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.)
Is this supposed to be exact, or approximate?
It does not hold exactly for n = 6 (admittedly not a huge number), so I suspect that it does not hold exactly for all huge numbers.
For n = 6, there are 3 girls (2, 3 and 5) and 2 boys (4,6).
In fact, it obviously cannot be true whenever the number of GIRLs is odd, which I suspect is the case for approximately half of all arbitrarily huge n.
Menage a trois
