Let n be some arbitrarily huge number; call each prime between 1 and n a 'GIRL'; call each even semiprime between 1 and n a 'BOY'.
Prove that there are two GIRLs for every BOY.
(An even semiprime is a composite number one of whose two prime factors is 2.)
BOYs can be restated as the number of primes between 1 and n/2
Then two GIRLs for every BOY implies there are the same number of primes between 1 and n/2 as between n/2 and n.
This doesn't seem possible as the primes get more sparse. There are fewer primes from n/2 to n. So it would not seem to be true.
The prime number counting function is roughly the Logarithmic integral function. If the shape of this function becomes basically a straight line this would imply the proof. Well the natural logarithm function does flatten out as n increases. So maybe it is true.
Posted by Jer
on 2011-09-27 11:13:57