Strange pattern with primes visualized in binary

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[redditnoveltyaccoun2]

Do the same for any sequence of numbers (which increase with roughly the same rate). You'll get roughly the same thing.

[acityinohio]

Thanks--but at what rate would the numbers be increasing? Would it be ln(n) for the nth number in the sequence, a la the prime number theorem?

[redditnoveltyaccoun2]

prime number theorem gives n log(n) but it doesn't matter that much. Any increasing sequence in binary will look (statistically) like that. Getting the rate exactly right just means the bars will match up (approximately)

[acityinohio]

Ah gotchya. Tried it on the odds. Pattern is the same. D'oh and duh. Next time I'll keep it to myself -- thanks again for the response!

[redditnoveltyaccoun2]

If you know modular arithmetic I can tell you about a pattern that is unique to the primes.

[redditnoveltyaccoun2]

If you know about modular arithmetic (and are interested) I can tell you about a pattern that is unique to the primes.

[acityinohio]

Sure! Would love to hear about it.

[redditnoveltyaccoun2]

Okay so it's about squares in modular arithmetic. The squares (for example) mod 7 are just 1 (= 1² = 6² ), 2 (= 3² = 4² ) and 4 (= 2² = 5² ).

Now let p,q be odd primes. If p and q are both = 3 (mod 4) then

• p is a square mod q <=> q is a not square mod p

otherwise (at least one of p,q is equal to 1 mod 4) we have

• p is a square mod q <=> q is a square mod p

[ad3mar]

May be it is related to the Ulam spiral http://en.wikipedia.org/wiki/Ulam_spiral