Problem

Source: II International Festival of Young Mathematicians Sozopol 2011, Theme for 10-12 grade

Tags: number theory, prime numbers, Sequence



Does there exist a strictly increasing sequence $\{a_n\}_{n=1}^\infty$ of natural numbers with the following property: for $\forall$ $c\in \mathbb{Z}$ the sequence $c+a_1,c+a_2,...,c+a_n...$ has finite number of primes? Explain your answer.