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Re: [PrimeNumbers] 3+ question

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  • Décio Luiz Gazzoni Filho
    ... Law of small numbers. It s hard to tell if this is true because you can t check much further than that -- n = 15 is about the limit given current
    Message 1 of 6 , Mar 4, 2005
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      On Friday 04 March 2005 15:01, you wrote:
      > I think the below is true, but I can't prove or disprove the
      > statement. Please help.
      >
      > If 3^(3^n)+3^(((3^n)+1)/2)+1 is prime then is 3^(3^n)-3^(((3^n)+1)/2)
      > +1 also prime, and vice-versa? I can't find any counter examples.
      >
      > true for n=0,1,2 up to 10(Till where I checked).

      Law of small numbers. It's hard to tell if this is true because you can't
      check much further than that -- n = 15 is about the limit given current
      technology.

      Of course, for all I can tell, there could be a proof of this, but I wouldn't
      be jumping to conclusions with such a small dataset.

      > Note:- The above terms are factors of 3^(3^(n+1))+1, hence will have
      > special factors only.
      >
      > Also, if 2*3^n+1 is prime then it divides these kind of numbers.
      >
      > I am also interested in sieving for these numbers, try to find the
      > smallest factor for each, does anyone have any software available,
      > or could write me one?

      I could in exchange for some CPU-time for my primo-factorial sieving and
      PRP-testing tasks (:

      Décio


      [Non-text portions of this message have been removed]
    • Milton Brown
      There is a Law of Small Numbers in statistics, but you seem to be using the term incorrectly; just dropping it in where it makes no sense. Milton L. Brown
      Message 2 of 6 , Mar 4, 2005
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        There is a Law of Small Numbers in statistics,
        but you seem to be using the term incorrectly;
        just dropping it in where it makes no sense.

        Milton L. Brown
        miltbrown at earthlink.net



        > [Original Message]
        > From: D�cio Luiz Gazzoni Filho <decio@...>
        > To: <primenumbers@yahoogroups.com>
        > Date: 3/4/2005 11:23:19 AM
        > Subject: Re: [PrimeNumbers] 3+ question
        >
        >
        > On Friday 04 March 2005 15:01, you wrote:
        > > I think the below is true, but I can't prove or disprove the
        > > statement. Please help.
        > >
        > > If 3^(3^n)+3^(((3^n)+1)/2)+1 is prime then is 3^(3^n)-3^(((3^n)+1)/2)
        > > +1 also prime, and vice-versa? I can't find any counter examples.
        > >
        > > true for n=0,1,2 up to 10(Till where I checked).
        >
        > Law of small numbers. It's hard to tell if this is true because you can't
        > check much further than that -- n = 15 is about the limit given current
        > technology.
        >
        > Of course, for all I can tell, there could be a proof of this, but I
        wouldn't
        > be jumping to conclusions with such a small dataset.
        >
        > > Note:- The above terms are factors of 3^(3^(n+1))+1, hence will have
        > > special factors only.
        > >
        > > Also, if 2*3^n+1 is prime then it divides these kind of numbers.
        > >
        > > I am also interested in sieving for these numbers, try to find the
        > > smallest factor for each, does anyone have any software available,
        > > or could write me one?
        >
        > I could in exchange for some CPU-time for my primo-factorial sieving and
        > PRP-testing tasks (:
        >
        > 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
        >
        >
        >
        >
        >
        >
      • Jens Kruse Andersen
        ... Googling Law of Small Numbers shows something in good agreement with Decio s use of the term, e.g.:
        Message 3 of 6 , Mar 5, 2005
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          Milton Brown wrote:

          > There is a Law of Small Numbers in statistics,
          > but you seem to be using the term incorrectly;
          > just dropping it in where it makes no sense.

          Googling "Law of Small Numbers" shows something in good agreement with Decio's
          use of the term, e.g.:
          http://primes.utm.edu/glossary/page.php?sort=LawOfSmall

          Milton's posts on the other hand, seem to often make no sense.

          Harsh Aggarwal wrote:

          > I think the below is true, but I can't prove or disprove the
          > statement. Please help.
          >
          > If 3^(3^n)+3^(((3^n)+1)/2)+1 is prime then is 3^(3^n)-3^(((3^n)+1)/2)+1
          > also prime, and vice-versa? I can't find any counter examples.
          >
          > true for n=0,1,2 up to 10(Till where I checked).

          Only true for n=0 if 1 is considered a prime. Then n = 0, 1, 2 gives 6 small
          primes: (7, 1), (37, 19), (19927, 19441).
          There are no other primes for n<=10. The number of digits approximately
          triples for each n. This growth is so fast that there are probably no more
          primes at all. That means Harsh's guess is actually likely to be true, but in
          an uninteresting way.

          PS: Do not use the default primeform Fermat 3-prp test on these base 3
          expressions.

          --
          Jens Kruse Andersen
        • jim_fougeron
          ... Cosigned, since the Law of Small Numbers makes perfect since in this case. Looking at the first 3 tiny pairs of numbers could lead someone to believe
          Message 4 of 6 , Mar 5, 2005
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            --- In primenumbers@yahoogroups.com, "Jens Kruse Andersen"
            <jens.k.a@g...>wrote:
            >Milton Brown wrote:
            >
            >>There is a Law of Small Numbers in statistics,
            >>but you seem to be using the term incorrectly;
            >>just dropping it in where it makes no sense.
            >
            >Googling "Law of Small Numbers" shows something in good agreement
            >with Decio's use of the term, e.g.:
            >http://primes.utm.edu/glossary/page.php?sort=LawOfSmall
            >
            >Milton's posts on the other hand, seem to often make no sense.

            Cosigned, since the "Law of Small Numbers" makes perfect since in
            this case. Looking at the first 3 tiny pairs of numbers could lead
            someone to believe that there is some law "causing" this to happen.
            Well, there "might" be such a law, but most likely it is due to
            blind luck, and such tiny numbers which are statistically rich in
            primes.

            One could also look at the "plus" form, and make a statement
            (although wrong), that since n=0 and n=1 and n=2 are all prime,
            then all will be prime (note a Great one, Fermat made such a wild
            claim in the past).

            Both of the above claims are cases where the "Law of Small Numbers"
            causes someone to make a false (or likely false) claim. However,
            for the claim of if "plus" prime, then "minus" prime, (if the
            stipulation of n>1 is added to the original question posed),
            "might" be true, due to the fact that it is likely there are no
            additional primes of either form. There is no "law" (that I am
            aware of), but simple blind luck happened to form these pairs.

            >Harsh Aggarwal wrote:
            >
            >>I think the below is true, but I can't prove or disprove the
            >>statement. Please help.
            >>
            >>If 3^(3^n)+3^(((3^n)+1)/2)+1 is prime then is 3^(3^n)-3^(((3^n)
            +1)/2)+1
            >>also prime, and vice-versa? I can't find any counter examples.
            >>
            >>true for n=0,1,2 up to 10(Till where I checked).
            >
            >Only true for n=0 if 1 is considered a prime. Then n = 0, 1, 2
            gives 6
            >small primes: (7, 1), (37, 19), (19927, 19441).
            >There are no other primes for n<=10. The number of digits
            approximately
            >triples for each n. This growth is so fast that there are probably
            no
            >more primes at all. That means Harsh's guess is actually likely to
            be
            >true, but in an uninteresting way.
            >
            >PS: Do not use the default primeform Fermat 3-prp test on these
            base 3
            >expressions.

            I don't know about that PS statement. It might be good to have some
            of the "newer" prime hunters use default Fermat-3 tests. Frequently
            a wrong answer (especially one which might smack someone right in the
            forehead) will help teach people willing to learn, better than a
            correct answer.

            >Jens Kruse Andersen
          • Milton Brown
            Responding people should surely do their research before making making such might be false statements: Well, there might be such a law, but most likely it
            Message 5 of 6 , Mar 5, 2005
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              Responding people should surely do their research before making
              making such "might" be false statements:

              "Well, there 'might' be such a law, but most likely it is due to
              blind luck ...

              Milton L. Brown
              miltbrown at earthlink.net

              > [Original Message]
              > From: jim_fougeron <jfoug@...>
              > To: <primenumbers@yahoogroups.com>
              > Date: 3/5/2005 5:54:29 AM
              > Subject: [PrimeNumbers] Re: 3+ question
              >
              >
              >
              > --- In primenumbers@yahoogroups.com, "Jens Kruse Andersen"
              > <jens.k.a@g...>wrote:
              > >Milton Brown wrote:
              > >
              > >>There is a Law of Small Numbers in statistics,
              > >>but you seem to be using the term incorrectly;
              > >>just dropping it in where it makes no sense.
              > >
              > >Googling "Law of Small Numbers" shows something in good agreement
              > >with Decio's use of the term, e.g.:
              > >http://primes.utm.edu/glossary/page.php?sort=LawOfSmall
              > >
              > >Milton's posts on the other hand, seem to often make no sense.
              >
              > Cosigned, since the "Law of Small Numbers" makes perfect since in
              > this case. Looking at the first 3 tiny pairs of numbers could lead
              > someone to believe that there is some law "causing" this to happen.
              > Well, there "might" be such a law, but most likely it is due to
              > blind luck, and such tiny numbers which are statistically rich in
              > primes.
              >
              > One could also look at the "plus" form, and make a statement
              > (although wrong), that since n=0 and n=1 and n=2 are all prime,
              > then all will be prime (note a Great one, Fermat made such a wild
              > claim in the past).
              >
              > Both of the above claims are cases where the "Law of Small Numbers"
              > causes someone to make a false (or likely false) claim. However,
              > for the claim of if "plus" prime, then "minus" prime, (if the
              > stipulation of n>1 is added to the original question posed),
              > "might" be true, due to the fact that it is likely there are no
              > additional primes of either form. There is no "law" (that I am
              > aware of), but simple blind luck happened to form these pairs.
              >
              > >Harsh Aggarwal wrote:
              > >
              > >>I think the below is true, but I can't prove or disprove the
              > >>statement. Please help.
              > >>
              > >>If 3^(3^n)+3^(((3^n)+1)/2)+1 is prime then is 3^(3^n)-3^(((3^n)
              > +1)/2)+1
              > >>also prime, and vice-versa? I can't find any counter examples.
              > >>
              > >>true for n=0,1,2 up to 10(Till where I checked).
              > >
              > >Only true for n=0 if 1 is considered a prime. Then n = 0, 1, 2
              > gives 6
              > >small primes: (7, 1), (37, 19), (19927, 19441).
              > >There are no other primes for n<=10. The number of digits
              > approximately
              > >triples for each n. This growth is so fast that there are probably
              > no
              > >more primes at all. That means Harsh's guess is actually likely to
              > be
              > >true, but in an uninteresting way.
              > >
              > >PS: Do not use the default primeform Fermat 3-prp test on these
              > base 3
              > >expressions.
              >
              > I don't know about that PS statement. It might be good to have some
              > of the "newer" prime hunters use default Fermat-3 tests. Frequently
              > a wrong answer (especially one which might smack someone right in the
              > forehead) will help teach people willing to learn, better than a
              > correct answer.
              >
              > >Jens Kruse Andersen
              >
              >
              >
              >
              >
              >
              > Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com
              > The Prime Pages : http://www.primepages.org/
              >
              >
              > Yahoo! Groups Links
              >
              >
              >
              >
              >
              >
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