Prime Numbers - A different View
The 3 bands above represent binary integers. The first bit of each value is at the top of the ribbon. As the integers progress in value the higher bits are drawn in under the first bit. You can make your own counting machine by counting the bits on and off. The first bit is always on then off. The 2nd bit remains on for two turns then off for two turns. The 3rd bit remains on for 4 turns then off for four turns. The 4th bit remains on for 8 turns then off for 8 turns. Each successive bit always has an on off count that is twice as much as the previous bit. To make it all work always begin the next greater binary bit in the progression with it’s bit counter set to “on” every time the entire stack of bits is all zero.
The integer picture looks like a pristine mountain range that never deviates from it’s perfect pattern. As you know from the above description it is easy to predict the next value no matter where you are in the range of integer values.
Prime numbers are only divisible by themselves and by the number one.
The next three bands represent prime numbers. Again the first bit of each value is at the top of the ribbon. The higher bits are drawn underneath the first bit. The chaos of the prime numbers runs rampant in the first 8 bits. The only thing that remains constant is the 1st bit or the zero bit, it is always on. If the 1st bit were off then the number represented would be divisible by two. The counting machine doesn’t work with prime numbers, the on then off bit count that was so precise above just doesn’t hold water with primes.
The prime picture is always changing, the bit progression isn’t predictable. The only thing that remains constant is the change. You can almost guarantee that the bit progression will be different as you progress upward through the values of the prime numbers.
The music on my "Prime Numbers in d Minor" CD represents the constant changing of the 2nd through the 8th bits of each prime number value. Each bit was monitored as the computer progressed through the primes. While the bit was off no note was played. When an “on” bit occurred after an off bit state a note was played, off, off, off, play, on, on, on, off, off, off, play, on, on, etc, prime numbers in D minor.
© 2007 Brian L Hughes