mersenneforum.org Special whole numbers...
 Register FAQ Search Today's Posts Mark Forums Read

2020-10-17, 21:55   #441
Dr Sardonicus

Feb 2017
Nowhere

23×13×43 Posts

Quote:
 Originally Posted by Viliam Furik Well, it's then either the fact it's the smallest non-supersingular prime, or that it is the mirror of Sheldon prime (73). I guess you meant the former.
You guess correctly. Go to the head of the class!

Your offering 3,560,600,696,674 has AFAIK defied analysis so far (I haven't figured out why it is special), so you're current.

2020-10-17, 23:32   #442
Viliam Furik

"Viliam Furík"
Jul 2018
Martin, Slovakia

2·223 Posts

Quote:
 Originally Posted by Dr Sardonicus You guess correctly. Go to the head of the class! Your offering 3,560,600,696,674 has AFAIK defied analysis so far (I haven't figured out why it is special), so you're current.
I can give a few hints:

1. It is a sum of a part of an infinite series of numbers
2. The series is related to the graph theory

 2020-11-01, 10:37 #443 mart_r     Dec 2008 you know...around... 32·71 Posts Hmm... I wanted to post a new number, but still can't figure out Viliam Furik's number. And I don't know much about graph theory either.
 2020-11-01, 21:46 #444 Dr Sardonicus     Feb 2017 Nowhere 23×13×43 Posts I'm afraid the hints haven't been enough for me, either. I don't know much about graph theory. In particular, I don't know why adding the terms of a graph-related sequence would be of significance.
 2020-11-01, 22:37 #445 Viliam Furik   "Viliam Furík" Jul 2018 Martin, Slovakia 2·223 Posts First of all, I admit the number is not as special as other numbers I could have chosen. 3,560,600,696,674 - number of tree graphs with at most 35 vertices. The specialness of this number lies in the Graceful Tree Conjecture, which states that all trees are graceful (there exists at least one graceful labelling for every tree graph). It has been verified by computers for all trees with at most 35 vertices. So far, every tree checked has at least one graceful labelling. This conjecture is of particular interest to me because I am trying to prove it, together with my schoolmate, but also because 6 mathematicians that have participated in its research were from Slovakia, namely Anton Kotzig and Alexander Rosa (these two, together with Gerhard Ringel, are the ones that conjectured it), Alfonz Haviar and Pavel Hrnčiar (published a result that every tree with a diameter at most 5 is graceful), and Miroslav Haviar and Michal Ivaška. ------- EDIT: I give up my turn to choose a new number. Last fiddled with by Viliam Furik on 2020-11-01 at 22:45
2020-11-02, 00:44   #446
Dr Sardonicus

Feb 2017
Nowhere

23×13×43 Posts

Quote:
 Originally Posted by Viliam Furik 3,560,600,696,674 - number of tree graphs with at most 35 vertices. The specialness of this number lies in the Graceful Tree Conjecture, which states that all trees are graceful (there exists at least one graceful labelling for every tree graph). It has been verified by computers for all trees with at most 35 vertices. So far, every tree checked has at least one graceful labelling.
(Google Google) Huh. "Number of trees with n vertices" turns up formula nn-2. Wait, those numbers are WAY too big. (Scribble scribble) Oh, that's if the vertices are labeled. Not what we want.

We want the number of "different" trees with n vertices. OK, got it. OEIS A000055. Number of trees with n unlabeled nodes.

Enough terms to verify the total are given at A000055 as a simple table.

 2020-11-13, 04:50 #447 swishzzz   Jan 2012 Toronto, Canada 3×19 Posts 66600049
 2020-11-13, 09:02 #448 LaurV Romulan Interpreter     Jun 2011 Thailand 11×853 Posts Not fun, it is the first link gugu gives. (however, we learned a couple of things from it! thanks for sharing, but the search was indeed not fun haha, too easy) Last fiddled with by LaurV on 2020-11-13 at 09:03

 Similar Threads Thread Thread Starter Forum Replies Last Post MooMoo2 Lounge 26 2016-05-06 20:35 Citrix Other Mathematical Topics 46 2012-03-06 14:55 xilman Soap Box 5 2009-06-05 08:20 kar_bon Riesel Prime Data Collecting (k*2^n-1) 1 2009-02-19 04:28 jeffowy Miscellaneous Math 2 2003-12-17 21:40

All times are UTC. The time now is 13:05.

Tue Apr 20 13:05:08 UTC 2021 up 12 days, 7:46, 0 users, load averages: 4.02, 3.24, 2.64