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

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  • Zak Seidov
    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,
    Message 1 of 8 , Jul 25, 2003
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      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...
    • Zak Seidov
      Mathematica gives 122334444555553 - minimumal prime 122334454545553 122334454554553 122334544455553 122334545545543 122334554545543 122334555545443
      Message 2 of 8 , Jul 25, 2003
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        Mathematica gives
        122334444555553 - minimumal prime
        122334454545553
        122334454554553
        122334544455553
        122334545545543
        122334554545543
        122334555545443
        122335444554553
        122335445454553
        122335445555443
        122335454554543
        122335455445453
        122335455454453
        122335455454543
        122335455455443
        122335544544553
        122335554444553
        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...
      • Zak Seidov
        Mathematica gives maximal prime: 555554444322331 Is it OK? Zak
        Message 3 of 8 , Jul 25, 2003
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          Mathematica gives
          maximal prime:
          555554444322331
          Is it OK?
          Zak

          --- In primenumbers@yahoogroups.com, "Zak Seidov" <seidovzf@y...>
          wrote:
          > Mathematica gives
          > 122334444555553 - minimumal prime
          > 122334454545553
          > 122334454554553
          > 122334544455553
          > 122334545545543
          > 122334554545543
          > 122334555545443
          > 122335444554553
          > 122335445454553
          > 122335445555443
          > 122335454554543
          > 122335455445453
          > 122335455454453
          > 122335455454543
          > 122335455455443
          > 122335544544553
          > 122335554444553
          > 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...
        • jim_fougeron
          ... No, that is the 3rd largest. Here are 2 larger: 555554444332123 555554444332213 ... Minimal: 122334444555566566663 122334444555656566663
          Message 4 of 8 , Jul 25, 2003
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            --- 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...
          • Zak Seidov
            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
            Message 5 of 8 , Jul 25, 2003
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              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...
            • Ken Davis
              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
              Message 6 of 8 , Jul 26, 2003
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                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...
              • 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 7 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 8 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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