Permutation Of Some Primes

[Leroy Quet]

Your solution is different than mine, so there are at least 2 solutions 
not including the   sequences' reflections and rotations.

I give my answer below.

Jim Nastos wrote:

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


My answer:

5, 2, 17, 29, 23, 11, 13, 19, 3, 7

primes:
7, 19, 23, 13, 17, 3, 2, 11, 5

(And we can also break the sequence between the 11 and the 13 , and then 
switch the halves around and reconnect; this is what I meant by 
"rotation" above.)

thanks,
Leroy Quet