Two primes which differ by 2 are known as twin primes. For example, 3 and 5...

 

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Two primes which differ by 2 are known as twin primes. For example, 3 and 5 are twin primes, 11 and 13 are, and 461 and 463 are. One of the great unsolved problems in number theory is whether there are infinitely many twin primes. Are there any twin primes of the form 2n. = 1, 21, for n > 2? If so, give an example, and if not, prove there aren't any. Hint: From class, k, k + 1, k + 2 is a complete residue system modulo 3, for any choice of k. Two primes which differ by 2 are known as twin primes. For example, 3 and 5 are twin primes, 11 and 13 are, and 461 and 463 are. One of the great unsolved problems in number theory is whether there are infinitely many twin primes. Are there any twin primes of the form 2n. = 1, 21, for n > 2? If so, give an example, and if not, prove there aren't any. Hint: From class, k, k + 1, k + 2 is a complete residue system modulo 3, for any choice of k.