Are there explanations why there should be about twice as much primes on the form $(2n-1)^2-2$ than on the form $(2n-1)^2+2$?
n f(n)-2 f(n)+2
10 6 4
100 33 17
1000 208 110
10000 1558 817
100000 12390 6440
1000000 102204 52980
Where f(n)=(2n-1)^2
Example:
for $10$ there are $6$ and $4$ primes of the kind for $1 \le n < 10$.
for $100$ there are $33$ and $17$ primes of the kind for $1 \le n < 100$.
(My test computations was not up to 10, 100 etc)