Comments on: Working on the railroad http://bit-player.org/2007/working-on-the-railroad An amateur's outlook on computation and mathematics. Wed, 08 Feb 2012 13:22:39 +0000 http://wordpress.org/?v=2.6.3 By: Barry Cipra http://bit-player.org/2007/working-on-the-railroad#comment-1429 Barry Cipra Tue, 13 Feb 2007 02:43:41 +0000 http://bit-player.org/?p=89#comment-1429 A triangle pyramid, aka cannonball arrangement, with 1 ball sitting on 3 sitting on 6 sitting on 10, etc., for a total of k layers, has a total of k(k+1)(k+2)/6 balls. This gives the very nice value 602,214,150,661,210,865,396,970 by setting k=153,450,179. Moreover, this value for k is, once again, a prime number! A triangle pyramid, aka cannonball arrangement, with 1 ball sitting on 3 sitting on 6 sitting on 10, etc., for a total of k layers, has a total of k(k+1)(k+2)/6 balls. This gives the very nice value

602,214,150,661,210,865,396,970

by setting k=153,450,179. Moreover, this value for k is, once again, a prime number!

]]> By: Barry Cipra http://bit-player.org/2007/working-on-the-railroad#comment-1428 Barry Cipra Mon, 12 Feb 2007 17:54:47 +0000 http://bit-player.org/?p=89#comment-1428 I'd like to suggest 602,214,205,251,903,400,125,971 as an alternative Avogadro's number. It's the only value in the Fox-Hill range that is the cube of a *prime* number. (My thanks to Paul Zorn for doing the exact arithmetic.) The prime, by the way, is 84,446,891. The Fox-Hill cube root is 84,446,888 = 8 x 17 x 620,933. I’d like to suggest 602,214,205,251,903,400,125,971 as an alternative Avogadro’s number. It’s the only value in the Fox-Hill range that is the cube of a *prime* number. (My thanks to Paul Zorn for doing the exact arithmetic.)

The prime, by the way, is 84,446,891. The Fox-Hill cube root is 84,446,888 = 8 x 17 x 620,933.

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