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Is the Answer 42 or 73?

Although 42 is the “Answer to the Ultimate Question of Life, the Universe, and Everything,” 73 is the Chuck Norris of numbers, being the only Sheldon Prime.

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As revealed in the Hitchhiker’s Guide to the Galaxy, which was gifted to us by the late, great Douglas Adams, the number 42 is the “Answer to the Ultimate Question of Life, the Universe, and Everything.” This was calculated by an enormous supercomputer named Deep Thought over a period of 7.5 million years. Unfortunately, no one knows what the question is. Thus, to calculate the Ultimate Question, a special computer the size of a small planet was built from organic components. This new computer was called “Earth.” As fate would have it, 42 turns out to be special in various ways. In addition to being the only natural number that succeeds 41 and precedes 43 (think about it), 42 is a pronic number (it’s the product of two consecutive integers, 6 * 7), a sphenic number (it’s a positive integer that’s the product of three distinct prime numbers, 2 * 3 * 7), and it’s an abundant number (the sum of its proper divisors is greater than itself; i.e., 1 + 2 + 3 + 6 + 7 + 14 + 21 = 54). Furthermore, following from an email sent by my chum Jay Dowling, I just discovered that 42 was the last remaining number below 100 that could not be expressed as the sum of three cubes (barring numbers for which this is known to be impossible); that is, until now. As we learn in this video from Numberphile, some folks who don’t get out as often as they should started a computer search in 1954 looking for numbers up to 100 to see which ones could be represented as the sum of three cubes (and they say academics don’t know how to have fun).  
It wasn’t until this year, 2019, following 65 years of numerical exploration, that they managed to track the last one down, and — wouldn’t you know it — this little scamp was 42. Oh no! Now I’m thinking of The 43 Peculiarity, which was the eighth episode of the sixth season of The Big Bang Theory. This was the one where Howard and Raj follow Sheldon to a locked room in the basement of the university where they work. After Sheldon has left, they pick the lock and enter the room, only to discover that it’s empty apart from a whiteboard bearing the number 43. They try to decipher the meaning behind this number in this video snippet. Later, Sheldon discovers what they are up to and convinces them that he’s created a wormhole generator and — as seen in this video morsel — the number 43 reflects the number of parallel universes he’s explored. Finally, all is revealed in this video fragment. But we digress… As interesting as the number 42 undoubtedly is, in The Alien Parasite Hypothesis, which was the tenth episode of the fourth season of The Big Bang Theory, Sheldon explains that, “The best number is 73. Why? 73 is the 21st prime number. Its mirror, 37, is the 12th, and its mirror, 21, is the product of multiplying 7 and 3.” Leonard isn’t impressed, saying, “We get it, 73 is the Chuck Norris of numbers!” To which Sheldon responds, “Chuck Norris wishes. In binary 73 is a palindrome, 1001001, which backwards is 1001001. All Chuck Norris backwards gets you is Sirron Kcuhc!”‘ Truth really is stranger than fiction because — although this all started out as a sitcom script — it ended up as a mathematical paper titled “The Sheldon Conjecture,” as we discover in this video.  
Published in 2015, this conjecture was that 73 is the only Sheldon Prime — that is, the only prime number with the product and mirror properties. Once again, it wasn’t until this year, 2019, that the paper “Proof of the Sheldon Conjecture” appeared in American Mathematical Monthly. I bet you are wondering what the point of all this is. I’m sorry; there is no point. The best rational I can come up with for this column is that it’s been a long week and I can hear a cold beer calling my name, “Max, Max, where are you?” To which I can only reply, “Don’t worry little one, daddy will be home soon!” How about you? Do you have any number-related trivia you’d care to share?

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David Ashton

Can’t remember Pi?? Easy. Write down the first three odd numbers twice each:

113355

move the last 3 over the first three

355
—-
113

and bingo, you get

3.1415929203539823008849557522124
The real Pi is
3.1415926535897932384626433832795

So it only differs in the 7th decimal place, and is

0.99999991508632855196134845721291 % accurate.

David Ashton

OOPS..that should be

99.999991508632855196134845721291 % accurate.

Why do you only notice these things after the edit link expires….
I need more coffee…or maybe one of Max’s beers…..

Aubrey Kagan

There’s an edit link? Even though I have registered on the site, it seems Max has to approve every post. I have yet to see anywhere that I can edit my post once I have hit Post.

I will check now…
OK. Now I see it, but there appears to be no way to delete the post other than to post a blank one.

Charles Pfeil

My only adventures in this realm is when I wake at night and squint at my digital clock looking for palindromes.

Aubrey Kagan
Aubrey Kagan

What layer includes a “chum”?

Aubrey Kagan

And I wonder if you recognise faces of people you don’t actually know, like movie stars or politicians, are these included or in addition to the 1500 people you can recognise.

Douglas

42 in BCD is also pallindromic: 0100 0010 ?

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