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Surf City Semiprimes (Posted on 2011-09-27) Difficulty: 2 of 5

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.)

See The Solution Submitted by broll    
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I don't think it's true. Maybe I do. | Comment 2 of 4 |
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
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