"Almost prime" and "very non-prime" numbers
Source: St. Petersburg MO, 2000., 10th grade, P7
April 22, 2023
number theoryprime numbersDivisibility
Problem Statement
We'll call a positive integer "almost prime", if it is not divisible by any prime from the interval . We'll call a number "very non-prime", if it has at least 2 primes from interval dividing it. What is the greatest amount of almost prime numbers can be selected, such that the sum of any two of them is a very non-prime number?
[I]Proposed by S. Berlov, S. Ivanov