3 ms·
See this animation by Ian Rust showing how the even values of n approach the GCD pattern as the values increase: https://streamable.com/l7r96 https://streamabl
by airesearcher 8y ago
See this animation by Ian Rust showing how the even values of n approach the GCD pattern as the values increase:
https://streamable.com/l7r96 https://streamable.com/l7r96
However, for odd values of n, it does not match GCD. So it's not simply a drawing of the GCD pattern.
- macawfish 8y agoThis is fascinating!
- svat 8y agoWell, for obvious reasons: when n is odd, and the row R is even (specifically, 2 mod 4, i.e. of the form 4k+2 for some k) and the column C is odd, then even if gcd(R, C) = 1, the set being considered contains only even numbers — note that it starts with R(R-1)N/2+C which will be even as R(R-1)/2 is odd and so is C - so you won't have any primes in it. (That is, you'll have a red cell, even where the gcd pattern has a black one.) And when n is even, there's also a heuristic argument that there are only finitely many counterexamples; i.e. you should expect to find the pattern from your process exactly match that from just the gcd, beyond a few counterexamples: https://news.ycombinator.com/item?id=17106648 https://news.ycombinator.com/item?id=17106648
- leereeves 8y ago> the even values of n approach the GCD pattern as the values increase Meaning that the chance of finding a prime in these sequences of N numbers approaches one, after eliminating the cases that make primes impossible (n odd and r=2 mod 4, gcd(r,c) > 1). Is there any deeper meaning to that, or is it simply that the probability of finding a prime in any sequence of n numbers approaches one as n increases, excluding sequences in which primes are impossible?