[SeqFan] <none>
Jud McCranie
jud.mccranie at mindspring.com
Mon Jun 15 18:30:21 CEST 1998
At 10:58 AM 6/15/98 -0400, David Wilson wrote:
...
>Thus is looks as if pi(n) is growing much more slowly than phi(n) relative=
n,
as one
>would expect.=A0 I highly suspect that pi(n) < phi(n) (the real pi(n)) for
sufficient n
>could be proved, ...
The best lower bound I know for phi(n) is sqrt(n/2) <=3D phi(n). And this=
is
insufficient to prove pi(n) < phi(n). =20
+--------------------------------------------------------------------+
| Jud McCranie jud.mccranie at mindspring.com or @camcat.com |
| |
| "We should regard the digital computer system as an instrument to |
| assist the number theorist in investigating the properties of his |
| universe - the natural numbers." D. H. Lehmer, 1974 (paraphrased) |
+--------------------------------------------------------------------+
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