- --- 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

Interesting. It's surprising to me that the number of odd digits

> 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

>

barely outnumbers the number of even digits in these primes with

maximum perms. Must be a good reason ...

Mark - --- In primenumbers@yahoogroups.com, "Mark Underwood"

<mark.underwood@...> wrote:>

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

> 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 - --- In primenumbers@yahoogroups.com, "David Broadhurst"

<d.broadhurst@...> wrote:

> I prefer

Thereafter, 11-digit primes become somewhat memory-intensive,

> zak(1123465789) = 152526 to

> zak(1023345679) = 156227 since

> the former does not invoke leading zeros.

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 > Thereafter, 11-digit primes become somewhat memory-intensive,

yes:

> 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 ?

zak(10123457689)

%1 = 2808500

2808500/2 \\ (symmetry factor for exchange of the two 1's)

%2 = 1404250

Maximilian