Hello folks. Newbie here. I hope this is the right place to post my question.
I'm trying to do a calculation and find it's beyond me. Here's the challenge.
Let S be the set of all primes up to P.
Let P! be the product of the primes in S.
For incrementally increasing values of P I want to calculate the square root of P! and estimate the quantity of primes between P and sqrtP! Then I want to add the reciprocals of those primes. Call this final result Rs (sum of reciprocals)
An exact figure is not required. I want to figure out where Rs is going as P increases.
Example. Where P = 7
P! = 210
Sqrt P! = 14-ish
Rs = 1/11 + 1/13
The range P to sqrtP! increases rapidly, and the only way to check how many primes there are in this range seems to be to look it up. But maybe there's a rough and ready method that would at least show the trend for Rs.
Can anyone help with this? If the question is not clear then my apologies.
I should add that I am not a mathematician so please keep it simple.