+1514)/2	85871	Stefano Morozzi	01/2020
5946	(2^285248+3738)/2	85868	Stefano Morozzi	01/2020
5947	(10^85864+53)/9	85864	Robert Price	01/2015
5948	2^285230+345	85863	Lelio R Paula	09/2013
5949	(5*10^85855-473)/9	85855	Robert Price	12/2017
5950	2^285199+75683	85854	Enzo Doria	04/2016
5951	(76*10^85847-211)/9	85848	Robert Price	10/2017
5952	p(17832)#/2+512	85845	Robert Price	05/2017
5953	(16*10^85839+167)/3	85840	Robert Price	10/2017
5954	11^82426-1230	85838	Enzo Doria	11/2012
5955	2^285113-109881	85828	Enzo Doria	04/2014
5956	(2^285033+1670)/2	85804	Stefano Morozzi	01/2020
5957	(2^285033+3854)/2	85804	Stefano Morozzi	01/2020
5958	(2^285035+3194)/2	85804	Stefano Morozzi	01/2020
5959	5^122746-92	85796	Lelio R Paula	10/2015
5960	2^285001-113461	85794	Enzo Doria	08/2014
5961	(11*10^85782-131)/3	85783	Robert Price	02/2017
5962	(2^284963+2778)/2	85783	Stefano Morozzi	01/2020
5963	(2^284960+3570)/2	85782	Stefano Morozzi	01/2020
5964	(2^284937+1706)/2	85775	Stefano Morozzi	01/2020
5965	2^284913-110491	85768	Enzo Doria	05/2014
5966	6^110220+47	85768	Lelio R Paula	12/2015
5967	3*6^110202-5	85755	Lelio R Paula	10/2014
5968	(157^39047-1)/156	85742	Alexander Zhirkov	06/2016
5969	(3^179705+7)/250	85739	Lelio R Paula	12/2012
5970	2^284734-6555	85714	Lelio R Paula	09/2013
5971	(10^85712+53)/9	85712	Robert Price	01/2015
5972	3*10^85703+11	85704	Robert Price	11/2017
5973	(6883*2^284668-1)/3	85697	Lelio R Paula	04/2015
5974	20^65855+83	85680	Lelio R Paula	01/2016
5975	6^110105+53	85679	Lelio R Paula	12/2015
5976	(10^85666-97)/3	85666	Robert Kinser	10/2017
5978	2^284567-7605	85664	Lelio R Paula	09/2013
5977	9*5^122555-2	85664	Lelio R Paula	10/2014
5979	5^122554-14	85662	Lelio R Paula	10/2015
5980	9*5^122543+4	85655	Lelio R Paula	10/2014
5982	3^179489-2^(179489-1)	85639	Robert Price	01/2016
5981	(2^284487+1970)/2	85639	Stefano Morozzi	01/2020
5983	(2^284477+1614)/2	85636	Stefano Morozzi	01/2020
5984	19690^19941+19941^19690	85632	Norbert Schneider	03/2020
5985	2^284429+177	85622	Lelio R Paula	08/2012
5986	2*3^179452+5	85621	Lelio R Paula	07/2014
5988	(19^66919+3^66919)/22	85572	Robert Price	07/2013
5987	(2^284265+602)/2	85572	Stefano Morozzi	01/2020
5991	66^47023-65	85561	Norbert Schneider	11/2014
5989	(2^284226+3802)/2	85561	Stefano Morozzi	01/2020
5990	(2^284228+2170)/2	85561	Stefano Morozzi	01/2020
5992	6^109943+13	85553	Lelio R Paula	12/2015
5993	2^284183-4747	85548	Yves Minet	05/2019
5994	(2^284167-509203)/34564775	85536	Lelio R Paula	01/2013
5995	(2^284136+2262)/2	85534	Stefano Morozzi	01/2020
5996	2^284133-3	85533	M. Frind & P. Underwood	07/2002
5997	2^284113+315	85527	Lelio R Paula	09/2013
5998	(2^284098+3082)/2	85522	Stefano Morozzi	01/2020
5999	(2^284070+1482)/2	85514	Stefano Morozzi	01/2020
6000	(2^284068+2866)/2	85513	Stefano Morozzi	01/2020

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Probable Primes Top 10000

(259919 PRPs in the top)