There is no prime in which the mean gap between the first n successive primes is exactly 22. [Dodson]
22 is the smallest number which can be expressed as the sum of two primes in three ways. [Murthy]
1(1) + 2(2) + 3(3) + 4(4) + ... + 22(22) is prime. [Poo Sung]
The smallest multi-digit square-free number such that all the digits are primes. [Russo]
The longest known arithmetic sequence of primes is currently 22, starting with the prime 11410337850553 and continuing with common difference 4609098694200 (found by Pritchard, Moran, and Thyssen in 1993).
22 is the smallest multidigit composite palindrome such that the concatenation (211) as well as the sum (13) of its prime factors are prime. [De Geest]
It is possible for a Queen to attack all 22 prime numbered squares on 9x9 Knight's Tour solution (Jacques Tramu, 2004).
22 is the smallest Hoax Number.
There are 22 twin prime pairs between 22 cubed and the next consecutive cube.
(There are 7 curios for this number that have not yet been approved by an editor.)