
Number Theory Number Theory Math Forum 
 LinkBack  Thread Tools  Display Modes 
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 
Senior Member Joined: Aug 2012 Posts: 2,332 Thanks: 723  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)) 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 × ... × (p1)/p = Π (p1)/p = Π 1(1/p) = Π 1p^(1) = 1/(Π 1/(1p^(1))) = 1/zeta(1) = 1/( 1+1/2+1/3+...+1/p) = 1/ln(p) q=p^2 1/2 × 2/3 × 4/5 × ... × (q1)/q = 1/ln(q) => (p1)/p × ... × (q1)/q = 1/ln(q) / 1/ln(p) = 1/ln(p^2) / 1/ln(p) = 1/2 

Tags 
counting, function, prime, result 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Approximation for the Prime Counting Function  numberguru1  Number Theory  3  November 6th, 2015 01:21 PM 
A property of the prime counting function.  Jonas Castillo T  Number Theory  6  May 9th, 2015 06:26 PM 
An equation of prime counting function.  jim198810  Number Theory  6  March 26th, 2015 07:31 PM 
Question on prime counting function \pi  fafa  Number Theory  24  June 22nd, 2013 12:55 AM 
Lower Bound for the Prime Counting Function  guynamedluis  Number Theory  2  April 21st, 2012 12:48 PM 