I came here to write that :-)
Actually there are π(N) ~ N / ln(N) primes less than N per the Prime Number Theorem, so π(2 ^ 160) ~ 2 ^ 153.2 - this only drops 7 bits. So that does increase the odds of collision but much less than what I expected!
alt Hacker News
Actually there are π(N) ~ N / ln(N) primes less than N per the Prime Number Theorem, so π(2 ^ 160) ~ 2 ^ 153.2 - this only drops 7 bits. So that does increase the odds of collision but much less than what I expected!