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Re: [PrimeNumbers] seeking numerical example

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  • Maximilian Hasler
    On Sat, Mar 10, 2012 at 1:31 PM, Maximilian Hasler ... forprime(p=1,999,forprime(q=1,p,issquare(p*q-1)&print1(p*q , )))
    Message 1 of 4 , Mar 10, 2012
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      On Sat, Mar 10, 2012 at 1:31 PM, Maximilian Hasler
      <maximilian.hasler@...> wrote:
      > On Sat, Mar 10, 2012 at 12:10 PM, Kermit Rose <kermit@...> wrote:
      >> Suppose we wish to look at the special subset of form { z such that z =
      >> (t^2 + 1) = p q, where t is integer, and p and q are primes.}
      >
      > depending on the size of the numbers,
      > I think it's faster to consider products of primes and check whether
      > pq-1 is a square.


      forprime(p=1,999,forprime(q=1,p,issquare(p*q-1)&print1(p*q",")))
      10,26,65,145,82,901,122,2501,2117,1157,485,5777,226,10001,1937,785,6401,362,20737,4097,3601,626,12997,18497,1765,10817,75077,111557,70757,842,64517,2305,81797,2705,7397,266257,1226,37637,23717,254017,11237,3365,320357,9217,144401,448901,1522,3845,207937,276677,60517,270401,527077,244037,104977,38417,712337,698897,

      This (in increasing order) is oeis.org/A144255 : semiprimes of the form n^2+1

      Maximilian
    • Kermit Rose
      ... Given that 10 = 3^2 + 1, I require that x1 x2 - y1 y2 = 1 and x1 y2 + x2 y1 = 3 and x1^2 + y1^2 = 5 and x2^2 + y2^2 = 2 This gives possible solution x1 =
      Message 2 of 4 , Mar 11, 2012
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        On 3/11/2012 9:03 AM, primenumbers@yahoogroups.com wrote:
        > 1c. Re: seeking numerical example
        > Posted by: "Maximilian Hasler"maximilian.hasler@... maximilian_hasler
        > Date: Sat Mar 10, 2012 9:37 am ((PST))
        >
        > On Sat, Mar 10, 2012 at 1:31 PM, Maximilian Hasler
        > <maximilian.hasler@...> wrote:
        >> > On Sat, Mar 10, 2012 at 12:10 PM, Kermit Rose<kermit@...> wrote:
        >>> >> Suppose we wish to look at the special subset of form { z such that z =
        >>> >> (t^2 + 1) = p q, where t is integer, and p and q are primes.}
        >> >
        >> > depending on the size of the numbers,
        >> > I think it's faster to consider products of primes and check whether
        >> > pq-1 is a square.
        > forprime(p=1,999,forprime(q=1,p,issquare(p*q-1)&print1(p*q",")))
        > 10,26,65,145,82,901,122,2501,2117,1157,485,5777,226,10001,1937,785,6401,362,20737,4097,3601,626,12997,18497,1765,10817,75077,111557,70757,842,64517,2305,81797,2705,7397,266257,1226,37637,23717,254017,11237,3365,320357,9217,144401,448901,1522,3845,207937,276677,60517,270401,527077,244037,104977,38417,712337,698897,
        >
        > This (in increasing order) is oeis.org/A144255 : semiprimes of the form n^2+1
        >
        > Maximilian


        Given that 10 = 3^2 + 1,

        I require that

        x1 x2 - y1 y2 = 1

        and

        x1 y2 + x2 y1 = 3

        and
        x1^2 + y1^2 = 5

        and

        x2^2 + y2^2 = 2

        This gives possible solution

        x1 = 2, y1 = 1, x2 = 1, y2 = 1


        Ok. Thank you Max.

        It appears that I have incompletely analyzed the requirements.

        I might or might not get back to you on this problem depending on
        my success in more completely analyzing the requirements of it.

        Kermit
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