PRIME NUMBERS

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PRIME NUMBERS 01/07/16 (Thu) 00:33:52 No.3717

for prime number-fags: I'm trying, just for fun, to figure out how to prove the following property of prime numbers: given three consecutive prime numbers a, b, c, the bigger they are the more their sum a\b + b\c + c\a tends to be 6. any suggestion?

01/07/16 (Thu) 01:59:09 No.3718

>given three consecutive prime numbers a, b, c, the bigger they are the more their sum a\b + b\c + c\a tends to be 6

wait a sec

doesn't that sum tend to be 3, since the prime number density falls roughly as 1/log(n) so they're getting relatively closer and closer, making all those ratios go to 1?

01/07/16 (Thu) 02:39:12 No.3720

>>3718

Yeah, that nigger op dun goofed.

If you take into account that any nth prime is smaller than 2n and a,b,c consecutive primes.

a/b < 2n/2(n+1)

a/b + b/c + c/a < n/(n+1) + (n+1)/(n+2) + (n+2)/n

And the limit of that last thing in positive infinity is 3 so…

I won't give up the last part because op should get some brains and if he wants to brag about solving math problems he could at least expend the effort to do those problems.