Famous Birthdays

The day is a two digit prime number. The two digits are consecutive numbers.

The number of days in the month is a multiple of the number of letters in the month's name.

The year was a leap year which began on a Saturday.
It is 22222₅ + 2

A prime numbers has two and only two factors.

Consecutive numbers are next to each other in the sequence of counting numbers.

Thirty days hath September,
April June and November.
All the rest have thirty-one
Excepting February alone,
Which has twenty-eight days clear,
But twenty-nine each Leap Year..

The number 22222 is given in base 5. It means:

2 x 625 +
2 x 125 +
2 x 25  +  
2 x 5   +   
2 x 1