3:48 PM
@Sil The tag examples-counterexamples seems reasonable on the linked questions - at least to some extent.
The current usage of the tag big-numbers seems a big vague to me. The [tag-wiki] says: "extremely large finite quantities that are not usually used in mainstream mathematics". (Which is a bit vague formulation, I'll admit.)
It would be nice to here from others some opinion on the tags for the type of the questions you linked.
3
Define a number to be cube-free if there is no prime factor that repeats more than once. Or, $n$ is cube-free if $\frac{n}{\operatorname{rad}(n)}$ is square-free, else $n$ is cube-full. I've tested numbers up to $10,000,000$ without finding more than $4$ consecutive cube-full numbers. Can thi...
5
It seems that non-trivial sums of squares of different non-zero integers aren't powers of two. Tested for sums of $2,3,4$ terms. Is there something known about this topic? Are there counter-examples?
2
Are there primes $p=47\cdot 2^n+1$, where $n\in\mathbb Z_+$? Tested for all primes $p<100,000,000$ without equality.
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