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

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  • Dr. Michael Hartley
    Of course - silly me - there are none with one 1 s... nine 9 s either... Oops! Yours, Mike H....
    Message 1 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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