HAYCORN — 6 April 2015

# Old Code & Large Numbers

Found an old passive aggressive (or maybe just aggressive) letter of mine that was published in an Australian science magazine for teens called *Double Helix*.

Horrible photo. It includes code, in BASIC. Numbered lines. There is a “clear screen” command though I seem to have avoided `GOTO`

.

Not really related, but while looking through Wikipedia for more information on this problem (it’s an an example of a Tag System), I came across some fascinating examples of conjectures that have extremely large (numeric) counter-examples. (i.e. conjectures resistant to computer-derived counter-examples, and common sense.)

They are:

- Pólya conjecture - initial counterexample was 1.845 × 10
^{361}, though now reduced to 906,150,257. - Mertens conjecture - upper bound is
*e*^{1.59×1040}. - Skewes’ number - somewhere around
*e*^{727.95133}.

Scott Aaronson has an intriguing blog post on the biggest number you can write down in 15 seconds using standard math notation.

See also Graham’s number.