[SeqFan] <none>

[Jud McCranie]

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) |
+--------------------------------------------------------------------+