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 April 3rd, 2019, 09:56 AM #11 Senior Member   Joined: Mar 2019 From: iran Posts: 312 Thanks: 13 for n=100000 p=317 and q=99991 when did we calculate it? April 3rd, 2019, 10:02 AM   #12
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Quote:
 Originally Posted by youngmath for n=100000 p=317 and q=99991 when did we calculate it?
How did "we" get enlisted for this project? It's five lines of Python.

Code:
Primes = [101, 103, etc.]  # You fill in the primes you care about.

product = 1
for prime in Primes :
product *= ((prime - 1)/prime)
print(str(product))
You initialize a list called Primes with the list of primes, which you can look up or calculate.

ps -- This is Python3, which defines '/' as real number division.

Last edited by Maschke; April 3rd, 2019 at 10:13 AM. April 11th, 2019, 05:52 AM #13 Senior Member   Joined: Mar 2019 From: iran Posts: 312 Thanks: 13 proof 1/2 × 2/3 × 4/5 × ... × (p-1)/p = Π (p-1)/p = Π 1-(1/p) = Π 1-p^(-1) = 1/(Π 1/(1-p^(-1))) = 1/zeta(1) = 1/( 1+1/2+1/3+...+1/p) = 1/ln(p) q=p^2 1/2 × 2/3 × 4/5 × ... × (q-1)/q = 1/ln(q) => (p-1)/p × ... × (q-1)/q = 1/ln(q) / 1/ln(p) = 1/ln(p^2) / 1/ln(p) = 1/2 Tags counting, function, prime, result Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post numberguru1 Number Theory 3 November 6th, 2015 01:21 PM Jonas Castillo T Number Theory 6 May 9th, 2015 06:26 PM jim198810 Number Theory 6 March 26th, 2015 07:31 PM fafa Number Theory 24 June 22nd, 2013 12:55 AM guynamedluis Number Theory 2 April 21st, 2012 12:48 PM

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