pairwise relatively prime

A list of integers is pairwise relatively prime if every pair of the items in the list are relatively prime. For example, the integers 121, 122, and 123 are pairwise relatively prime (even though they are each composite).

If two integers have greatest common divisor one, then they are pairwise relatively prime (since there is only one pair). This happens over 60% of the time (6/π²).

The list of integers involved may even be infinite! For example, the set of all Fermat numbers is pairwise relatively prime, as is the set of all Mersenne numbers with prime exponents. This fact is sometimes used to prove the number of primes is infinite.

See Also: GCD, MutuallyRelativelyPrime

Related pages (outside of this work)

• What is the probability that gcd(n,m)=1