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 (> 30000)	Who ?	When ?
5751	2^238389-110905	71763	Enzo Doria	05/2014
5752	(145*10^71760-1)/9	71762	Serge Batalov	12/2014
5753	7^84913+5062	71760	Mike Oakes	02/2010
5754	(F(11446)^31-F(11445)^31)/F(11444)	71753	Wayne Halsdorf	03/2012
5755	2^238268-97305	71726	Lelio R Paula	05/2012
5756	gcd(V(1330365),5F(266073)(F(266073)-1)+1)	71724	Serge Batalov	04/2015
5757	2^238235-113247	71716	Enzo Doria	07/2014
5758	2*12^66450-5^66450	71712	Mike Oakes	11/2010
5759	(2^238213+lucasV(1,2,238213)+1)/4	71709	Mike Oakes	11/2016
5760	2^238199-111817	71706	Enzo Doria	05/2014
5761	lucasU(46,1,43125)+lucasU(46,1,43124)	71696	Mike Oakes	04/2009
5762	2^238144+98765331	71689	Jason Earls	01/2009
5763	18^57102-4265	71679	Enzo Doria	03/2013
5764	(73*10^71670-1)/9	71671	Robert Price	01/2015
5765	2^238081+1155*238081	71670	Henri Lifchitz	02/2005
5766	2^238067-111925	71666	Enzo Doria	05/2014
5767	36^46030+35	71637	Norbert Schneider	04/2014
5768	2^237905-91	71617	Lelio R Paula	02/2012
5769	(31*2^237902-1)/123	71616	Lelio R Paula	01/2014
5770	(15185*2^237866-1)/43967	71605	Lelio R Paula	04/2015
5771	(24737*2^237841+1)/25	71601	Lelio R Paula	06/2014
5772	2^237846+1299	71599	Lelio R Paula	05/2012
5773	6^92004+199801	71594	Mike Oakes	02/2011
5774	159^32516+2	71581	Lelio R Paula	05/2013
5775	2^237781+855	71580	Lelio R Paula	05/2012
5776	2^237720-4079	71561	Yves Minet	06/2011
5777	2^237698-110945	71555	Enzo Doria	05/2014
5778	2^237695-113239	71554	Enzo Doria	07/2014
5779	8*5^102362-9	71549	Lelio R Paula	10/2014
5780	(4*10^71546-31)/9	71546	Erik Branger	05/2011
5781	2^237650+37	71540	Lelio R Paula	02/2012
5782	18^56977-4391	71522	Enzo Doria	03/2013
5783	(22699*2^237565+1)/4136637	71512	Lelio R Paula	06/2014
5784	((1+sqrt(7)+sqrt(6))^48479-1)((1+sqrt(7)-sqrt(6))^48479-1)((1-sqrt(7)+sqrt(6))^48479-1)*((1-sqrt(7	71512	Mike Oakes	05/2009
5785	(26*10^71503+7)/3	71504	Erik Branger	11/2013
5786	(4*10^71498+173)/3	71499	Robert Price	01/2017
5787	3^149848+110	71496	Lelio R Paula	11/2014
5788	2^237498+513	71495	Lelio R Paula	05/2012
5789	2^237485+107	71491	Lelio R Paula	02/2012
5790	(2^237465+9)/2419	71481	Lelio R Paula	05/2012
5791	2^237439-112237	71477	Enzo Doria	06/2014
5792	2^237407-9787	71467	Lelio R Paula	11/2009
5793	2^237383+72953	71460	Enzo Doria	04/2016
5794	82^37337-81^37337	71457	Robert Price	01/2015
5795	(1017*2^237313-1)/19	71441	Lelio R Paula	04/2015
5796	2^237311+191	71438	Lelio R Paula	02/2012
5797	2^237280-59	71429	Lelio R Paula	02/2012
5798	11^68564-98	71403	Lelio R Paula	01/2015
5799	2^237173+74801	71397	Enzo Doria	04/2016
5800	15^60697+56	71386	Lelio R Paula	01/2015
5801	2^237118+177	71380	Lelio R Paula	02/2012
5802	2^237110+69	71378	Lelio R Paula	02/2012
5803	15^60690-58	71377	Lelio R Paula	01/2015
5804	(5*2^237125-1)/599851191	71374	Lelio R Paula	01/2014
5805	(3^149567+2)/539	71359	Lelio R Paula	06/2012
5806	(5*10^71357-143)/3	71358	Robert Price	04/2016
5807	2^237039-114621	71356	Enzo Doria	05/2015
5808	12^66116-37	71352	Lelio R Paula	02/2015
5809	(3^149497+2^149497)/5	71328	Jean-Louis Charton	10/2010
5810	2^236941-66945	71327	Lelio R Paula	05/2012
5811	2^236911-1147	71318	Yves Minet	10/2009
5812	65^39337+42	71315	Lelio R Paula	01/2016
5813	6*10^71299+7	71300	Dmitry Domanov	11/2010
5814	(25*2^236843+1)/3753	71295	Lelio R Paula	06/2012
5815	10^71291+15187	71292	Patrick De Geest	03/2016
5817	10^71291-5587309119	71291	Robert Price	03/2015
5816	10^71291-273581	71291	Patrick De Geest	03/2016
5818	-numer(bernoulli(22808)/22808)	71290	T. D. Noe	09/2005
5819	(2^236738+9)/13	71265	Lelio R Paula	05/2012
5820	5^101949+42	71260	Lelio R Paula	07/2014
5821	5*10^71237+9	71238	Dmitry Domanov	11/2010
5822	2^236634-16025	71234	Enzo Doria	04/2013
5823	71^38478+70	71233	Norbert Schneider	12/2014
5824	9*7^84280+8	71226	Lelio R Paula	10/2014
5825	(10^71223+59)/3	71223	Serge Batalov	12/2014
5826	(15185*2^236569-1)/453	71216	Lelio R Paula	04/2015
5827	51829#+(216091#)/(51829#)	71208	Makoto Morimoto	03/2016
5828	2^236528-173	71203	Lelio R Paula	02/2012
5829	3*2^236511-5	71198	Lelio R Paula	04/2014
5830	2^236477-99	71187	Lelio R Paula	02/2012
5831	11^68356-2130	71186	Enzo Doria	12/2012
5832	11^68355-3120	71185	Enzo Doria	12/2012
5833	36^45737-35^45737	71181	Robert Price	10/2012
5834	2^236432+25	71174	Lelio R Paula	02/2012
5835	5^101818-12806	71168	Enzo Doria	02/2013
5836	65^39253+62	71163	Lelio R Paula	01/2016
5837	39^44718+38	71150	Norbert Schneider	05/2014
5838	2^236296-407	71133	Yves Minet	02/2012
5839	2^236286-117	71130	Lelio R Paula	02/2012
5840	2^236257-111193	71121	Enzo Doria	05/2014
5841	7^84149-36	71115	Lelio R Paula	08/2014
5842	2^236209-112123	71106	Enzo Doria	06/2014
5843	18^56644-4985	71104	Enzo Doria	03/2013
5844	21^53753+2	71074	Ray Chandler	08/2011
5845	2^236081-110923	71068	Enzo Doria	05/2014
5846	(293*27^49642-1736)/13	71058	Curtis Bright	05/2015
5847	65^39192+22	71052	Lelio R Paula	01/2016
5848	(439#+1)^397-439#^397	71038	Mike Oakes	11/2010
5849	7^84050-2	71031	Lelio R Paula	09/2013
5850	20^54558-23	70982	Lelio R Paula	01/2015
5851	2^235793-112555	70981	Enzo Doria	06/2014
5852	49936!3-3^49936	70981	Robert Price	08/2015
5853	2^235787-78795	70979	Lelio R Paula	05/2012
5854	Perrin(581132)	70970	Eric W. Weisstein	02/2011
5855	14^61913-97	70961	Lelio R Paula	01/2015
5856	2^235720+16321	70959	Yves Minet	03/2010
5857	2^235718+16095	70959	Lelio R Paula	05/2012
5858	163841#+349933	70957	Nicolas PALAU	11/2016
5859	2^235710+7	70956	Lelio R Paula	02/2012
5860	2^235635-112087	70934	Enzo Doria	06/2014
5862	2^235575-1965	70916	Lelio R Paula	05/2012
5861	6^91133+101	70916	Lelio R Paula	01/2015
5863	(21181*2^235505+1)/3	70898	Lelio R Paula	06/2014
5864	5^101425+84	70894	Lelio R Paula	07/2014
5865	177^31536+2	70893	Lelio R Paula	05/2013
5866	43*71^38292+4	70891	Serge Batalov	03/2016
5867	(29*2^235506-1)/112029785	70888	Lelio R Paula	01/2014
5868	11^68045-1530	70862	Enzo Doria	12/2012
5869	5*10^70858+21	70859	Robert Price	01/2017
5871	2^235326+3	70841	Donovan Johnson	02/2006
5870	34523!2+4	70841	Robert Price	02/2015
5872	(31*2^235307+1)/3	70836	Lelio R Paula	06/2012
5873	2^235308+135	70835	Lelio R Paula	02/2012
5874	r(35414,90)*1000+911	70831	Patrick De Geest	07/2004
5875	2^235274+159	70825	Lelio R Paula	02/2012
5876	3^148409+70	70810	Lelio R Paula	11/2014
5877	(19*10^70794+17)/9	70795	Robert Price	03/2015
5878	2^235108-232709	70775	Paul Bourdelais	03/2013
5879	(2^235099-2^117550+1)/5	70772		11/2006
5880	19^55325-6	70748	Lelio R Paula	08/2014
5881	257^29356+29356^257	70746	Norbert Schneider	10/2014
5882	2^234956+11715	70729	Lelio R Paula	05/2012
5883	(7*10^70727-43)/9	70727	Robert Price	10/2014
5884	2^234890-30341	70709	Enzo Doria	11/2012
5885	17^57461+14	70703	Lelio R Paula	01/2015
5886	(9179*2^234834-1)/5	70696	Lelio R Paula	04/2015
5887	123^33822-122	70685	Norbert Schneider	01/2015
5888	(21*2^234772-1)/2095	70672	Lelio R Paula	01/2014
5889	(29*2^234686-1)/21145	70645	Lelio R Paula	01/2014
5890	(15*2^234688-1)/5278141	70643	Lelio R Paula	01/2014
5892	2^234655-67	70639	Lelio R Paula	02/2012
5891	(79*10^70638-61)/9	70639	Robert Price	10/2015
5893	2^234652-173	70638	Lelio R Paula	02/2012
5894	2^234618-3645	70628	Lelio R Paula	05/2012
5895	(2^234610-5)/19	70624	Lelio R Paula	05/2012
5896	4*5^101038+9	70624	Lelio R Paula	10/2014
5897	2^234603+71963	70623	Enzo Doria	04/2016
5898	2^234600-113129	70622	Enzo Doria	07/2014
5899	2^234586+9	70618	Lelio R Paula	02/2012
5900	3^148008+26	70618	Robert Price	11/2013
5901	65^38947+32	70608	Lelio R Paula	01/2016
5902	(2^234488-3)/11	70587	Lelio R Paula	05/2012
5903	(3*2^234451+1)/35	70576	Lelio R Paula	08/2012
5904	Phi(159495,10)	70560	Maksym Voznyy	09/2015
5905	2^234383-4035	70557	Lelio R Paula	05/2012
5906	2^234315-111241	70536	Enzo Doria	05/2014
5907	14^61526+97	70517	Lelio R Paula	01/2015
5908	(3*2^234170+1)/13	70492	Lelio R Paula	08/2012
5909	51^41281-50^41281	70491	Robert Price	02/2013
5910	2^234141-112123	70484	Enzo Doria	06/2014
5911	2^234139+12285	70483	Lelio R Paula	04/2012
5912	2^234133-3163	70482	Yves Minet	04/2009
5913	2^234115+83	70476	Lelio R Paula	02/2012
5914	2^234114-1595	70476	Lelio R Paula	05/2012
5915	24^51061-23^51061	70475	Robert Price	07/2012
5916	19471^16428-2	70467	Faysal YAtim	09/2005
5917	7^83381+12	70466	Robert Price	01/2014
5918	2^234067-111427	70462	Enzo Doria	05/2014
5919	(266*10^70457+1)/3	70459	Robert Price	02/2016
5920	(31*2^234041-1)/97	70453	Lelio R Paula	01/2014
5921	2^234026+12909	70449	Lelio R Paula	04/2012
5922	2^233965-19	70431	Lelio R Paula	02/2012
5923	(5*2^233932-1)/179	70419	Lelio R Paula	01/2014
5924	2^233908-17109	70414	Enzo Doria	05/2013
5925	695^24772+24772^695	70402	Norbert Schneider	09/2016
5926	3*5^100719-2	70401	Lelio R Paula	10/2014
5927	2^233829-111355	70390	Enzo Doria	05/2014
5928	(19775^16384+1)/2	70388	Henri Lifchitz	03/2007
5929	7*3^147519+8	70386	Lelio R Paula	04/2014
5930	5*7^83265+2	70368	Lelio R Paula	10/2014
5931	(23*10^70363+97)/3	70364	Robert Price	02/2017
5932	(23*2^233749-1)/35325	70363	Lelio R Paula	01/2014
5934	5^100652-13916	70353	Enzo Doria	02/2013
5933	45^42555-2	70353	Lelio R Paula	08/2013
5935	2^233661-61	70339	Lelio R Paula	02/2012
5936	2^233523-112249	70298	Enzo Doria	06/2014
5937	5*3^147324-8	70293	Lelio R Paula	04/2014
5938	2^233488-13065	70287	Enzo Doria	11/2012
5939	(3^147322+8)/42851	70286	Lelio R Paula	06/2012
5940	(22*10^70259+161)/3	70260	Robert Price	02/2017
5941	2^233388+465	70257	Lelio R Paula	11/2012
5942	14^61299+59	70257	Lelio R Paula	01/2015
5943	2^233383+94065	70256	Lelio R Paula	04/2012
5944	49471!3-6561	70253	Robert Price	11/2015
5945	7^83121+6^(83121-1)	70246	Robert Price	03/2016
5946	23*10^70240-7	70242	Robert Price	03/2016
5947	(71*10^70227-53)/9	70228	Robert Price	10/2015
5948	(2^233247-9)/17	70214	Lelio R Paula	05/2012
5949	(11^67421-2^67421)/9	70211	Robert Price	01/2013
5950	(23*10^70209-41)/9	70210	Robert Price	03/2015
5951	(29*10^70194-11)/9	70195	Robert Price	04/2015
5952	3^147109+196	70189	Lelio R Paula	05/2014
5953	(34*10^70191-7)/9/3/40583/573047	70181	Makoto Morimoto	05/2016
5954	9^73538+8^(73538+1)	70174	Robert Price	06/2016
5955	2*5^100391+7	70171	Lelio R Paula	10/2014
5956	99^35156-2	70159	Lelio R Paula	08/2013
5957	(68*10^70148+7)/3	70150	Robert Price	03/2016
5958	11^67360-6030	70149	Enzo Doria	01/2013
5959	49391!3+3^49391	70128	Robert Price	09/2015
5960	(229*10^70122-1)/3	70124	Robert Price	12/2016
5961	7^82975-92	70123	Lelio R Paula	07/2014
5962	65^38670+58	70106	Lelio R Paula	01/2016
5963	105^34684+34684^105	70103	Serge Batalov	05/2014
5964	134^32955-133	70099	Norbert Schneider	03/2015
5966	2^232836-227903	70091	Enzo Doria	12/2012
5965	2^232837-1859173	70091	Enzo Doria	03/2016
5967	3*2^232820+5	70087	Lelio R Paula	04/2014
5969	2^232799+90195	70080	Lelio R Paula	02/2013
5968	2^232799-112237	70080	Enzo Doria	06/2014
5970	2^232759+262145	70068	Lelio R Paula	04/2012
5971	3*2^232750+7	70066	Lelio R Paula	04/2014
5972	12^64918-11	70059	Lelio R Paula	01/2015
5973	7^82899-12	70058	Lelio R Paula	09/2013
5974	(22*10^70051-13)/9	70052	Robert Price	03/2015
5975	(2^232685-7)/2514625	70039	Lelio R Paula	04/2012
5976	18^55786-5363	70027	Enzo Doria	03/2013
5977	(2^(77537*3+1)+243)/7	70023	Kevin Acres	11/2013
5978	2^232602+169	70021	Lelio R Paula	02/2012
5979	2^232580+72133	70014	Enzo Doria	04/2016
5980	4*6^89958-7	70002	Lelio R Paula	09/2014
5981	10^70000+80487	70001	Milton L. Brown	05/2006
5982	10^69999+134857	70000	Patrick De Geest	02/2007
5984	10^70000-9273	70000	Patrick De Geest	08/2009
5983	(79*10^69999-7)/9	70000	Robert Price	01/2015
5987	((2^43112609)/10^38420)%10^70000	70000	Michael Vang	10/2016
5985	(2^756839/10^36014)%10^70000	70000	Michael Vang	12/2016
5986	(2^74207281/10^32641)%10^70000	70000	Michael Vang	12/2016
5988	10^69999-88251	69999	Patrick De Geest	08/2009
5989	2^232507+1089	69992	Lelio R Paula	04/2012
5990	(17*2^232445+1)/5	69974	Lelio R Paula	08/2012
5991	7^82778+48	69956	Lelio R Paula	09/2013
5992	7*2^232381+3	69955	Lelio R Paula	04/2014
5993	2^232362-110541	69948	Enzo Doria	05/2014
5994	2^232326-112391	69938	Enzo Doria	06/2014
5995	3^146575+236	69935	Lelio R Paula	09/2013
5996	30^47341-29	69929	Norbert Schneider	02/2014
5997	5^100040-68	69925	Lelio R Paula	09/2013
5998	2^232045-17295	69853	Lelio R Paula	04/2012
5999	(2^231987+78557)/95	69834	Lelio R Paula	05/2012
6000	2^231955+74243	69826	Yves Minet	03/2011

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PRP Records

Probable Primes Top 10000

(174961 PRPs in the top)