Friday, April 28, 2017

[bvahtsov] Cunningham sculpture

Create a sculpture, probably something like a long wall, onto which the Cunningham project, maybe just base 2, is inscribed.  Leave blank spaces for unfactored cofactors.  New factors get inscribed over time: the sculpture changes.  Maybe ceremonies for new factors.

Probably separate removable panels to make easier inscribing new factors offsite and correcting errors.

What format should be inscribed?  Semi-compressed like in the Cunningham book, or full factorization to make it easily comprehensible to the general public?  Base 10 or binary?  Binary seems apt, especially for the base 2 table.  Many of the prime factors have pretty patterns when written in binary.  Previously, base 32.  Maybe barcode format (e.g., QR) for good error correction -- the sculpture serves as a (very) hard copy, more resistant to destruction than paper or electronic.    If preservation and longevity are goals, how should the sculpture be designed: what material, what styles and techniques of engraving?

QR codes can be constructed out of square tiles, and archaeology shows tiles can last a very long time.

Vaguely inspired by: Vietnam Memorial Wall, New England Holocaust Memorial (which consists of many numbers).

Previously, Mersenne.  Cunningham has an advantage over Mersenne in that Cunningham is self-certifying.  Anyone can verify that the list of factorizations (excluding blank spaces) is complete up to the maximum exponent; anyone can verify that the factorizations are correct.  In contrast, it is pretty difficult for someone to verify the primality of the large Mersenne primes, and it is very difficult for anyone to verify that a list is complete, that there are no skipped primes in the gaps.

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