Permutation Of Some Primes

[Jim Nastos]

On Thu, 1 Apr 2004, Leroy Quet wrote:

> I leave as a challenge, which I did myself in not too much time by 
> trial-and-error and by-hand,
> find the permutation of the first 10 primes (those primes <= 29) so that 
> the greatest prime divisors form a permutation of the first 9 primes
> (those primes <= 23).

  Hint: there's only one way to build the primes 19 and 23, which then 
imply only one way to build 11.

(Spoiler space)





















Leroy,
you mention "the permutation" of the first 10 primes... did you 
exhaustively show this is unique (of course, unique up to reversal of the 
permuation.) I suppose with the facts I mention above, an exhaustive 
search wouldn't be too hard.
The answer I got was 23 7 5 29 17 2 11 3 19 13 yielding the 10-1 distinct 
primes 5 3 17 23 19 13 7 11 2

J