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Set theory, intersection of two sets

  1. May 24, 2015 #1
    1. The problem statement, all variables and given/known data
    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?

    2. Relevant equations


    3. 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.
     
  2. jcsd
  3. May 24, 2015 #2

    Dick

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    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.
     
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