4181

This number is a composite.

The smallest composite Fibonacci number not divisible by a Fibonacci prime. [Honaker]

The smallest composite Fibonacci number with a prime index. [Gupta]

4181 is the smallest semiprime Fibonacci number whose reversal is a different semiprime. [Post]

The smallest Frobenius pseudoprime with respect to the Fibonacci polynomial x^2-x-1. [Luen]

The smallest semiprime Fibonacci number with emirp factors, i.e., 37 * 113. [Honaker]

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]