In the following link:
https://oeis.org/A079796/b079796.txt
we can see the first 10,000 prime numbers $p$ with the property that both
$(3p)^2 + p^2 + 3^2$
and
$(3p)^2 - p^2 - 3^2$ are primes
The primes $p$ with this property satisfie that both $10p^2 + 9$ and $8p^2-9$ are also primes. How can I extend the list to find how many primes are up to $N$ beyond the $10,000$ such primes listed in the link, using Wolfram Alpha?
I don't have mathematica, so maybe there's a limitation in the computational power available in Wolfram Alpha for this kind of operation.
If someone can find quickly how many such primes there are, let's say, up to $100,000,000$, I will appreciate the help.
Select[Range[1,1000], PrimeQ[#]&& PrimeQ[(3*#)^2+#^2+3^2]&& PrimeQ[(3*#)^2-#^2-3^2]&]
and checks numbers from 1 up to 1000 to see which of those qualify. If you change that range then you can check other numbers. I don't know how large a range your WolframAlpha will accept. $\endgroup$ – Bill Aug 18 '18 at 3:38