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Jan 1, 2012 at 22:26 comment added Will Jagy Dear David, Hardy and Wright really is very good, and the one math book I noticed on the bookshelves of computer science professors when I was a student. The topic of explicit upper bounds (improving on lim sup results) is more recent and often comes with the names Jean-Louis Nicolas (Lyon) and Guy Robin (Limoges), see mathoverflow.net/questions/43103/… and mathoverflow.net/questions/84266/on-robins-criterion-for-rh/… . A typical result is something <= something * (asymptotic series in 1/loglogn)
Jan 1, 2012 at 18:51 history edited David Spivak CC BY-SA 3.0
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Jan 1, 2012 at 6:20 comment added Anthony Quas $PF(N)$ is certainly not $\approx \log\log N$. $PF(N)$ varies a lot according to $N$ (if $N$ is large and prime, $PF(N)=1$, while if $N$ is of the form $2^k$, then $PF(N)=\log_2 N$). The statements people have been talking about are about the average value of $PF(N)$ (i.e. $E(N)$)
Jan 1, 2012 at 0:12 history answered David Spivak CC BY-SA 3.0