## Wednesday, 9 March 2011

### Math, Shakespeare, and some good ol' limericks

It's time for the Schools Shakespeare Festival here in Lakenheath, and to get in the mood, without giving up my bias toward mathematics, a few collected themes to celebrate math with a poetic leaning...

First  a couple of my favorite math limericks...
This is how the mathematician would see the limerick

$\frac{12 + 144 + 20 + 3 \sqrt{4}}{7} + (5 \times 11) = 9^2+0$
And for the others... it reads like this in English:

dozen, a gross, and a score

Plus three times the square root of four
Divided by seven
Plus five times eleven
Is nine squared and not a bit more.

Just down the road at Cambridge is Trinity College, where many of the mathematical greats of England (and the world) were, and still are, trained...

A graduate student at Trinity
Computed the square of infinity.
But it gave him the fidgets
To put down the digits,
So he dropped math and took up divinity.

It turns out that recently John  D. Cook  posted some "limerick primes" at his Endeavour blog .  The rhyme scheme for a limerick is a,a,b,b,a, so a number like 33223 would be a "limerick" number.  It turns out that of all the numbers you can write that way, only eight are prime:
• 11551
• 33113
• 33223
• 33773
• 77447
• 77557
• 99119
• 99559
Ok, but it's not a limerick festival... it's a Shakespeare Festival.  Now his sonnets, as you learned from your Enlish teacher, must have 14 lines and a rhyme scheme like this...
a-b-a-b     c-d-c-d     e-f-e-f     g-g

so a number like 31314040252566   would be a Sonnet Number... and Cook the Computer Master has found all of the prime versions of those as well.  It turns out there are 16,942 sonnet primes, at least according to John, I have not verified that count.   John has provided the largest and smallest of them: "the smallest of these primes is 10102323454577. The largest is 98987676505033."