#math trivia #59 solution

The property of 60 that makes adjacent twin primes possible is that 60 is divisible by 6.

If 60 were not divisible by 2, then both of its neighbors would have to be, so neither could be a prime.

If 60 were not divisible by 3, then one of its neighbors would have to be, so the pair of neighbors would not be primes.

It also helps a little that 60 is divisible by 5.  If 60 were not divisible by 5, then there would be a 50% probability that one of its neighbors would be divisible by 5, and for that reason not prime.  (Consider the first four numbers divisible by 6 but not 5:  6, 12, 18, 24.  Two have neighbors divisible by 5, and two don’t.)

So, being neighbors of a number by 6 is a necessity for twin primes, and being neighbors of a number divisible by 30 or 60 is even better.

 

 

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s