Dissonance in b-Smooth
Inspired by Adi Shamir's TWINKLE optical device for finding smooth numbers, which works at GHz, I wrote an audio device for finding smooth numbers, which works at low kHz. In absence of a good, screeching acronym, I'd call it Dysphony in b-Smooth.
The idea is to convert the smaller prime factors of numbers into sound. The code does this by keeping
ncounters, each of which is increased modulo its individual prime. At the moment, these are the first 1000 primes. After every increment the counters that contain a zero are collected and a sine wave is constructed from the associated frequencies (
index*(2000/n) + 40Hz) at an amplitude proportional to the logarithm of the prime (so that the frequent divisors 2,3,5,etc have a low impact). Each sound lasts a small fraction of a second. If a loud noise is audible, it is the representation of a number with many different and/or larger prime factors.
The scientific value of this is approaching zero from the left, but it was a nice exercise to have the computer produce sound after my last attempts in 1987 on an Atari ST.
Thu, 08 Mar 2012
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