MathDB

A sequence of primes

p_1, p_2, \dots

is given by two initial primes

p_1

and

p_2

, and

p_{n+2}

being the greatest prime divisor of

p_n + p_{n+1} + 2018

for all

n \ge 1

. Prove that the sequence only contains finitely many primes for all possible values of

p_1

and

p_2

2