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Re: primes with sero 0's, one 1, two 2's, three 3's,...

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  • Zak Seidov
    Ken Davis wrote to me: I did have fun finding the minimal 28 digit primes of your type. Here are the results
    Message 1 of 8 , Jul 31, 2003
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      Ken Davis <kraden@...>
      wrote to me:

      <skip>
      I did have fun finding the minimal 28 digit primes of your type.
      <skip> Here are the results <skip>

      1223334444555556666677767777
      1223334444555556666776776777
      1223334444555556666677767777
      1223334444555556666677767777
      1223334444555556666776776777
      1223334444555556666777767677
      1223334444555556667667776777
      1223334444555556667667777677
      1223334444555556676666777777
      1223334444555556676677667777
      1223334444555556676776766777
      1223334444555556677667776767
      1223334444555556677677676677
      1223334444555556677677677667
      1223334444555556677677766767
      1223334444555556677766676777
      1223334444555556677767676767
      1223334444555556677777667667
      1223334444555556677777676667
      1223334444555556766667767777

      All the above have been certified
      prime by either pfgw or Primo.
      Of the following all except those
      marked with an * are certified prime by pfgw.
      Those marked with an asterix have only been
      shown to be Fermat and Lucas PRP!s
      I haven't run primo on them to prove
      their primality but they almost certainly are.

      1223334444555556766677767767 *
      1223334444555556766677776677 *
      1223334444555556766766677777
      1223334444555556766767667777
      1223334444555556766767767677
      1223334444555556766777776667
      1223334444555556767667777667
      1223334444555556767766777667
      1223334444555556767777766667
      1223334444555556776667776767
      1223334444555556776667777667
      1223334444555556776676677677
      1223334444555556776676766777
      1223334444555556776677676677
      1223334444555556776766677677
      1223334444555556777676677667
      1223334444555556777766667767 *
      1223334444555557666676677777 *
      1223334444555557666677677677
      1223334444555557666767677677
      1223334444555557666767767677
      1223334444555557666776677767 *
      1223334444555557667667677677
      1223334444555557667676676777 *
      1223334444555557667677667767 *
      1223334444555557667677767667
      1223334444555557667766766777 *
      1223334444555557667766767767
      1223334444555557667777766667 *
      1223334444555557676666677777
      1223334444555557676667776767
      1223334444555557676676767677
      1223334444555557676677667767
      1223334444555557677666667777
      1223334444555557677676767667 *
      1223334444555557677766667767
      1223334444555557677766767667 *
      1223334444555557677776666767 *
      1223334444555557766666767777
      1223334444555557766667777667
      1223334444555557766766676777
      1223334444555557766766766777
      1223334444555557766767676767 *
      1223334444555557767666676777
      1223334444555557767776666767
      1223334444555557776667676767
      1223334444555557776667776667
      1223334444555557776676766677 *
      1223334444555557776677676667
      1223334444555557776766766677
      1223334444555557776767766667 *
      1223334444555557777666767667 *
      <skip to end>

      Anyone may wish to check these numbers?

      zak


      --- In primenumbers@yahoogroups.com, "Ken Davis" <kraden@y...> wrote:
      > Hi All,
      > Firstly my apologies if this turns up twice.
      > My first post seems to have dissappeared into the ether
      >
      > 7's maximal is 7777777666666555554444323213
      > Primality testing 7777777666666555554444323213 [N-1/N+1, Brillhart-
      > Lehmer-Selfridge]
      > Calling N-1 BLS with factored part 31.52% and helper 8.70% (105.43%
      > proof)
      > 7777777666666555554444323213 is prime! (0.016000 seconds)
      >
      > And this is the largest as all 8's and 9's are divisible by 3.
      > Cheers
      > Ken
      >
      > --- In primenumbers@yahoogroups.com, "Zak Seidov" <seidovzf@y...>
      > wrote:
      > > And now:
      > > a) add seven 7's,
      > > b) add eight 8's,
      > > c) add nines 9's, and...
      > > we'll go for something else!
      > > zak
      > > you know
      > > the best things (in this world) still are free...
      > >
      > > --- In primenumbers@yahoogroups.com, "jim_fougeron" <jfoug@c...>
      > > wrote:
      > > > --- In primenumbers@yahoogroups.com, "Zak Seidov"
      <seidovzf@y...>
      > > > wrote:
      > > > > Mathematica gives
      > > > > maximal prime:
      > > > > 555554444322331
      > > > > Is it OK?
      > > > > Zak
      > > >
      > > > No, that is the 3rd largest. Here are 2 larger:
      > > > 555554444332123
      > > > 555554444332213
      > > >
      > > > >> What about six 6's??
      > > >
      > > > Minimal:
      > > > 122334444555566566663
      > > > 122334444555656566663
      > > > 122334444555656666563
      > > > 122334444555666566563
      > > >
      > > > Maximal:
      > > > 666666555554444233231
      > > > 666666555554444312323
      > > > 666666555554444323321
      > > > 666666555554444331223
      > > >
      > > > >
      > > > > --- In primenumbers@yahoogroups.com, "Zak Seidov"
      > <seidovzf@y...>
      > > > > wrote:
      > > > > > Mathematica gives
      > > > > > 122334444555553 - minimumal prime
      > > > > > 122334454545553
      > > > > > 122334454554553
      > > > > > 122334544455553
      > > > > clip
      > > > > > 122335554445453
      > > > > > 122335554544543
      > > > > > Are these primes OK?
      > > > > > What about maximal prime?
      > > > > > What about six 6's??
      > > > > > Zak
      > > > > >
      > > > > > --- In primenumbers@yahoogroups.com, "Zak Seidov"
      > > > <seidovzf@y...>
      > > > > > wrote:
      > > > > > > Just sent to Prime Curio:
      > > > > > >
      > > > > > > 123323
      > > > > > > 132233
      > > > > > > 223133
      > > > > > > 223313
      > > > > > > 223331
      > > > > > > 231323
      > > > > > > 233231
      > > > > > > 312233
      > > > > > > 321323
      > > > > > > 323123
      > > > > > >
      > > > > > > Each of these 10 curious primes uses exactly
      > > > > > > zero 0's, one 1, two 2's, and three 3's!
      > > > > > > There are no primes with exactly
      > > > > > > zero 0's, one 1, two 2's, three 3's, and four 4's!
      > > > > > > But what about primes with exactly
      > > > > > > zero 0's, one 1, two 2's, three 3's, four 4's, and five
      > 5'?!
      > > > > > > And you may wish add also six 6's...
      > > > > > > Hint: I don't know answer...
    • Dr. Michael Hartley
      Of course - silly me - there are none with one 1 s... nine 9 s either... Oops! Yours, Mike H....
      Message 2 of 8 , Aug 4, 2003
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        Of course - silly me - there are none with one 1's... nine 9's either...

        Oops!

        Yours, Mike H....


        > -----Original Message-----
        > From: Zakir Seidov [mailto:seidovzf@...]
        > Sent: 04 August 2003 20:16
        > To: Dr. Michael Hartley
        > Subject: Re: primes with sero 0's, one 1, two 2's, three 3's,...
        >
        >
        > Sure there are no numbers
        > with... eight 8's,
        > and are no numbers
        > with... nine 9's,
        > zak
        > --- mike40033 <michael@...> wrote:
        > >
        > > There are none with one 1's...eight 8's.
        > >
        > > Probably about 6x10^32 with one 1's... nine 9's.
        > >
        > >
        > > --- In primenumbers@yahoogroups.com, "Zak Seidov"
        > > <seidovzf@y...>
        > > wrote:
        > > > Ken Davis <kraden@y...>
        > > > wrote to me:
        > > >
        > > > <skip>
        > > > I did have fun finding the minimal 28 digit
        > > primes of your type.
        > > > <skip> Here are the results <skip>
        > > >
        > > > 1223334444555556666677767777
        > > > 1223334444555556666776776777
        > > > 1223334444555556666677767777
        > > > 1223334444555556666677767777
        > > > 1223334444555556666776776777
        > > > 1223334444555556666777767677
        > > > 1223334444555556667667776777
        > > > 1223334444555556667667777677
        > > > 1223334444555556676666777777
        > > > 1223334444555556676677667777
        > > > 1223334444555556676776766777
        > > > 1223334444555556677667776767
        > > > 1223334444555556677677676677
        > > > 1223334444555556677677677667
        > > > 1223334444555556677677766767
        > > > 1223334444555556677766676777
        > > > 1223334444555556677767676767
        > > > 1223334444555556677777667667
        > > > 1223334444555556677777676667
        > > > 1223334444555556766667767777
        > > >
        > > > All the above have been certified
        > > > prime by either pfgw or Primo.
        > > > Of the following all except those
        > > > marked with an * are certified prime by pfgw.
        > > > Those marked with an asterix have only been
        > > > shown to be Fermat and Lucas PRP!s
        > > > I haven't run primo on them to prove
        > > > their primality but they almost certainly are.
        > > >
        > > > 1223334444555556766677767767 *
        > > > 1223334444555556766677776677 *
        > > > 1223334444555556766766677777
        > > > 1223334444555556766767667777
        > > > 1223334444555556766767767677
        > > > 1223334444555556766777776667
        > > > 1223334444555556767667777667
        > > > 1223334444555556767766777667
        > > > 1223334444555556767777766667
        > > > 1223334444555556776667776767
        > > > 1223334444555556776667777667
        > > > 1223334444555556776676677677
        > > > 1223334444555556776676766777
        > > > 1223334444555556776677676677
        > > > 1223334444555556776766677677
        > > > 1223334444555556777676677667
        > > > 1223334444555556777766667767 *
        > > > 1223334444555557666676677777 *
        > > > 1223334444555557666677677677
        > > > 1223334444555557666767677677
        > > > 1223334444555557666767767677
        > > > 1223334444555557666776677767 *
        > > > 1223334444555557667667677677
        > > > 1223334444555557667676676777 *
        > > > 1223334444555557667677667767 *
        > > > 1223334444555557667677767667
        > > > 1223334444555557667766766777 *
        > > > 1223334444555557667766767767
        > > > 1223334444555557667777766667 *
        > > > 1223334444555557676666677777
        > > > 1223334444555557676667776767
        > > > 1223334444555557676676767677
        > > > 1223334444555557676677667767
        > > > 1223334444555557677666667777
        > > > 1223334444555557677676767667 *
        > > > 1223334444555557677766667767
        > > > 1223334444555557677766767667 *
        > > > 1223334444555557677776666767 *
        > > > 1223334444555557766666767777
        > > > 1223334444555557766667777667
        > > > 1223334444555557766766676777
        > > > 1223334444555557766766766777
        > > > 1223334444555557766767676767 *
        > > > 1223334444555557767666676777
        > > > 1223334444555557767776666767
        > > > 1223334444555557776667676767
        > > > 1223334444555557776667776667
        > > > 1223334444555557776676766677 *
        > > > 1223334444555557776677676667
        > > > 1223334444555557776766766677
        > > > 1223334444555557776767766667 *
        > > > 1223334444555557777666767667 *
        > > > <skip to end>
        > > >
        > > > Anyone may wish to check these numbers?
        > > >
        > > > zak
        > > >
        > > >
        > > > --- In primenumbers@yahoogroups.com, "Ken Davis"
        > > <kraden@y...>
        > > wrote:
        > > > > Hi All,
        > > > > Firstly my apologies if this turns up twice.
        > > > > My first post seems to have dissappeared into
        > > the ether
        > > > >
        > > > > 7's maximal is 7777777666666555554444323213
        > > > > Primality testing 7777777666666555554444323213
        > > [N-1/N+1,
        > > Brillhart-
        > > > > Lehmer-Selfridge]
        > > > > Calling N-1 BLS with factored part 31.52% and
        > > helper 8.70%
        > > (105.43%
        > > > > proof)
        > > > > 7777777666666555554444323213 is prime! (0.016000
        > > seconds)
        > > > >
        > > > > And this is the largest as all 8's and 9's are
        > > divisible by 3.
        > > > > Cheers
        > > > > Ken
        > > > >
        > > > > --- In primenumbers@yahoogroups.com, "Zak
        > > Seidov"
        > > <seidovzf@y...>
        > > > > wrote:
        > > > > > And now:
        > > > > > a) add seven 7's,
        > > > > > b) add eight 8's,
        > > > > > c) add nines 9's, and...
        > > > > > we'll go for something else!
        > > > > > zak
        > > > > > you know
        > > > > > the best things (in this world) still are
        > > free...
        > > > > >
        > > > > > --- In primenumbers@yahoogroups.com,
        > > "jim_fougeron"
        > > <jfoug@c...>
        > > > > > wrote:
        > > > > > > --- In primenumbers@yahoogroups.com, "Zak
        > > Seidov"
        > > > <seidovzf@y...>
        > > > > > > wrote:
        > > > > > > > Mathematica gives
        > > > > > > > maximal prime:
        > > > > > > > 555554444322331
        > > > > > > > Is it OK?
        > > > > > > > Zak
        > > > > > >
        > > > > > > No, that is the 3rd largest. Here are 2
        > > larger:
        > > > > > > 555554444332123
        > > > > > > 555554444332213
        > > > > > >
        > > > > > > >> What about six 6's??
        > > > > > >
        > > > > > > Minimal:
        > > > > > > 122334444555566566663
        > > > > > > 122334444555656566663
        > > > > > > 122334444555656666563
        > > > > > > 122334444555666566563
        > > > > > >
        > > > > > > Maximal:
        > > > > > > 666666555554444233231
        > > > > > > 666666555554444312323
        > > > > > > 666666555554444323321
        > > > > > > 666666555554444331223
        > > > > > >
        > > > > > > >
        > > > > > > > --- In primenumbers@yahoogroups.com, "Zak
        > > Seidov"
        > > > > <seidovzf@y...>
        > > > > > > > wrote:
        > > > > > > > > Mathematica gives
        > > > > > > > > 122334444555553 - minimumal prime
        > > > > > > > > 122334454545553
        > > > > > > > > 122334454554553
        > > > > > > > > 122334544455553
        > > > > > > > clip
        > > > > > > > > 122335554445453
        > > > > > > > > 122335554544543
        > > > > > > > > Are these primes OK?
        > > > > > > > > What about maximal prime?
        > > > > > > > > What about six 6's??
        > > > > > > > > Zak
        > > > > > > > >
        > > > > > > > > --- In primenumbers@yahoogroups.com,
        > > "Zak Seidov"
        > > > > > > <seidovzf@y...>
        > > > > > > > > wrote:
        > > > > > > > > > Just sent to Prime Curio:
        > > > > > > > > >
        > > > > > > > > > 123323
        > > > > > > > > > 132233
        > > > > > > > > > 223133
        > > > > > > > > > 223313
        > > > > > > > > > 223331
        > > > > > > > > > 231323
        > > > > > > > > > 233231
        > > > > > > > > > 312233
        > > > > > > > > > 321323
        > > > > > > > > > 323123
        > > > > > > > > >
        > > > > > > > > > Each of these 10 curious primes uses
        > > exactly
        > > > > > > > > > zero 0's, one 1, two 2's, and three
        > > 3's!
        > > > > > > > > > There are no primes with exactly
        > > > > > > > > > zero 0's, one 1, two 2's, three 3's,
        > > and four 4's!
        > > > > > > > > > But what about primes with exactly
        > > > > > > > > > zero 0's, one 1, two 2's, three 3's,
        > > four 4's, and
        > > five
        > > > > 5'?!
        > > > > > > > > > And you may wish add also six 6's...
        > > > > > > > > > Hint: I don't know answer...
        > >
        >
        >
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