## Re: Primes from permutation of prime digits

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• ... Interesting. It s surprising to me that the number of odd digits barely outnumbers the number of even digits in these primes with maximum perms. Must be a
Message 1 of 7 , Feb 13, 2009
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--- In primenumbers@yahoogroups.com, zak seidov <zakseidov@...> wrote:

> > > We have the next table of
> > > minimal primes p with given perm:
> > > {perm,p)
> > > {1,2}
> > > {10,1097}
> > > {100,1006991}
> > > {1000,12338449}
...
> > zak(12338449)
> > = 4000
> > Using your definition & my code the first with
> > perm>10^4 I found
> > (without exhaustive search) is:
> > 11111117 15120
...
> first case of perm(p)>10^4 is perm(100123697)=10042
> and of course i mean "distinct primes",
> otherwise perm(11)=2 - curious enough.
> maximal perm for first 2*10^7 primes is
> perm(102345697)=30852 (distinct primes!)
> zak
>

Interesting. It's surprising to me that the number of odd digits
barely outnumbers the number of even digits in these primes with
maximum perms. Must be a good reason ...

Mark
• ... Scrap that. It s not that surprising to me anymore. :) Mark
Message 2 of 7 , Feb 13, 2009
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<mark.underwood@...> wrote:
>

> Interesting. It's surprising to me that the number of odd digits
> barely outnumbers the number of even digits in these primes with
> maximum perms. Must be a good reason ...
>

Scrap that. It's not that surprising to me anymore. :)

Mark
• I prefer zak(1123465789) = 152526 to zak(1023345679) = 156227 since the former does not invoke leading zeros. David
Message 3 of 7 , Feb 14, 2009
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I prefer
zak(1123465789) = 152526 to
zak(1023345679) = 156227 since
the former does not invoke leading zeros.

David
• ... Thereafter, 11-digit primes become somewhat memory-intensive, in my simple-minded implementation, using GP s vecsort . Might Zak and/or Maximilian confirm
Message 4 of 7 , Feb 14, 2009
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> I prefer
> zak(1123465789) = 152526 to
> zak(1023345679) = 156227 since
> the former does not invoke leading zeros.

Thereafter, 11-digit primes become somewhat memory-intensive,
in my simple-minded implementation, using GP's "vecsort".

Might Zak and/or Maximilian confirm that
zak(10123457689) = 1404250
without duplication of primes, but allowing Zak's leading zeros ?

David
• ... yes: zak(10123457689) %1 = 2808500 2808500/2 (symmetry factor for exchange of the two 1 s) %2 = 1404250 Maximilian
Message 5 of 7 , Feb 15, 2009
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> Thereafter, 11-digit primes become somewhat memory-intensive,
> in my simple-minded implementation, using GP's "vecsort".
>
> Might Zak and/or Maximilian confirm that
> zak(10123457689) = 1404250
> without duplication of primes, but allowing Zak's leading zeros ?

yes:
zak(10123457689)
%1 = 2808500
2808500/2 \\ (symmetry factor for exchange of the two 1's)
%2 = 1404250

Maximilian
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