You're missing the point. Asymptotically, we have much better bound than 1.25506 -- the asymptotic bound is indeed 1+e for any e > 0, as the prime number theore

You're missing the point. Asymptotically, we have much better bound than 1.25506 -- the asymptotic bound is indeed 1+e for any e > 0, as the prime number theorem explicitly says that lim pi(n)/(n/log n)) = 1. The constant 1.25506... = 30 * log(113)/113 is only relevant because that's the the smallest global bound, which is there to take care of n = 113. If you rewrite it to log_2, you get the 1.442... constant, which throws your calculations off by "almost 50%" I mentioned in my comment above. And yeah, it doesn't change anything in the qualititative analysis of storage needs, but that's not my point -- my point is that in math, you should avoid saying things that are explicitly wrong, unless there are very good reasons to do so.