4181

This number is a composite.

4181 is the first number n such that n, n+2, n+6, and n+8 are all composite, but none of the numbers are divisible by 2, 3, 5, 7, or 11. Amazingly, none of the numbers 4181, 4183, 4187, 4189 are divisible by 13, 17, 19, 23, 29, or 31. (4181=37*113, 4183=47*89, 4187=53*79, 4189=59*71) [Jacobs]