Utomo theorem

Number Theory Level 4

$\begin{array} {rc} A: & 2^{23}-1 \\ B: & 2^{19}-1 \\ C: & 2^{13}-1 \\ D: & 2^{31}-1 \\ E: & 2^{7}-1 \end{array}$

From the above choices, which one is a composite number?

A D B E C

2 solutions

Keanu Ac
May 8, 2017

I guess 23 is the only prime which is not written in the form 6k+1

I don't see how that's relevant. Could you please explain?

Joe Mansley - 3 years, 8 months ago

Budi Utomo
Mar 21, 2017

You can used my theorem :)

$23$ is the only non-Mersenne prime out of the list $7,13,19,23,31$ .The $6K + 1$ hypothesis fails as $37$ is a non-Mersenne prime.

Samuel Sturge - 1 year, 8 months ago