CZ-SK-MO 2009 Problem 1

Knowing that the numbers $p, 3p+2, 5p+4, 7p+6, 9p+8$ , and $11p+10$ are all primes, prove that $6p+11$ is a composite number.

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.