Smallest n to ensure a prime
Source: APMO 1995
March 11, 2006
number theoryrelatively primenumber theory unsolved
Problem Statement
Let , , , be a sequence of integers with values between 2 and 1995 such that:
(i) Any two of the 's are relatively prime,
(ii) Each is either a prime or a product of primes.
Determine the smallest possible values of to make sure that the sequence will contain a prime number.