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AlbertJayNock

Numbers other than 37

In last Friday's entry I spoke of my fondness for the number 37. To be fair to other deserving numbers, and to show that I wasn't just jumping on the 37 bandwagon, there are other interesting numbers I'd like to mention here.

You can like a particular number for both mathematical and non-mathematical reasons. The best numbers are the ones that are likable in both ways. For instance 37 is very interesting mathematically, mostly due to the fact that it is 1/3 of 111, but also has some interesting non-mathematical properties such as being the number of plays Shakespeare wrote, the Celsius temperature of the human body, and having once appeared on an episode of Seinfeld.

43 is another favorite number of mine for some very personal reasons. I was 43 years old during the presidency of the 43rd president (George W Bush.) My father and I were both 43 when our fathers died.

There are not as many mathematically interesting things about 43 as there are about 37. But it is a prime number, and not only is it a prime number it is a twin prime. (Twin primes are primes numbers that differ by 2). It's twin is 41, and George W. Bush's father was the 41st president. So it's associated with a president and my father, and it also connects the same president to HIS father.

Wow.

I am currently 47 years old. This is also a prime number, and has an additional interesting property.
There are some primes that can be generated by multiplying another prime by 2 and adding 1. For instance, 3*2+1=7. 47 also has this property since 23 is prime and 2*23+1=47. Not only that, but it is the last in a long chain of primes generated that way:

2,5,11,23,47.

You can't generate another one from 47.

A prime that generates another prime this way is called a Sophie Germaine prime.(Note that 47 itself is not a Sophie Germaine prime...it is just generated from one). I first learned this term when I saw the movie Proof (and was 47 at the time). There is also a scene in the movie where the Gwyenth Paltrow character is driving and takes exit 47.

47 has been described as the quintessential random number. That is, if you ask somebody to name a number it (supposedly) will be mentioned more often than other numbers. I suspect a lot of it has to do with the last digit being 7. That extra syllable makes it float more easily off the tongue.

It is famous for showing up on Star Trek a lot and is also the number of miracles of Jesus recorded in the bible. That's a tough combo to beat.

There is both a website (where you can find a lot of factoids I'm not going to get into here) and a livejournal community dedicated to the number 47.



A week from today I will be 48. That is not very interesting number. Alas.

I also like 91. If you reverse it's digits, you get 19 (Louis Farrakhans favorite number). And if you multiply 91 by 19 you get 1729, mathematical folklore's most beloved number. It is the subject of an anecdote involving the mathematician G.H. Hardy and his protege Srinivasa Ramanujan. Hardy writes in his autobiography:

I remember once going to see him when he was ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways."

This story is to math history what George Washington chopping down the cherry tree is to American History. Some might say this is an unfortunate analogy since the George Washington story is apocryphal, an invention of bookseller and parson Mason Lock Weems. But it might not be, since I have suspicions about Hardy's story. 1729 is a Carmichael number, which is certainly interesting, and I can't believe a mathematician of Hardy's stature didn't know that or think about that. I am not the only one who has these suspicions.

1729 also appears in Proof. There is a touching little scene where the Anthony Hopkins character is telling Hardy's anecdote to his daughter (played by Gwyneth Paltrow). It is such a heartwarming scene one hardly cares that the story might not be true.

Anyway, being a factor of 1729 makes 91 interesting. 91 also appears in the same episode of Seinfeld that 37 was in. It was also in a hoax website a few years ago purporting to show the IQ's of various American presidents. According to this website, Bill Clinton's IQ is 182 and George W. Bush's is 91.
Although a lot of people bought into this, a quick look at the numbers should make anyone suspicious. What are the odds that Bill Clinton's IQ is EXACTLY twice Bush's IQ? Very slim, regardless of how dumb you might think Bush is. The website was later revealed to be bogus.

I'd mentioned a Seinfeld episode on which 91 appeared. In this episode, Elaine's birthday was coming up, and Jerry insisted that he spend twice as much as George did for her gift. Both gave her cash.
George gave her (drum roll) $91 and Jerry gave her $182. The website hoax had already been exposed when I noticed this, but I still felt like Chaz Palmenteri at the end of The Usual Suspects.
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Marry me.
I knew those math skills would pay off someday. :)
48 is interesting. It's the smallest number with 10 divisors (1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.) I suppose it will have a non-mathametical reason to be interesting when it is your age next week.

The 'interesting numbers' paradox is a good example of a self-referential set.

Assuming there are interesting and non-interesting numbers, the first number that isn't interesting has the interesting quality of being the smallest non-interesting number. That number then joins the set, causing a paradox.

Gödel loves to chase us around...