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Numbers and words
This morning I tried to return a phone call. I managed to dial the wrong number three times at widely separated intervals, and (I later worked out) on all three occasions I transposed the same pair of adjacent digits. And despite carefully cross-
I'm actually quite worried by that. I've always prided myself on my ability to remember long strings of digits, and found it repeatedly useful. I've known for a while that I was prone to occasionally transpose adjacent digits in a number I'd only just seen, but I usually notice on the second attempt. This is the first time I've spent hours completely blind to the difference between the right and wrong versions and I don't like the feeling. :-(
My best guess for how it might have happened is that the transposition turned a trailing 245 into a trailing 425, and my brain might have found the latter more plausible because it's common to see round-
In other news, I visited my niece at the weekend, and she's just learned to say my name. (She's one and a half.) I'm not usually all that susceptible to the cuteness of toddlers, but when they repeatedly look at me and say ‘Si-
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0800 because it's free, 9 ach nein, 541 5=4+1 203 twins - oh wait - triplets
If I didn't do this I would never phone a right number again except that my phone remembers them for me!
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Separately, the thing that really puzzles me is the way that after a couple of years of regular typing, I started writing typos by hand. Looking down at a page of notes and realising that you've written both "teh" and "adn" out in longhand leaves you (well, me, at any rate) wondering precisely which parts of my brain are now being
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My first thought was that maybe your subconscious was rearranging digits to make the number prime — which would be a feat of Ramanujan proportions. Though clearly both the real number and your transposition ending in 5 militated against this possibility.
But now I'm pondering collections of digits that form a prime number however they are arranged. For example, (1,1,3) where 113 131 and 311 are all prime. It feels displeasing to have repeated digits in the collection, but with that constraint it soon becomes clear no examples of more than two digits exist in base ten. Without the constraint, repunit primes like (1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1) become especially degenerate examples.
Considering other bases, binary is especially unedifying since Mersenne primes are the only examples. Being a curious sort, I wondered if larger collections of distinct digits worked in other bases. Having written a quick program, I find that all permutations of the digits (1,3,9) and (3,6,A) in base 11 are prime; plenty more in higher bases.
I have a proof that no collections of four digits exist in any base such that all permutations of those digits are prime. But this comment is too small to contain it. And I don't for a moment believe that's actually true, but it's certainly true up to base 100 and a brute force search is O(n4).
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In my defence, the Wikipedia article on prime numbers does not link to that page. Guess where I went looking. )-8
At least my conclusions seem to have been correct. And, especially, at least I didn't waste time looking for any more base-ten permutable primes after I'd found the three-digit ones.
That Wikipedia article doesn't touch on
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Also my oldest friend's little boy visited me a while back and kept calling me Pelix. There is something about them isn't there :)
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The end you don't wear.
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