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).
