the caveat being that the complexity of computing the formula is at best on the order of preexisting techniques, so nifty deep math, but nothing new from a computational point of view (barring more insight happening)
I just looked at the article again (blog article, not maths), and I must admit the gcd in the equation does not make it seem so exciting. gcd seems algorithmically very close to other algorithms for computing primes.
On the other hand, playing around with it would probably be fun :-/