Loading ...
Sorry, an error occurred while loading the content.

Re: [PrimeNumbers] Infinite Number of Twin Primes

Expand Messages
  • Jud McCranie
    ... How do you know that will work (that you will always obtain a pair of twins for that factorial)?
    Message 1 of 13 , May 5, 2005
    • 0 Attachment
      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)?
    • Décio Luiz Gazzoni Filho
      ... 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
      Message 2 of 13 , May 5, 2005
      • 0 Attachment
        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.

        Décio


        [Non-text portions of this message have been removed]
      • Jud McCranie
        ... I knew that, of course, and was pressing him.
        Message 3 of 13 , May 5, 2005
        • 0 Attachment
          At 07:13 PM 5/5/2005, Décio Luiz Gazzoni Filho wrote:

          > 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,

          I knew that, of course, and was pressing him.
        • 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 4 of 13 , May 5, 2005
          • 0 Attachment
            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]
            >
            >
            >
            >
            > Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
            > The Prime Pages : http://www.primepages.org/
            >
            >
            > Yahoo! Groups Links
            >
            >
            >
            >
            >
          • Décio Luiz Gazzoni Filho
            ... Milton, are you really this stupid, or do you somehow enjoy being humiliated in public? In the latter case, you should seek psychiatric help. ... Emphasis
            Message 5 of 13 , May 5, 2005
            • 0 Attachment
              On Thursday 05 May 2005 21:36, Milton Brown wrote:
              > 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, are you really this stupid, or do you somehow enjoy being humiliated
              in public? In the latter case, you should seek psychiatric help.

              From your message that started the thread:

              > 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.

              Emphasis on `prior pairs'. Now tell me which values of n,k generate (n! + k,
              n! + k + 2) = (59,61).

              Décio


              [Non-text portions of this message have been removed]
            • Décio Luiz Gazzoni Filho
              ... Moreover, a PARI/GP search plus a clever shell script using PFGW (guess I should learn PFGW s scripting language instead, but...) confirms my previous
              Message 6 of 13 , May 5, 2005
              • 0 Attachment
                On Thursday 05 May 2005 20:13, you wrote:
                > Finally, 7! doesn't produce any values. And thus Milton's conjecture is
                > demolished, as about anything that he brainfarts on this list.

                Moreover, a PARI/GP search plus a clever shell script using PFGW (guess I
                should learn PFGW's scripting language instead, but...) confirms my previous
                findings, and adds failures at n! for n = 10, 12-14, 16, 17, 22-64, 66-70,
                72-135, 137-361, 363-683,685-900; that's as far as I'm willing to take this
                search. I have reason to believe that only finitely many twin prime pairs are
                generated by this process.

                Additionally, in the course of running this code, I discovered a bug in
                PARI/GP 2.2.9:

                ? isprime(42542905343533366778773944705953203289361426945380795183689)
                *** isprime: impossible inverse modulo: Mod(0,
                42542905343533366778773944705953203289361426945380795183689).

                Ironically, Milton's work was not 100% in vain.

                Décio

                PS: in principle one can actually check my conjecture that the sequence is
                finite: if p, p+2 is the largest twin prime pair generated, then test all n's
                up to n = p. Obviously p! shares a factor with all twin primes in the set,
                and so does n! for all n > p. Thus, no new twin prime pairs can be generated
                from then on. Of course, exhausting the range up to n! when n is in the
                thousands of digits isn't exactly practical.


                [Non-text portions of this message have been removed]
              • Milton Brown
                Even a computer search does not help you! (3629027, 3629029) = (10!+227, 10!+229) Unless n=10 means something else to you. (Maybe its not the computer after
                Message 7 of 13 , May 5, 2005
                • 0 Attachment
                  Even a computer search does not help you!

                  (3629027, 3629029) = (10!+227, 10!+229)

                  Unless n=10 means something else to you.

                  (Maybe its not the computer after all)

                  Milton L. Brown

                  > [Original Message]
                  > From: D�cio Luiz Gazzoni Filho <decio@...>
                  > To: <primenumbers@yahoogroups.com>
                  > Date: 5/5/2005 8:06:20 PM
                  > Subject: Re: [PrimeNumbers] Infinite Number of Twin Primes
                  >
                  > On Thursday 05 May 2005 20:13, you wrote:
                  > > Finally, 7! doesn't produce any values. And thus Milton's conjecture is
                  > > demolished, as about anything that he brainfarts on this list.
                  >
                  > Moreover, a PARI/GP search plus a clever shell script using PFGW (guess I
                  > should learn PFGW's scripting language instead, but...) confirms my
                  previous
                  > findings, and adds failures at n! for n = 10, 12-14, 16, 17, 22-64,
                  66-70,
                  > 72-135, 137-361, 363-683,685-900; that's as far as I'm willing to take
                  this
                  > search. I have reason to believe that only finitely many twin prime pairs
                  are
                  > generated by this process.
                  >
                  > Additionally, in the course of running this code, I discovered a bug in
                  > PARI/GP 2.2.9:
                  >
                  > ? isprime(42542905343533366778773944705953203289361426945380795183689)
                  > *** isprime: impossible inverse modulo: Mod(0,
                  > 42542905343533366778773944705953203289361426945380795183689).
                  >
                  > Ironically, Milton's work was not 100% in vain.
                  >
                  > D�cio
                  >
                  > PS: in principle one can actually check my conjecture that the sequence
                  is
                  > finite: if p, p+2 is the largest twin prime pair generated, then test all
                  n's
                  > up to n = p. Obviously p! shares a factor with all twin primes in the
                  set,
                  > and so does n! for all n > p. Thus, no new twin prime pairs can be
                  generated
                  > from then on. Of course, exhausting the range up to n! when n is in the
                  > thousands of digits isn't exactly practical.
                  >
                  >
                  > [Non-text portions of this message have been removed]
                  >
                  >
                  >
                  >
                  > Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
                  > The Prime Pages : http://www.primepages.org/
                  >
                  >
                  > Yahoo! Groups Links
                  >
                  >
                  >
                  >
                  >
                • Décio Luiz Gazzoni Filho
                  ... Besides being a moron, are you also unable to read? Here, let me reproduce my ... What part of this don t you understand? Just replace (59,61) by
                  Message 8 of 13 , May 5, 2005
                  • 0 Attachment
                    On Friday 06 May 2005 01:04, Milton Brown wrote:
                    > Even a computer search does not help you!
                    >
                    > (3629027, 3629029) = (10!+227, 10!+229)
                    >
                    > Unless n=10 means something else to you.
                    >
                    > (Maybe its not the computer after all)

                    Besides being a moron, are you also unable to read? Here, let me reproduce my
                    reply to your prior `objection':

                    > From your message that started the thread:
                    >
                    > > 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.
                    >
                    > Emphasis on `prior pairs'. Now tell me which values of n,k generate (n! + k,
                    > n! + k + 2) = (59,61).

                    What part of this don't you understand? Just replace (59,61) by (227,229). I
                    think I should write a shell script to automatically answer your emails.

                    I once wrote an opinion piece for a computer magazine about how computers
                    should require a license to operate, akin to a driver's license. My argument
                    at the time was that computer-illiterate users were polluting the internet
                    with viruses, trojan/worm traffic (not to mention stupid rehashed jokes,
                    chain letters, hoaxes and the like). Guess I should have extended the
                    proposal to morons with IQ < 50 and serious learning/reading/comprehension
                    and psychological issues, which waste other people's time through posts like
                    this on newsgroups and forums. Milton Brown and JSH from sci.math would be
                    the perfect posterchilds for such a proposal.

                    Why don't you do a favor to humanity and throw yourself off a tall building?

                    Décio


                    [Non-text portions of this message have been removed]
                  • Milton Brown
                    More addition for your computer: (479001791, 479001793) = (12!+191, 12!+193) And, again you said 12 didn t work! Milton L. Brown ... reproduce my ... of ...
                    Message 9 of 13 , May 6, 2005
                    • 0 Attachment
                      More addition for your computer:

                      (479001791, 479001793) = (12!+191, 12!+193)

                      And, again you said 12 didn't work!

                      Milton L. Brown


                      > [Original Message]
                      > From: D�cio Luiz Gazzoni Filho <decio@...>
                      > To: <primenumbers@yahoogroups.com>
                      > Date: 5/5/2005 9:35:46 PM
                      > Subject: Re: [PrimeNumbers] Infinite Number of Twin Primes
                      >
                      > On Friday 06 May 2005 01:04, Milton Brown wrote:
                      > > Even a computer search does not help you!
                      > >
                      > > (3629027, 3629029) = (10!+227, 10!+229)
                      > >
                      > > Unless n=10 means something else to you.
                      > >
                      > > (Maybe its not the computer after all)
                      >
                      > Besides being a moron, are you also unable to read? Here, let me
                      reproduce my
                      > reply to your prior `objection':
                      >
                      > > From your message that started the thread:
                      > >
                      > > > 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.
                      > >
                      > > Emphasis on `prior pairs'. Now tell me which values of n,k generate (n!
                      + k,
                      > > n! + k + 2) = (59,61).
                      >
                      > What part of this don't you understand? Just replace (59,61) by
                      (227,229). I
                      > think I should write a shell script to automatically answer your emails.
                      >
                      > I once wrote an opinion piece for a computer magazine about how computers
                      > should require a license to operate, akin to a driver's license. My
                      argument
                      > at the time was that computer-illiterate users were polluting the
                      internet
                      > with viruses, trojan/worm traffic (not to mention stupid rehashed jokes,
                      > chain letters, hoaxes and the like). Guess I should have extended the
                      > proposal to morons with IQ < 50 and serious
                      learning/reading/comprehension
                      > and psychological issues, which waste other people's time through posts
                      like
                      > this on newsgroups and forums. Milton Brown and JSH from sci.math would
                      be
                      > the perfect posterchilds for such a proposal.
                      >
                      > Why don't you do a favor to humanity and throw yourself off a tall
                      building?
                      >
                      > D�cio
                      >
                      >
                      > [Non-text portions of this message have been removed]
                      >
                      >
                      >
                      >
                      > Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
                      > The Prime Pages : http://www.primepages.org/
                      >
                      >
                      > Yahoo! Groups Links
                      >
                      >
                      >
                      >
                      >
                    • 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 10 of 13 , May 6, 2005
                      • 0 Attachment
                        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 11 of 13 , May 6, 2005
                        • 0 Attachment
                          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 12 of 13 , May 6, 2005
                          • 0 Attachment
                            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?
                          Your message has been successfully submitted and would be delivered to recipients shortly.