## April 2008 riddle

Let us divide the prime numbers into bins. Prime p will go into bin number floor(p/1000).

Let us pick a subset of the naturals by first selecting a set of bins, then taking all the naturals that have only primes inside the selected bins as their factors. (So, for example, to pick the number 3999991=1997*2003, we will need to first select at least both of bin number 1 [for 1997] and bin number 2 [for 2003]).

The harmonic series is the sum of 1/n over n=1,2,...

This series is known to diverge.

By selecting a set of bins, we are effectively picking a subset of the naturals. Let us calculate the partial harmonic series that is calculated solely over this (infinite) subset.

This month's question: what is the minimum number of bins that needs to be selected for the sub-series to diverge?

### List of solvers:

Hongcheng Zhu (1 April 13:11)
Rani Hod (2 April 01:18)
Omer Angel (2 April 02:03)
Ross Millikan (3 April 06:23)
Mark Tilford (5 April 02:48)
Itsik Horovitz (15 April 17:15)
Bojan Bašić (20 April 01:15)
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