mersenneforum.org  

Go Back   mersenneforum.org > Great Internet Mersenne Prime Search > Math
Reload this Page The Størmer Problem (Lehmer's method etc)
Register FAQ Today's Posts Search

Reply
Page 5 of 5 1234 5
 
Thread Tools
Old 2012-06-26, 07:37   #45
XYYXF
 
XYYXF's Avatar
 
Jan 2005
Minsk, Belarus

24·52 Posts
Default
Quote:
Originally Posted by LaurV View Post
You (or the guy behind of primefan.ru) should report that here.
The guy behind of primefan.ru is me :-)

I already reported these results here:
http://oeis.org/A193943
http://oeis.org/A193944
http://oeis.org/A193945
http://oeis.org/A193946
http://oeis.org/A193947
http://oeis.org/A193948
http://oeis.org/A199407
http://oeis.org/A200566
http://oeis.org/A200567
http://oeis.org/A200568
http://oeis.org/A200569
http://oeis.org/A200570
http://oeis.org/A209837
http://oeis.org/A209838
http://oeis.org/A209839

There are numbers n such that p(n,k) < p(i,k) for all i > n, where p(n,k) is the largest prime factor of \prod\limits_{d=0}^k (n+d).

Note that log n grows nearly as \sqrt{p(n,k)} irrespective of k:
http://www.primefan.ru/stuff/math/maxs_plots.gif
(the plot is taken from the Excel file noted before)

For k=1, the case being discussed there, we have \log{n} \approx 5.154\sqrt{p} + 7.276. Any thoughts about these constants?
Last fiddled with by XYYXF on 2012-06-26 at 07:51
XYYXF is offline   Reply With Quote
Old 2016-12-30, 23:48   #46
XYYXF
 
XYYXF's Avatar
 
Jan 2005
Minsk, Belarus

6208 Posts
Default
27129807647978258459761875 * 27129807647978258459761876 is 157-smooth, according to http://bbs.emath.ac.cn/thread-4652-1-1.html

683232593267939977798585217 * 683232593267939977798585218 is 173-smooth, according to http://forum.index.hu/Article/showAr...6539&t=9087484

See also http://doi.org/10.1090/S0025-5718-2010-02381-6 and http://dx.doi.org/10.1080/10586458.2013.768483
Last fiddled with by XYYXF on 2016-12-31 at 00:09
XYYXF is offline   Reply With Quote
Reply
Page 5 of 5 1234 5

« Previous Thread | Next Thread »


Similar Threads
Thread Thread Starter Forum Replies Last Post
B1 and B2 in P-1 method Miszka Math 13 2013-12-27 20:23
New Method Unregistered Miscellaneous Math 14 2013-05-24 10:55
Lucas-Lehmer Dougal Information & Answers 9 2009-02-06 10:25
Emma Lehmer R.D. Silverman Information & Answers 1 2007-08-28 06:20
Størmer's theorem grandpascorpion Factoring 0 2006-09-10 04:59

All times are UTC. The time now is 18:18.


Fri Jul 16 18:18:44 UTC 2021 up 49 days, 16:06, 1 user, load averages: 3.39, 2.64, 2.19

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2021, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.