[Physicists] are planning soon to start sending petabytes (10^15)
over the Internet. 10^15 is getting interesting close to the size of
Rubik's cube (never mind that I thought that the proper term for
10^15 bytes was terabytes.)

I thought it was

kilo	10^3
mega	10^6
giga	10^9
tera	10^12
peta	10^15
exa	10^18

except, of course, that as applied to quantities that tend to come in
powers of two, like bytes, they normally refer to 2^10, 2^20, 2^30,
2^40, 2^50, and 2^60 instead. (This is a common problem when buying
disks: manufacturers like to quote capacities in terms of powers of
ten, because it makes their disks seem larger than they really are. A
"2.1G" disk, for example, typically has a capacity of about 2.1e9
bytes...which is really only about 1.956Gb. The error can be roughly
estimated as 2.5% per power of 10^3: 2.5% for K, 5% for M, 7.5% for G,
etc. Semiconductor memory manufacturers generally get this right,
probably because doing other than powers of two would be hard for them.)

It also means that a certain well-known manufacturer of data drives for
8mm videotape is being extremely arrogant with their choice of name. :-)

As for the 10^18 bytes of storage estimated (probably only about half
that, if we consider that we really need only 5*.9e18 bits, less if we
resort to some of the clever coding tricks recently mentioned)...that's
about a gig of storage each across a million machines. The net's not
quite to the point where it can be done distributed.

Yet. :-)

Incidentally, someone mentioned that you need only store two bits, or
even only one if you don't use H turns, per position, because you don't
need to know more than how to get closer to Start...and then said that
it would be nice to have the full depth available nevertheless. If you
have this enormous database of .9e18 positions available in the compact
form, all that's needed to get the full depth for a position is to take
the short walk through the tree back to Start.

Also note that the Cube database storage size requires the highest
prefix we have. Time to get SI to think up some more, I guess :-)

der Mouse

mouse@collatz.mcrcim.mcgill.edu