are all twin primes relatively prime?
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Two integers are relatively prime (or coprime) if there is no integer greater than one that divides them both (that is, their greatest common divisor is one). For example, 12 and 13 are relatively prime, but 12 and 14 are not.
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As it turns out, if the greatest common divisor (gcd) of 2 numbers a and b is 1 (i.e. gcd(a, b) = 1) then a and b are relatively prime. As a result, determining whether two numbers are relatively prime consists simply of finding if the gcd is 1.
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