TITLE: Parity of primes
QUESTION [6 upvotes]: While working on a completely different (combinatorial) problem, I ran a simple program to calculate the parity of the first ~50000 primes (number of 1s in their binary representation modulo 2). The following graph summarizes the result:

The number of primes having even parity seems to grow slower.

Is there a math explanation ?

I looked to the correspoding OEIS entry, but it doesn't provide any detail.

REPLY [7 votes]: It was shown (amongst other things) by Gel'fond that the asymptotic growth rates of the primes with even and odd parity base 2 expansions are the same:
Gelʹfond, A. O.
Sur les nombres qui ont des propriétés additives et multiplicatives données. (French)
Acta Arith. 13 1967/1968 259–265. 
A more recent paper on this is due to Mauduit and Rivat.