Prime Number Theorem

From: Barnaby Finch (barnabyfinch_at_verizon.net)
Date: 08/30/04 

Date: Mon, 30 Aug 2004 18:29:12 GMT

The Prime Number Theorem article in Mathworld.com states that the upper
bound for the first equivalence of Pi(x) (the prime counting function) and
Li(x) (the logarithmic integral - the "European" definition) is less than
10^371. Has any further progress been made on this upper bound?

Could someone explain why the finding the exact value of the first crossing
is so computationally intractable in an era when computers are finding the
41st Mersenne prime? Would one have to have the complete list of primes less
than the upper bound in order to solve this problem?

Barnaby

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