On Jun 18, 4:00 pm, Transfer Principle <david.l.wal...@lausd.net> wrote: > On Jun 18, 11:02 am, Archimedes Plutonium > > <plutonium.archime...@gmail.com> wrote: > > So, does there exist a number that is between 10^603 and 10^604 that > > is a [power] of 120, that is 120^n [...] > > No, no such number exists. The powers of closest to this range are: > > 120^290 = 9.174055302...*10^602 > 120^291 = 1.100886636...*10^605 > > As 291 is a multiple of three, 120^291 is a perfect cube -- its > cube root would be 120^97.
Thanks Transfer, I had some inkling that the gap was going to be larger than 10^603 by loosening the reins over floor pi but did not expect it to go out to 10^605. If it is not too difficult, can you compute the perfect cube 120^n immediately below 120^291? Maybe it is 10^600???
If I have to accept 120^291, that leaves me a problem of reconciling pi for the sphere pseudosphere area. They have to be equal in area at infinity. So if infinity starts at 120^291, I would be required to use pi at 10^-605