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April 3rd, 2019, 09:56 AM  #11 
Member Joined: Mar 2019 From: iran Posts: 64 Thanks: 6 
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: 2,265 Thanks: 690  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 
Member Joined: Mar 2019 From: iran Posts: 64 Thanks: 6 
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 

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counting, function, prime, result 
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