There is no simple answer because there is no simple rule for primes: it is certainly NOT an arithmetic progression.
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The Fundamental theorem of arithmetic.
Any two prime numbers will be relatively prime. Numbers are relatively prime if they do not have any prime factors in common. Prime numbers have only themselves as prime factors, so all prime numbers are relatively prime to the others.
Products of prime numbers are composite numbers.
The opposite of prime numbers are composite numbers.
There are more than 25 prime numbers; there are an infinite number of prime numbers.