Problem
NT-B1-M08-P014 Four Composite Numbers in a Row
#14
★★★☆☆ Level 3 of 5
Find \(n\) such that \(n+2,n+3,n+4,n+5\) are composite numbers.
Make \(n\) divisible by \(2,3,4,5\).
Take \(n=60\). Then \(n+2=62\) is divisible by \(2\), \(n+3=63\) by \(3\), \(n+4=64\) by \(4\), and \(n+5=65\) by \(5\). All these numbers are larger than the corresponding divisors, so they are composite.
This is essentially CRT with residue \(0\) for \(n\) itself.