1. Stuck on proof

1. True or False: for any odd prime p, the set{p+406,p+408,p+410,···,p+1000}

True. the set is a set of odd numbers because an even number plus an odd number always results in an odd number -> (proof: (2k+1) + 2r = 2k + 2r + 1 = 2(k+r) + 1)

-this is where i get stuck. all i can infer is that the set is a set of odd numbers.