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Re: [PrimeNumbers] seeking numerical example

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  • Maximilian Hasler
    ... 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. Maximilian
    Message 1 of 4 , Mar 10, 2012
      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.}
      >
      > We can identify elements of that subset by:
      >
      > Pick x1,x2,y1,y2 such that x1 x2 - y1 y2 = 1 and
      > x1^2 + y1^2 is prime and x2^2 + y2^2 is prime.
      >
      > Is it possible to do this?


      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.

      Maximilian
    • 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 2 of 4 , Mar 10, 2012
        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 3 of 4 , Mar 11, 2012
          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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