Does the sequence $ a_n = \left|-\frac{n^4}{6}+\frac{3n^3}{2}-\frac{13n^2}{3}+6n-1\right|$ contain an infinite number of primes?
I tried to find some theorems on this matter, but apparently the problem in general form is not solved. I will be happy with any results or suggestions, thank you.
Bunyakovsky's conjecture says that if an irreducible polynomial $f(x)\in\mathbb{Z}[x]$ satisfies $1=\mathrm{gcd}\{f(1), f(2), f(3), f(4), \dots\}$ then $f(n)$ is prime for infinitely many $n$. It has not been proven for any polynomial of degree greater than $1$. According to this we conjecture that $ a_n = \left|-\frac{n^4}{6}+\frac{3n^3}{2}-\frac{13n^2}{3}+6n-1\right|$ contains an infinite number of primes.