53 is notable for being the first prime not to be part of a twin or cousin prime pair.
Its two closest primes are 47 and 59, both of which are sexy primes with 53.
The first prime not to be part of a twin, cousin, or sexy prime pair
is /you tell me/.
To exclude number 2 as the trivial answer one wore should be inserted into the 1st sentence:
..."53 is notable for being the first ODD prime not to be part of a twin or cousin prime pair."...