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edited Apr 13, 2017 at 12:39

Python 2, 106 bytes

from fractions import*
n=input()
F=k=P=1
while n:b=P%k>0;n-=b;F*=1-Fraction(2*b,k*k+1);P*=k*k;k+=1
print F

The first and fourth lines hurt so much... it just turned out that using Fraction was better than multiplying separately and using gcd, even in Python 3.5+ where gcd resides in math.

Prime generation adapted from @xnor's answer here here, which uses Wilson's theorem.

Python 2, 106 bytes

from fractions import*
n=input()
F=k=P=1
while n:b=P%k>0;n-=b;F*=1-Fraction(2*b,k*k+1);P*=k*k;k+=1
print F

The first and fourth lines hurt so much... it just turned out that using Fraction was better than multiplying separately and using gcd, even in Python 3.5+ where gcd resides in math.

Prime generation adapted from @xnor's answer here, which uses Wilson's theorem.

Python 2, 106 bytes

from fractions import*
n=input()
F=k=P=1
while n:b=P%k>0;n-=b;F*=1-Fraction(2*b,k*k+1);P*=k*k;k+=1
print F

The first and fourth lines hurt so much... it just turned out that using Fraction was better than multiplying separately and using gcd, even in Python 3.5+ where gcd resides in math.

Prime generation adapted from @xnor's answer here, which uses Wilson's theorem.

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created Mar 23, 2016 at 16:18

Sp3000

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Python 2, 106 bytes

from fractions import*
n=input()
F=k=P=1
while n:b=P%k>0;n-=b;F*=1-Fraction(2*b,k*k+1);P*=k*k;k+=1
print F

The first and fourth lines hurt so much... it just turned out that using Fraction was better than multiplying separately and using gcd, even in Python 3.5+ where gcd resides in math.

Prime generation adapted from @xnor's answer here, which uses Wilson's theorem.