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A lot of the pattern comes down to primes being relatively prime to smaller numbers, which means, for example, they're 1 modulo 2, 1 or 2 modulo 3, etc. You com
by jowiar 12y ago
A lot of the pattern comes down to primes being relatively prime to smaller numbers, which means, for example, they're 1 modulo 2, 1 or 2 modulo 3, etc. You combine these together and find that, for example, they're all (aside from 2 or 3) going to be 1 or 5 modulo 6. Which would mean that if you lined all the numbers up in rows of 6, all primes (aside from 2 or 3) would be in the first or fifth columns.
So properties can give them a "shape", but they won't identify them.
- headShrinker 12y agoI wrote a very simple tool to visualize primes in the manor you describe; shifting columns. [link redacted]
- jowiar 12y agoThat's pretty sweet!
- MrBra 12y agoNice! Great little tool :) Could you explain a bit better the coloring legend? Thanks!
- headShrinker 12y agoSure! You can type any number up to 10,000,000,000 and it will show up to 10,000 consecutive numbers. Color key: Prime or 1 = Purple Divisible by 2 = pink Divisible by 3 = green Divisible by 5 = blue Divisible by 7 = yellow Composite number = gray Clicking any color will other than prime will turn any numbers with that factor gray.
- MrBra 12y agoThanks. Is the choice of using different colors only up to 7 an arbitrary choice or is the result of some particular property/theory?
- headShrinker 12y agoGood question. The first of the odd primes up to 7 occur as the most frequent factors, other than 2. So 3,5,7 are most often reoccurring. Because of the patterns they illustrate especially when modulating the columns it seemed to make sense. While all of that is true, the original concept for the project was based off the Sieve of Eratosthenes. http://simple.wikipedia.org/wiki/Eratosthenes#Other_discoveries_and_inventions http://simple.wikipedia.org/wiki/Eratosthenes#Other_discover...
- MrBra 12y agoHehe I asked because time ago I implemented something similar (using console though) and by instinct I was doing the same, coloring numbers based on divisors to see patterns, and primes, but just when I wanted to get some conclusion out that, I had to stop and do something else, so it kinda remained in my brain as something I had to finish to consciously understand. Thanks for explaining then, so what we did is a Sieve of Eratosthenes... But I have to admit that I also coded it to see which particular patterns (if any) primes were drawing on screen.. :)
- deleted 12y ago[deleted]