a cute result from number theory
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There is a cute result from number theory that states that for sufficiently large n the product of
the primes less than n is less than or equal to e**n and that as n grows, this becomes a tight
bound (that is, the ratio of the product of the primes to e**n gets close to 1 as n grows).
Computing a product of a large number of prime numbers can result in a very large number,
which can potentially cause problems with our computation. So we can convert the product of a set of
primes into a sum of the logarithms of the primes by applying logarithms to both parts of this
conjecture. In this case, the conjecture above reduces to the claim that the sum of the
logarithms of all the primes less than n is less than n, and that as n grows, the ratio of this sum
to n gets close to 1.
(Product => sum of logarithms)
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