Old Code & Large Numbers
6 April 2015
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
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.)
- Pólya conjecture - initial counterexample was 1.845 × 10361, though now reduced to 906,150,257.
- Mertens conjecture - upper bound is e1.59×1040.
- Skewes’ number - somewhere around e727.95133.
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.