Numbers

The mathematics world is abuzz with the verification of a new largest known prime number.  The number, , is a Mersenne Prime, and has over 17 million digits.  The previous largest known prime was , which had a mere 12.9 million or so digits.

It’s interesting to note that, while it has been known for thousands of years that there are infinitely many primes, it is a challenge even today to find large ones.

It is also interesting to note how many primes were missed in jumping from the previous largest prime to this new largest prime.

A well-known and elegant result, Bertrand’s Postulate, states that there is always a prime number between n and 2n, for n > 1.  For example, the prime 3 is between 2 and 4; the prime 5 is between 3 and 6; the prime 11 is between 10 and 20; and so on.

In particular, this says that there must be a prime between and , since .

Thus, there must be a prime between and , and another between  and , and so on!

Thus, there are at least 57,885,161 – 43,112,609 = 14,772,552 primes between and !  We can therefore safely say there are at least 14,772,551 primes between the largest and second-largest known primes!

Let’s hope it’s not another 4 years until we have a new largest prime on the block.

Today we celebrate our final Permutation Day of the year!  I call days like today permutation days because the digits of the day and month can be rearranged to form the year.

Not only is today a permutation day, but it is also a transposition day!  A transposition is a rearrangement that simply swaps too things, like ’12’ and ’20’.

Celebrate Permutation Day by mixing things up!  Try doing things in a different order today, or maybe try swapping two things in your schedule to honor today’s transposition!

Today we celebrate another Permutation Day!  I call days like today permutation days because the digits of the day and month can be rearranged to form the year.

We’ve enjoyed several permutation day this year, and we’re not done yet!

Celebrate Permutation Day by mixing things up!  Try doing things in a different order today.  Just remember, for some operations, order definitely matters!

Happy European Palindrome Day!

Expressing today’s date in the typical European style [ Day / Month / Year ] gives us a palindromic date!  Definitely a cause for mathematical celebration.  Or at least mathematical appreciation.

I admit that, as an American, this doesn’t resonate with me as much as another recent Palindrome Day, but it’s always nice to take a moment and appreciate a good number.