105

This number is a composite.

Paul Erdős conjectured that this is the largest number n such that the positive values of n - 2^k are all prime.

105/π⁴ = (1 + 1/2⁴)(1 + 1/3⁴)(1 + 1/5⁴)(1 + 1/7⁴)(1 + 1/11⁴) … . [Ramanujan]

The first product of 3 distinct odd primes p. Note that p +/- 2 are primes. [Gallardo]

105 is the first degree for which the cyclotomic polynom factor are not all 1, 0 or -1. [Cristian]

The largest natural number n for which all odd numbers k relatively prime to n, with 1 < k < n, are primes. It is also the largest for which 2n-p is prime for each prime p in [n, 2n-2]. [Capelle]

The only 3-digit number n whereby subtracting from it each of the first eight powers 2^n, (n=1 to 8), then taking the absolute values of the results, produce prime numbers, i.e., 105-2^1 = 103, 105-2^2 = 101, 105-2^3 = 97, 105-2^4 = 89, 105-2^5 = 73, 105-2^6 = 41, |105-2^7|= 23, |105-2^8| = 151. [Loungrides]

The British mathematician James Joseph Sylvester proved that any odd perfect number cannot be divisible by 105.

James Maynard proved that if an "admissible" set of integers has at least 105 members, then at least two of those integers must be prime infinitely often. [Fiess]

The smallest sphenic deficient number. [Gupta]