A challenge by John Carlos Baez

See The Riemann Hypothesis Says 5040 is the Last and this challenge posted on twitter. Given the prime number factorization of a natural number n, this haskell program calculates the value of

sigma n / (n * log (log n))

We can use it to find numbers for which this value approaches exp gamma ~ 1.7810724. With the first 1 million primes and suitable exponents we get to 1.7810465:

exponents :: [Integer]
exponents = [24,14,12,10,10,9,9,9,9,8,8,8,7,7,7,6,6,6,6,6,6,5,5,5,5,5,5,5,5,5,
  4,4,4,4,4,4,4,4,4,4,4,4] ++ replicate 45 3 ++ replicate 500 2 ++ repeat 1

Revisiting after one week

• I found an interesting paper of 2006 by Keith Briggs, going much deeper into this subject.
• I now realize we can get better efficiency if we handle those big products with a "divide and conquer" approach.