A vision of primes
- Hello all,
That last discussion got me to thinking about something I use as a
visualization to understand primes and their distribution. I'd like
to share it with you and get your thoughts.
I have this vision in my head that I'd love to see in real life
sometime. Picture all the numbers through infinity laid out in a
straight line. Then picture a wave that starts at the number two and
goes up and down throughout infinity only touching the line on the
multiples of two. The same thing happens with the numbers three,
five, seven, and so on. Each one starts only when there isn't a wave
already crossing it. It helps me to see how much or how little a
number affects where primes are.
Can you picture where all the lines intersect? The more lines the
more likely that nearby numbers will be prime.
Can you see times when none of the lines come together but seem to
just miss? One after another on the number line they just seem to
block everything out. Those areas are the prime gaps.
As you get larger and larger numbers the waves get larger and
larger. It helps show how little they affect the number line, but
every once in a while, they meet up with a single other line. Those
places are the prime multiples. On this picture there might be a lot
of them since two and three are included.
But I think you get the idea.
Anyway, that's what I have stuck in my head at times to help me
understand primes. If it helps you, Great! If not, I'm sorry to
have to taken your time.
Enjoy your day,