# Primes, Twin Primes, and My Mom’s Bday

Today is my mom’s birthday and something very special happened… We’re 5 in our family, my brother, my sister, me, my mom and my dad, and all our ages are prime numbers: 29, 31, 37, 61, 67!

I thought this was very cool, and decided to explore more.

Just to recall, a **prime number** is a natural number greater than 1, that has only 1 and itself as a divisor. **Twin primes** are pairs of prime numbers of the form (*p*, *p*+2), for example (3, 5), (5, 7), (11, 13). And then we’ll generalize, but let’s start talking about birthdays.

The first 25 prime numbers (all the primes less than 100) are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97. Thus, a person leaving 100 years will celebrate **25 prime birthdays**.

Prime numbers are infinite, and so if a person could live infinitely many years, she’d celebrate infinitely many prime birthdays.

There are **8 twin prime birthdays** below 100 years old:

(3, 5)

(5, 7)

(11, 13)

(17, 19)**(29, 31) — my brother and sister**(41, 43)

(59, 61)

(71, 73)

And so my sibling will have 3 more twin prime birthdays to celebrate, at

(41, 43), (59, 61), and (71, 73).