Set theory, intersection of two sets

[BadatPhysicsguy]

Homework Statement

We have the set D which consists of x, where x is a prime number. We also have the set F, which consists of x, belongs to the natural numbers (positive numbers 1, 2, 3, 4, 5..) that is congruent with 1 (modulo 8). What numbers are in the intersection of these two sets?

Homework Equations

The Attempt at a Solution

So the set F consists of numbers that when divided by 8 gives the remainder 1. So, 1, 9, 17, 25, 33, 41, and so on. The set D is prime numbers. So: 2 3 5 7 11 13 17 19 23 29 31 37 and so on. I am to find the numbers that are in both of these sets. But how can I do this? I have no idea except for making a long list of numbers and matching them.

 

[Dick]

Homework Statement

We have the set D which consists of x, where x is a prime number. We also have the set F, which consists of x, belongs to the natural numbers (positive numbers 1, 2, 3, 4, 5..) that is congruent with 1 (modulo 8). What numbers are in the intersection of these two sets?

Homework Equations

The Attempt at a Solution

So the set F consists of numbers that when divided by 8 gives the remainder 1. So, 1, 9, 17, 25, 33, 41, and so on. The set D is prime numbers. So: 2 3 5 7 11 13 17 19 23 29 31 37 and so on. I am to find the numbers that are in both of these sets. But how can I do this? I have no idea except for making a long list of numbers and matching them.

It would have to be a very very long list. The number of primes of the form 8k+1 is known to be infinite. I don't know any nice form to express the intersection besides that.