## 24128Re: [PrimeNumbers] seeking numerical example

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• 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
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