1
$\begingroup$

Let $\ p\ $ and $\ q:=2\cdot p+1\ $ be primes — they are called Germain prime siblings. Such a pair belongs to the first type $\ \Leftarrow:\Rightarrow\ \frac{q^2-1}8\equiv\pm1\mod8,\ $ and to the second type $\ \Leftarrow:\Rightarrow\ \frac{q^2-1}8\equiv\pm3\mod8.\ $

Do you know any results (in print or your own) about the frequency of the two types?

Improve this question
$\endgroup$
4
  • 1
    $\begingroup$ Perhaps you should add the [reference-request] tag, @WlodAA? $\endgroup$
    – Jose Arnaldo Bebita
    Commented Sep 17, 2021 at 7:17
  • $\begingroup$ @ArnieBebita-Dris, thank you -- I've followed your suggestion. $\endgroup$
    – Wlod AA
    Commented Sep 17, 2021 at 7:19
  • 1
    $\begingroup$ I suggest you initially have a look at the Wikipedia page on properties of Sophie Germain primes and safe primes, and thereby review the references contained therein. $\endgroup$
    – Jose Arnaldo Bebita
    Commented Sep 17, 2021 at 7:22
  • 2
    $\begingroup$ $(q^2-1)/8$ can also be even, e.g., $p=11$, $q=23$, $(q^2-1)/8=66\equiv2\bmod8$. $\endgroup$
    – Gerry Myerson
    Commented Sep 18, 2021 at 13:19

0

Reset to default

You must log in to answer this question.

Browse other questions tagged .