Someone on this list asked a question about a theorem that was proven
by Paul Erdos and Mark Kac. The information was in the latest issue of
Science. The theorem is: "...a graph of the number of prime factors of
very large numbers forms a bell curve ..." The statement is incomplete
because it does not say what is plotted along the abscissa. I can only
give an educated guess. I think it is a plot of the number of times a
given prime number appears in the prime-factor decomposition of a natural
number versus the prime number itself. For example, the number 120 has
the prime 2 appears three times, the prime 3 appears once and the prime
5 appears once. So, if my guess is right, very large numbers will have
a prime factor that will appear more than any other and then both smaller
prime factors and larger prime factors will occur with less frequency,
giving the bell-shaped curve.