## Re: [PrimeNumbers] seeking numerical example

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• 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
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 =
Message 2 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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