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Re: [PrimeNumbers] Infinite Number of Twin Primes

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  • Milton Brown
    Perhaps a computer search would be better for you. Or, see the link http://primes.utm.edu/lists/small/1ktwins.txt (7!+59, 7!+61) = (5099, 5101) is a prime
    Message 1 of 13 , May 5 5:36 PM
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      Perhaps a computer search would be better for you.

      Or, see the link http://primes.utm.edu/lists/small/1ktwins.txt

      (7!+59, 7!+61) = (5099, 5101) is a prime pair.

      Milton L. Brown


      > [Original Message]
      > From: D�cio Luiz Gazzoni Filho <decio@...>
      > To: <primenumbers@yahoogroups.com>
      > Date: 5/5/2005 4:14:35 PM
      > Subject: Re: [PrimeNumbers] Infinite Number of Twin Primes
      >
      > On Thursday 05 May 2005 19:49, you wrote:
      > > At 04:54 PM 5/5/2005, Milton Brown wrote:
      > > >This is the pattern: Start at the next factorial and add prior pairs of
      > > >twin primes,
      > > >until you obtain a pair of twin primes for that factorial.
      > >
      > > How do you know that will work (that you will always obtain a pair of
      twins
      > > for that factorial)?
      >
      > The answer is, he doesn't, because it won't work. This one didn't even
      need a
      > computer search; it fell to a search by hand. I would appreciate a third
      > check (I've already double-checked locally).
      >
      > Start from (3,5).
      >
      > 2!+3, 2!+5 adds (5,7). Values found until now: (3,5), (5,7).
      >
      > 3!+5, 3!+7 adds (11,13). 3!+11, 3!+13 adds (17,19).
      > Values found until now: (3,5), (5,7), (11,13), (17,19).
      >
      > 4!+5, 4!+7 adds (29,31). 4!+17, 4!+19 adds (41,43).
      > Values found until now: (3,5), (5,7), (11,13), (17,19), (29,31), (41,43).
      >
      > 5!+17, 5!+19 adds (137,139). 5!+29, 5!+31 adds (149,151). 5!+149, 5!+151
      adds
      > (269,271).
      > Values found until now: (3,5), (5,7), (11,13), (17,19), (29,31), (41,43),
      > (137,139), (149,151), (269,271).
      >
      > 6!+137, 6!+139 adds (857,859).
      > Values found until now: (3,5), (5,7), (11,13), (17,19), (29,31), (41,43),
      > (137,139), (149,151), (269,271), (857,859).
      >
      > Finally, 7! doesn't produce any values. And thus Milton's conjecture is
      > demolished, as about anything that he brainfarts on this list.
      >
      > D�cio
      >
      >
      > [Non-text portions of this message have been removed]
      >
      >
      >
      >
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      >
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      >
      >
      >
    • Jacques Tramu
      How many fact-twins are there ? A pair of fact-twins are twins primes (ft, ft+2) if exists n such as ft = n! + p, where p and p+2 are twin primes; The
      Message 2 of 13 , May 6 9:32 AM
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        How many fact-twins are there ?

        A pair of fact-twins are twins primes (ft, ft+2) if exists n such as
        ft = n! + p, where p and p+2 are twin primes;

        The following table count the number of fact-twins in intervals of length
        10^9 starting at
        0, up to 10^18.

        pi = number of primes in the interval [from, from+10^9]
        twins = number of twins
        fact-twins : number of fact-twins
        % = fact-twins * 100 / twins

        from pi twins fact-twins
        %
        1 50847534 3424506 999836 29,20%
        10^9 47374753 2963535 815419 27,51%
        10^10 43336106 2477174 674611 27,23%
        10^11 39475591 2055627 547106 26,62%
        10^12 36190991 1730012 386360 22,33%
        10^13 33405006 1473196 318563 21,62%
        10^14 31019409 1270499 265221 20,88%
        10^15 28946421 1105560 225366 20,38%
        10^16 27153205 972510 194566 20,01%
        10^17 25549226 861742 153809 17,85%
        10^18 24127085 769103 135977 17,68%
      • Jud McCranie
        ... the point is that you gave this procedure for producing more and more twin primes from factorials and the previously found twin primes. Other than a
        Message 3 of 13 , May 6 10:06 AM
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          At 03:09 AM 5/6/2005, Milton Brown wrote:
          >More addition for your computer:
          >
          > (479001791, 479001793) = (12!+191, 12!+193)
          >
          >And, again you said 12 didn't work!

          the point is that you gave this procedure for producing more and more twin
          primes from factorials and the previously found twin primes. Other than a
          finite number of twin primes as seeds and the ones previously generated by
          your procedure, your procedure doesn't know any other twin primes. The
          procedure has to bootstrap itself and keep going forever. IIRC, he showed
          that 191 and 193 can't be generated that way, so you can't use them for 12!.
        • Mark Underwood
          Jud s point is well taken. Milton s original offering was that twin primes would be generated from only previously generated twin primes. I took the liberty to
          Message 4 of 13 , May 6 10:43 AM
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            Jud's point is well taken. Milton's original offering was that twin
            primes would be generated from only previously generated twin primes.

            I took the liberty to modify Milton's original offering to this:

            Starting with n=3 and (5,7) as the first twin prime pair, if we add
            *or subtract* a (previously generated) twin prime pair from n! to
            generate more twin prime pairs, how far can n go before there is a
            failure to produce twins? Answer : n=22.

            But if instead of n! we use p#, then we can get as high as p = 61
            before there is a failure to produce. (61 is the only prime to fail
            before 103. After that failures become more common, as one might
            expect.)


            Mark


            PS to certain others: Where is the love? How can there ever be peace
            in the world if we respect our own knowledge or sensibilities or
            tradition over our fellow human beings?
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