Hey evthim.
One proof can be based on the prime number theorem, but I get a feeling you may have not covered something like this.
What kinds of things have you covered in your class?
- True or False: for any odd prime p, the set{p+406,p+408,p+410,···,p+1000}
contains a prime integer. Justify your answer.
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.
please help.