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	(16^60013-5^60013)/11	72262	Robert Price	07/2013
5752	7^85507-30	72262	Lelio R Paula	08/2014
5753	(19*2^240026-1)/15	72256	Lelio R Paula	02/2014
5754	(3^151426-2)/661337	72243	Lelio R Paula	06/2012
5755	gcd(V(1296375),5F(259275)(F(259275)-1)+1)	72227	Serge Batalov	04/2015
5756	2^239863-112267	72206	Enzo Doria	06/2014
5757	2^239853-114853	72203	Enzo Doria	05/2015
5758	(4*10^72174+149)/9	72174	Robert Price	03/2017
5760	(2^239671+9)/296131	72143	Lelio R Paula	05/2012
5759	2^239651-110665	72143	Enzo Doria	05/2014
5761	(29*2^239650-1)/3305	72140	Lelio R Paula	01/2014
5762	241^30280+30280^241	72128	Norbert Schneider	11/2014
5763	(68*10^72120-23)/9	72121	Robert Price	10/2015
5764	(9^75571+8^75571)/17	72112	Robert Price	12/2012
5765	(15*2^239530-1)/173	72105	Lelio R Paula	01/2014
5766	2^239513-112519	72101	Enzo Doria	06/2014
5767	(10^72097+149)/3	72097	Serge Batalov	12/2014
5768	2^239442-6555	72080	Lelio R Paula	05/2012
5769	2*5^103106+3	72069	Lelio R Paula	10/2014
5770	2^239402-197	72068	Lelio R Paula	02/2012
5771	2^239356-111875	72054	Enzo Doria	05/2014
5772	(38*10^72050-119)/9	72051	Robert Price	11/2016
5773	2^239339+15015	72049	Lelio R Paula	01/2013
5774	159^32728+2	72048	Lelio R Paula	05/2013
5775	15^61259-38	72047	Lelio R Paula	01/2015
5776	92^36683-91^36683	72038	Robert Price	08/2015
5777	2^239280+54615	72031	Lelio R Paula	05/2012
5778	(47*2^239267+1)/77	72027	Lelio R Paula	04/2015
5779	(85*10^72025-1)/3	72027	Robert Price	07/2017
5780	2^239236-97305	72018	Lelio R Paula	05/2012
5781	2^239169+59	71998	Lelio R Paula	02/2012
5782	lucasU(2010,1,21796)-lucasU(2010,1,21795)	71994	Mike Oakes	05/2009
5783	(15*2^239171-1)/106301	71994	Lelio R Paula	01/2014
5784	(29^49211-1)/28	71965	Robert Price	04/2012
5786	L(344293)	71953	Renaud Lifchitz	09/2003
5785	V(344293)	71953	Serge Batalov	03/2015
5787	6*10^71951+7	71952	Dmitry Domanov	11/2010
5788	3^150798+40	71949	Lelio R Paula	01/2015
5789	2^238961+95	71935	Lelio R Paula	02/2012
5790	2^238936-407	71927	Yves Minet	02/2012
5791	2^238923-28635	71923	Lelio R Paula	05/2012
5792	10^71910+25119	71911	Patrick De Geest	05/2016
5793	10^71910-801	71910	Robert Price	04/2016
5794	2^238845-112651	71900	Enzo Doria	06/2014
5795	2^238792-111245	71884	Enzo Doria	05/2014
5796	6*7^85059+5	71884	Lelio R Paula	10/2014
5797	2^238752-110589	71872	Enzo Doria	05/2014
5798	12^66581+7	71853	Lelio R Paula	07/2014
5799	(7*2^238691+1)/41229	71850	Lelio R Paula	06/2012
5800	4*3^150568-5	71840	Lelio R Paula	04/2014
5801	6^92301+67	71825	Lelio R Paula	01/2015
5802	2^238568+98765331	71817	Jason Earls	01/2009
5803	2^238541-112723	71808	Enzo Doria	06/2014
5804	2^238529-15949	71805	Enzo Doria	04/2013
5805	9*5^102721-8	71800	Lelio R Paula	10/2014
5806	2^238494-165	71794	Lelio R Paula	02/2012
5807	2^238389-110905	71763	Enzo Doria	05/2014
5808	(145*10^71760-1)/9	71762	Serge Batalov	12/2014
5809	7^84913+5062	71760	Mike Oakes	02/2010
5810	(F(11446)^31-F(11445)^31)/F(11444)	71753	Wayne Halsdorf	03/2012
5811	2^238268-97305	71726	Lelio R Paula	05/2012
5812	gcd(V(1330365),5F(266073)(F(266073)-1)+1)	71724	Serge Batalov	04/2015
5813	2^238235-113247	71716	Enzo Doria	07/2014
5814	2*12^66450-5^66450	71712	Mike Oakes	11/2010
5815	(2^238213+lucasV(1,2,238213)+1)/4	71709	Mike Oakes	11/2016
5816	2^238199-111817	71706	Enzo Doria	05/2014
5817	lucasU(46,1,43125)+lucasU(46,1,43124)	71696	Mike Oakes	04/2009
5818	2^238144+98765331	71689	Jason Earls	01/2009
5819	18^57102-4265	71679	Enzo Doria	03/2013
5820	(73*10^71670-1)/9	71671	Robert Price	01/2015
5821	2^238081+1155*238081	71670	Henri Lifchitz	02/2005
5822	2^238067-111925	71666	Enzo Doria	05/2014
5823	36^46030+35	71637	Norbert Schneider	04/2014
5824	2^237905-91	71617	Lelio R Paula	02/2012
5825	(31*2^237902-1)/123	71616	Lelio R Paula	01/2014
5826	(15185*2^237866-1)/43967	71605	Lelio R Paula	04/2015
5827	(24737*2^237841+1)/25	71601	Lelio R Paula	06/2014
5828	2^237846+1299	71599	Lelio R Paula	05/2012
5829	6^92004+199801	71594	Mike Oakes	02/2011
5830	159^32516+2	71581	Lelio R Paula	05/2013
5831	2^237781+855	71580	Lelio R Paula	05/2012
5832	2^237720-4079	71561	Yves Minet	06/2011
5833	2^237698-110945	71555	Enzo Doria	05/2014
5834	2^237695-113239	71554	Enzo Doria	07/2014
5835	8*5^102362-9	71549	Lelio R Paula	10/2014
5836	(4*10^71546-31)/9	71546	Erik Branger	05/2011
5837	2^237650+37	71540	Lelio R Paula	02/2012
5838	18^56977-4391	71522	Enzo Doria	03/2013
5839	(22699*2^237565+1)/4136637	71512	Lelio R Paula	06/2014
5840	((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
5841	(26*10^71503+7)/3	71504	Erik Branger	11/2013
5842	(4*10^71498+173)/3	71499	Robert Price	01/2017
5843	3^149848+110	71496	Lelio R Paula	11/2014
5844	2^237498+513	71495	Lelio R Paula	05/2012
5845	2^237485+107	71491	Lelio R Paula	02/2012
5846	(2^237465+9)/2419	71481	Lelio R Paula	05/2012
5847	2^237439-112237	71477	Enzo Doria	06/2014
5848	2^237407-9787	71467	Lelio R Paula	11/2009
5849	2^237383+72953	71460	Enzo Doria	04/2016
5850	82^37337-81^37337	71457	Robert Price	01/2015
5851	(1017*2^237313-1)/19	71441	Lelio R Paula	04/2015
5852	2^237311+191	71438	Lelio R Paula	02/2012
5853	2^237280-59	71429	Lelio R Paula	02/2012
5854	11^68564-98	71403	Lelio R Paula	01/2015
5855	2^237173+74801	71397	Enzo Doria	04/2016
5856	15^60697+56	71386	Lelio R Paula	01/2015
5857	2^237118+177	71380	Lelio R Paula	02/2012
5858	2^237110+69	71378	Lelio R Paula	02/2012
5859	15^60690-58	71377	Lelio R Paula	01/2015
5860	(5*2^237125-1)/599851191	71374	Lelio R Paula	01/2014
5861	(3^149567+2)/539	71359	Lelio R Paula	06/2012
5862	(5*10^71357-143)/3	71358	Robert Price	04/2016
5863	2^237039-114621	71356	Enzo Doria	05/2015
5864	12^66116-37	71352	Lelio R Paula	02/2015
5865	(3^149497+2^149497)/5	71328	Jean-Louis Charton	10/2010
5866	2^236941-66945	71327	Lelio R Paula	05/2012
5867	2^236911-1147	71318	Yves Minet	10/2009
5868	65^39337+42	71315	Lelio R Paula	01/2016
5869	6*10^71299+7	71300	Dmitry Domanov	11/2010
5870	(25*2^236843+1)/3753	71295	Lelio R Paula	06/2012
5871	10^71291+15187	71292	Patrick De Geest	03/2016
5873	10^71291-5587309119	71291	Robert Price	03/2015
5872	10^71291-273581	71291	Patrick De Geest	03/2016
5874	-numer(bernoulli(22808)/22808)	71290	T. D. Noe	09/2005
5875	(2^236738+9)/13	71265	Lelio R Paula	05/2012
5876	5^101949+42	71260	Lelio R Paula	07/2014
5877	5*10^71237+9	71238	Dmitry Domanov	11/2010
5878	2^236634-16025	71234	Enzo Doria	04/2013
5879	71^38478+70	71233	Norbert Schneider	12/2014
5880	9*7^84280+8	71226	Lelio R Paula	10/2014
5881	(10^71223+59)/3	71223	Serge Batalov	12/2014
5882	(15185*2^236569-1)/453	71216	Lelio R Paula	04/2015
5883	51829#+(216091#)/(51829#)	71208	Makoto Morimoto	03/2016
5884	2^236528-173	71203	Lelio R Paula	02/2012
5885	3*2^236511-5	71198	Lelio R Paula	04/2014
5886	2^236477-99	71187	Lelio R Paula	02/2012
5887	11^68356-2130	71186	Enzo Doria	12/2012
5888	11^68355-3120	71185	Enzo Doria	12/2012
5889	36^45737-35^45737	71181	Robert Price	10/2012
5890	2^236432+25	71174	Lelio R Paula	02/2012
5891	5^101818-12806	71168	Enzo Doria	02/2013
5892	65^39253+62	71163	Lelio R Paula	01/2016
5893	39^44718+38	71150	Norbert Schneider	05/2014
5894	2^236296-407	71133	Yves Minet	02/2012
5895	2^236286-117	71130	Lelio R Paula	02/2012
5896	2^236257-111193	71121	Enzo Doria	05/2014
5897	7^84149-36	71115	Lelio R Paula	08/2014
5898	2^236209-112123	71106	Enzo Doria	06/2014
5899	18^56644-4985	71104	Enzo Doria	03/2013
5900	21^53753+2	71074	Ray Chandler	08/2011
5901	2^236081-110923	71068	Enzo Doria	05/2014
5902	(293*27^49642-1736)/13	71058	Curtis Bright	05/2015
5903	65^39192+22	71052	Lelio R Paula	01/2016
5904	(439#+1)^397-439#^397	71038	Mike Oakes	11/2010
5905	7^84050-2	71031	Lelio R Paula	09/2013
5906	20^54558-23	70982	Lelio R Paula	01/2015
5907	2^235793-112555	70981	Enzo Doria	06/2014
5908	49936!3-3^49936	70981	Robert Price	08/2015
5909	2^235787-78795	70979	Lelio R Paula	05/2012
5910	Perrin(581132)	70970	Eric W. Weisstein	02/2011
5911	14^61913-97	70961	Lelio R Paula	01/2015
5913	2^235720+16321	70959	Yves Minet	03/2010
5912	2^235718+16095	70959	Lelio R Paula	05/2012
5914	163841#+349933	70957	Nicolas PALAU	11/2016
5915	2^235710+7	70956	Lelio R Paula	02/2012
5916	2^235635-112087	70934	Enzo Doria	06/2014
5918	2^235575-1965	70916	Lelio R Paula	05/2012
5917	6^91133+101	70916	Lelio R Paula	01/2015
5919	(21181*2^235505+1)/3	70898	Lelio R Paula	06/2014
5920	5^101425+84	70894	Lelio R Paula	07/2014
5921	177^31536+2	70893	Lelio R Paula	05/2013
5922	43*71^38292+4	70891	Serge Batalov	03/2016
5923	(29*2^235506-1)/112029785	70888	Lelio R Paula	01/2014
5924	11^68045-1530	70862	Enzo Doria	12/2012
5925	5*10^70858+21	70859	Robert Price	01/2017
5927	2^235326+3	70841	Donovan Johnson	02/2006
5926	34523!2+4	70841	Robert Price	02/2015
5928	(31*2^235307+1)/3	70836	Lelio R Paula	06/2012
5929	2^235308+135	70835	Lelio R Paula	02/2012
5930	r(35414,90)*1000+911	70831	Patrick De Geest	07/2004
5931	2^235274+159	70825	Lelio R Paula	02/2012
5932	3^148409+70	70810	Lelio R Paula	11/2014
5933	(19*10^70794+17)/9	70795	Robert Price	03/2015
5934	2^235108-232709	70775	Paul Bourdelais	03/2013
5935	(2^235099-2^117550+1)/5	70772		11/2006
5936	19^55325-6	70748	Lelio R Paula	08/2014
5937	257^29356+29356^257	70746	Norbert Schneider	10/2014
5938	2^234956+11715	70729	Lelio R Paula	05/2012
5939	(7*10^70727-43)/9	70727	Robert Price	10/2014
5940	2^234890-30341	70709	Enzo Doria	11/2012
5941	17^57461+14	70703	Lelio R Paula	01/2015
5942	(9179*2^234834-1)/5	70696	Lelio R Paula	04/2015
5943	123^33822-122	70685	Norbert Schneider	01/2015
5944	(21*2^234772-1)/2095	70672	Lelio R Paula	01/2014
5945	(29*2^234686-1)/21145	70645	Lelio R Paula	01/2014
5946	(15*2^234688-1)/5278141	70643	Lelio R Paula	01/2014
5948	2^234655-67	70639	Lelio R Paula	02/2012
5947	(79*10^70638-61)/9	70639	Robert Price	10/2015
5949	2^234652-173	70638	Lelio R Paula	02/2012
5950	2^234618-3645	70628	Lelio R Paula	05/2012
5951	(2^234610-5)/19	70624	Lelio R Paula	05/2012
5952	4*5^101038+9	70624	Lelio R Paula	10/2014
5953	2^234603+71963	70623	Enzo Doria	04/2016
5954	2^234600-113129	70622	Enzo Doria	07/2014
5956	2^234586+9	70618	Lelio R Paula	02/2012
5955	3^148008+26	70618	Robert Price	11/2013
5957	65^38947+32	70608	Lelio R Paula	01/2016
5958	(2^234488-3)/11	70587	Lelio R Paula	05/2012
5959	(3*2^234451+1)/35	70576	Lelio R Paula	08/2012
5960	Phi(159495,10)	70560	Maksym Voznyy	09/2015
5961	2^234383-4035	70557	Lelio R Paula	05/2012
5962	2^234315-111241	70536	Enzo Doria	05/2014
5963	14^61526+97	70517	Lelio R Paula	01/2015
5964	(3*2^234170+1)/13	70492	Lelio R Paula	08/2012
5965	51^41281-50^41281	70491	Robert Price	02/2013
5966	2^234141-112123	70484	Enzo Doria	06/2014
5967	2^234139+12285	70483	Lelio R Paula	04/2012
5968	2^234133-3163	70482	Yves Minet	04/2009
5969	2^234115+83	70476	Lelio R Paula	02/2012
5970	2^234114-1595	70476	Lelio R Paula	05/2012
5971	24^51061-23^51061	70475	Robert Price	07/2012
5972	19471^16428-2	70467	Faysal YAtim	09/2005
5973	7^83381+12	70466	Robert Price	01/2014
5974	2^234067-111427	70462	Enzo Doria	05/2014
5975	(266*10^70457+1)/3	70459	Robert Price	02/2016
5976	(31*2^234041-1)/97	70453	Lelio R Paula	01/2014
5977	2^234026+12909	70449	Lelio R Paula	04/2012
5978	2^233965-19	70431	Lelio R Paula	02/2012
5979	(5*2^233932-1)/179	70419	Lelio R Paula	01/2014
5980	2^233908-17109	70414	Enzo Doria	05/2013
5981	695^24772+24772^695	70402	Norbert Schneider	09/2016
5982	3*5^100719-2	70401	Lelio R Paula	10/2014
5983	2^233829-111355	70390	Enzo Doria	05/2014
5984	(19775^16384+1)/2	70388	Henri Lifchitz	03/2007
5985	7*3^147519+8	70386	Lelio R Paula	04/2014
5986	5*7^83265+2	70368	Lelio R Paula	10/2014
5987	(23*10^70363+97)/3	70364	Robert Price	02/2017
5988	(23*2^233749-1)/35325	70363	Lelio R Paula	01/2014
5989	5^100652-13916	70353	Enzo Doria	02/2013
5990	45^42555-2	70353	Lelio R Paula	08/2013
5991	2^233661-61	70339	Lelio R Paula	02/2012
5992	2^233523-112249	70298	Enzo Doria	06/2014
5993	5*3^147324-8	70293	Lelio R Paula	04/2014
5994	2^233488-13065	70287	Enzo Doria	11/2012
5995	(3^147322+8)/42851	70286	Lelio R Paula	06/2012
5996	(22*10^70259+161)/3	70260	Robert Price	02/2017
5997	2^233388+465	70257	Lelio R Paula	11/2012
5998	14^61299+59	70257	Lelio R Paula	01/2015
5999	2^233383+94065	70256	Lelio R Paula	04/2012
6000	49471!3-6561	70253	Robert Price	11/2015

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Probable Primes Top 10000

(180278 PRPs in the top)