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  • Peter Boos
    If one multiplies prime numbers add one (or minus one). It seams to turn out to be always a prime. And even other tricks seams to apply to turn out a prime My
    Message 1 of 5 , Oct 30, 2002
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      If one multiplies prime numbers add one (or minus one).
      It seams to turn out to be always a prime.
      And even other tricks seams to apply to turn out a prime
      My math knowledge is average.
      Hhave these 3 types of geting prime numbers a name?

      Is 2*3*5*7*11*13* ..... +1 always prime ?
      2*3+1=7
      2*3*5+1=31
      2*3*5*7=211
      ...
      .

      Also 2*3*5*7*22*13*.... -1 seams to be alaway prime (not sure yet).
      2*3-1=5
      2*3*5-1=29
      2*3*5*7-1=209
      ..
      .

      playing with the set a bit more.
      This might work just because there are a lot of low primes.
      It also doesn't always produce primes sometime near primes.
      Well I didn't tested it with big sets since i only had a simple
      calculator wgen writing this Email.

      multiply prime set - same set whitout one element Z + 1
      (z = one prime of the same set replaced by number 1 )

      2*3*5 - 2*3*z +1 = (10) not a prime
      2*3*5 - 2*z*5 +1 = 11
      2*3*5 - z*3*5 +1 = 16 not a prime (*>> -part has no 2

      2*3*5*7 - 2*3*5*z +1 = 281 prime
      2*3*5*7 - 2*3*z*7 +1 = 269 prime
      2*3*5*7 - 2*z*5*7 +1 = 141 near prime -1 instead of +1 is prime
      2*3*5*7 - z*3*5*7 +1 = 106 not a prime (*>> -part has no 2


      2*3*5*7*11 -2*3*5*7*z +1 = 2101 near prime -1 instead of +1 is prime
      2*3*5*7*11 -2*3*5*z*11+1 = 2081 prime
      2*3*5*7*11 -2*3*z*7*11+1 = 1849 near prime -1 instead of +1 is prime
      2*3*5*&*11 -2*z*5*7*11+1 = 1901 prime
      2*3*5*&*11 -z*3*5*7*11+1 = 1156 not a prime (*>> -part has no 2


      *>> part has no 2 will never be prime since numbers multiply will
      always resurl in even numbers, so 2 is required.
    • Paul Leyland
      ... Wrong. ... The product of all the primes up to and including p is generally known as p#, or p primorial (by analogy with factorial). ... No. ...
      Message 2 of 5 , Oct 30, 2002
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        > If one multiplies prime numbers add one (or minus one).
        > It seams to turn out to be always a prime.

        Wrong.

        > And even other tricks seams to apply to turn out a prime
        > My math knowledge is average.
        > Hhave these 3 types of geting prime numbers a name?

        The product of all the primes up to and including p is generally known as p#, or p primorial (by analogy with factorial).

        > Is 2*3*5*7*11*13* ..... +1 always prime ?

        No.

        > 2*3+1=7
        > 2*3*5+1=31
        > 2*3*5*7=211

        2*3*5*7*11*13 + 1 = 59 * 509

        > Also 2*3*5*7*22*13*.... -1 seams to be alaway prime (not sure yet).
        > 2*3-1=5
        > 2*3*5-1=29
        > 2*3*5*7-1=209

        209 = 11 * 19

        Nice try, but you don't win the prize.


        Paul
      • Peter Boos
        Paul what do you think about the 3th type?. It produces a remarkable list i think. Later I used a internet list of the first 10000 primes. I should have tested
        Message 3 of 5 , Oct 30, 2002
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          Paul what do you think about the 3th type?.
          It produces a remarkable list i think.

          Later I used a internet list of the first 10000
          primes.
          I should have tested the first 2 types also :(
          So far I have not tested larger sets then the previous
          post. If I have time perhaps I can program it in VB
          but now i have not much time anymore.



          --- Paul Leyland <pleyland@...> wrote:
          > > If one multiplies prime numbers add one (or minus
          > one).
          > > It seams to turn out to be always a prime.
          >
          > Wrong.
          >
          > > And even other tricks seams to apply to turn out a
          > prime
          > > My math knowledge is average.
          > > Hhave these 3 types of geting prime numbers a
          > name?
          >
          > The product of all the primes up to and including p
          > is generally known as p#, or p primorial (by analogy
          > with factorial).
          >
          > > Is 2*3*5*7*11*13* ..... +1 always prime ?
          >
          > No.
          >
          > > 2*3+1=7
          > > 2*3*5+1=31
          > > 2*3*5*7=211
          >
          > 2*3*5*7*11*13 + 1 = 59 * 509
          >
          > > Also 2*3*5*7*22*13*.... -1 seams to be alaway
          > prime (not sure yet).
          > > 2*3-1=5
          > > 2*3*5-1=29
          > > 2*3*5*7-1=209
          >
          > 209 = 11 * 19
          >
          > Nice try, but you don't win the prize.
          >
          >
          > Paul
          >


          =====
          Kind regards Peter Booshttp://www.geocities.com/Peter_Boos

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        • Paul Jobling
          ... Peter, Download a copy of PFGW from http://groups.yahoo.com/group/primeform/files/20020515_OpenPFGW.zip This is a very fast primality prover for many types
          Message 4 of 5 , Oct 30, 2002
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            > Paul what do you think about the 3th type?.
            > It produces a remarkable list i think.

            Peter,

            Download a copy of PFGW from
            http://groups.yahoo.com/group/primeform/files/20020515_OpenPFGW.zip

            This is a very fast primality prover for many types of number, this included.
            The product of the primes up to n, called the "primorial" (like the
            factorial), and is conveniently written as n#. To use PFGW, enter something
            like

            pfgw -q"13#+1"

            which will test 2x3x5x7x11x13+1 for (probably) primality.

            You can investigate your third form using ABC2 files - see the documentation.
            Basically you create a file called (say) 37test.txt containing something like
            this:

            ABC2 37#/$a+1
            a: primes from 3 to 37

            then you call PFGW giving it the parameter 37test.txt:

            P:\pfgw>pfgw 37test.txt
            PFGW Version 20021007.Win_Dev (Alpha software, 'caveat utilitor') (Woltman
            22.7lib w/P4 fixes)

            Recognized ABC Sieve file: ABC2 File
            Switching to Exponentiating using GMP
            37#/2+1 is composite: [21B7D0D749F] (0.000000 seconds)
            37#/3+1 is composite: [1412642F4E8] (0.000000 seconds)
            37#/5+1 is composite: [D5B2EC019A] (0.000000 seconds)
            37#/7+1 is 3-PRP! (0.000000 seconds)
            37#/11+1 is composite: [5010B73FC9] (0.000000 seconds)
            37#/13+1 is composite: [3732BC9436] (0.000000 seconds)
            37#/17+1 is composite: [6E91841F2] (0.000000 seconds)
            37#/19+1 is 3-PRP! (0.000000 seconds)
            37#/23+1 is 3-PRP! (0.000000 seconds)
            37#/29+1 is composite: [22D547146F] (0.000000 seconds)
            37#/31+1 is 3-PRP! (0.000000 seconds)
            37#/37+1 is 3-PRP! (0.000000 seconds)

            Oh - I spy a bug! Why did it test 37#/2+1???

            Regards,

            Paul (another one).


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          • Rob Binnekamp
            Hi Paul, How can I (we) get pfgw Version 20021007 ? Greetings, Rob
            Message 5 of 5 , Oct 31, 2002
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              Hi Paul,

              How can I (we) get pfgw Version 20021007 ?

              Greetings, Rob
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