Chromatic number of associahedron ★★

Author(s): Fabila-Monroy; Flores-Penaloza; Huemer; Hurtado; Urrutia; Wood

Conjecture   Associahedra have unbounded chromatic number.

Keywords: associahedron, graph colouring, chromatic number

Are there infinite number of Mersenne Primes? ★★★★

Author(s):

Conjecture   A Mersenne prime is a Mersenne number \[ M_n  = 2^p  - 1 \] that is prime.

Are there infinite number of Mersenne Primes?

Keywords: Mersenne number; Mersenne prime

Are all Mersenne Numbers with prime exponent square-free? ★★★

Author(s):

Conjecture   Are all Mersenne Numbers with prime exponent $ {2^p-1} $ Square free?

Keywords: Mersenne number