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sum of 4 primes with 5 <p <q <r <s <p + 10 is divisible by 60

Source: 2019 Austrian Mathematical Olympiad Junior Regional Competition , Problem 4

December 18, 2020
number theoryprimesdivisibledivides

Problem Statement

Let p,q,rp, q, r and ss be four prime numbers such that 5<p<q<r<s<p+10.5 <p <q <r <s <p + 10. Prove that the sum of the four prime numbers is divisible by 6060.
(Walther Janous)
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