/sci/ - Science & Math

[Anonymous No.5707920]

Could there be a pattern here? Check out how the period lengths graph: http://oeis.org/A002371/graph

And... how likely is the existence of a formula generating the primes?

[Anonymous No.5707928]

>The decimal expansion of 1/n is purely periodic if and only of n is prime.
But that's wrong. Consider 1/2 (which is not purely periodic, despite 2 being prime) and 1/9 (which is).

[Anonymous No.5707934]

>>5707920
The likelihood of formulas generating the primes is 100%. There are many of them and they're easy to deduce.

http://recursed.blQgspot.com/2013/01/no-formula-for-prime-numbers.html replace Q with o

[Anonymous No.5707960]

This graphs the period lengths of 1/(n-th prime). It reminds me of the patterns evident in Ulam spirals – you can see 5 or 6 distinct lines in the scatter plot. Is this significant or trivial?

>>5707928
You're right! I got this from a book called Recreational Mathematics (http://www.readbag.com/math-fau-yiu-recreationalmathematics2003))

>>5707934
How about a single formula generating all the primes successively?

[Anonymous No.5707974]

>>5707960
>How about a single formula generating all the primes successively?

Yes, routine. Any function you can program in a computer, you can hash out a formula for.

[Anonymous No.5707977]

>>5707960
>You're right! I got this from a book called Recreational Mathematics (http://www.readbag.com/math-fau-yiu-recreationalmathematics2003))
My guess (but keep in mind that it's only a guess) is that a fraction a/b is purely periodic if and only if b is not divisible by 2 or 5.

[tn No.5707997]

>>5707960
Looks a bit like the Euler totient graph. Not exactly, but somewhat.

I'm however assuming that it has a strong connection with the fact that we're in base 10, so whatever you do, if "10" or "2*5" don't appear clearly in your analysis, you've missed something.