'Prime silence' - Composite numbers divisors music

Last modified: 
24/11/2016
  • Opus 1 (C major):
  • Opus 2 (whole-tone scale on C): Note that all composite numbers and their divisors (and thus all primes) can be found using the following algorithm:
    • On the equation y=1/2x, every composite number &/or divisor can be found by evaluating y at x=4, and subsequently by evaluating x in steps of 2 (thus at 6, 8, 10,...).
    • On the equation y=1/3x, every composite number &/or divisor can be found by evaluating y at x=6, and subsequently by evaluating x in steps of 3 (thus at 9, 12, 15,...).
    • On the equation y=1/4x, every composite number &/or divisor can be found by evaluating y at x=8, and subsequently by evaluating x in steps of 4 (thus at 12, 16, 20,...).
    • On the equation y=1/...x, every composite number &/or divisor can be found by evaluating y at x=8, and subsequently by evaluating x in steps of ...).
    • ...
    To retrieve all composite numbers and their divisors up the first N natural numbers, one will need (N/2)-1 such equations.
    • E.g., if one wishes to retrieve all composite numbers and their divisors, for the first 100 natural numbers; one will need 49 such equations (thus from y=1/2x, y=1/3x, y=1/4x to ... y=1/48x, y=1/49x, y=1/50x).

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