prime gaps 4*n+1 or 4*n+3

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Take the two prime gaps of $4*n+1$ and $4*n+3$ and the first ten million primes. Will we find that the number of gaps for each is about the same? One could see the possibilility of a prime gap race similar to that for primes of the form $4*n+1$ and $4*n+3$. Has anyone done this?