Definitely, the illustration of the case of 4 is simply because I have a hard time expressing it in general terms but yes, the system grows with n and I certainly do not limit the question to 4 lines. The question I ask is whether or not SumsData(i) will remain below 1 at all times as i goes to...
I'm attaching here the Matlab code used to generate the previous figure in case someone wants to reproduce the empirical algorithm. It's currently going very slow because I use the function nchoosek, there is probably much faster available.
n = 87;
SumsData = [];
PrimesOriginal = 5:n...
So I've used your approach empirically (that is, divide all lines by all primes in the set) and I have moved the "1" that resulted to the left side of the equation so we have:
1 > 1/P1 + 1/P2 + 1/P3 ...
- 2/(P1P2) - 2/(P1P3) ...
+ 2/(P1P2P3) ...
- 2/(P1P2P3P4) ...
and I just wanted to show you...
Brilliant! You are so much better than me it is both helpful and shameful at the same time. This means I have to reformulate my statement of the problem. I'm quite convinced that what I'm after is true, but I haven't been completely honest in my original post. For your curiosity, and if you are...
I have checked and indeed 109 is the prime at which the 1 > ... inequality is violated. Thank you very much for pointing that out, I guess I now have to go back to the workbench and see what reformulation I could find and what kind of boundaries I would put on m and n.
I've been working on a problem for a couple of days now and I wanted to see if anyone here had an idea whether this was already proven or where I could find some guidance. I feel this problem is connected to the multinomial theorem but the multinomial theorem is not really what I need . Perhaps...
Hum well the fact that 3 5 are the smallest primes to start with and that the other primes have to be at least double of 3 and 5 guarantees that this is the smallest pair.
As for the understanding, I think I do understand that this is the set of primes where the difference between the 1st and...
I tried a couple and can't find the example. You found some without using 2, which isn't odd ?
3*(13 - 1),5*(11-1)
5*(17 - 1),7*(11-1)
5*(17 - 1),7*(13-1)
3*(17 - 1),7*(13-1)
3*(17 - 1),5*(13-1)
3*(23 - 1),5*(13-1)
3*(29 - 1),5*(19-1)
and many other all gave me inequalities, although I'd love...
Thank you very much for helping me like that I really appreciate.
Not being a mathematician, here's what I could come up with, tell me if that makes sense.
From your equation and from knowing that z-1 is even and has prime factor x, and that y-1 is even and has prime factor w, I get...
Interesting.
I also would add the following conditions:
Since the equality Px(Py-1) = Pw(Pz-1) needs to reflect 1 integer that has a unique prime factorization, (Py-1) is an even number with prime factor Pw and (Pz-1) is an even number with prime factor Px.
Still struggle to get to...
Hi everyone,
I've been bumping on this problem for a while and wondered if any of you had any clue on how to approach it. My question is whether the following equality is possible for 4 distinct prime numbers :
PxPy + Pw = PwPz + Px
where Px, Py, Pw, Pz are odd prime numbers, and each...
Here's a supplement figure, to show a more generalized idea of what I did in Figure 4, at least for when N/2 is odd. Basically, is there any series of odd numbers from 1 to N/2 that would produce what we see on this graph (black dots intersecting the rational curves of the square of the odd at...
Video illustration
Hello,
Me and a friend, David Barrack, are non-mathematicians but we've been having fun lately with the Goldbach conjecture. I thought I'd share some of our tools with you guys, some of you might be interested in helping us to progress on this problem - that would be greatly...