$ \frac{\pi}{4} = \frac{3}{4} \times \frac{5}{4} \times \frac{7}{8} \times \frac{11}{12} \times \cdots$ (just primes in the numerator) How to prove the following equality?
$$ \frac{\pi}{4} = \frac{3}{4} \times \frac{5}{4} \times \frac{7}{8} \times \frac{11}{12} \times \frac{13}{12} \times \frac{17}{16} \times \frac{19}{20} \times \frac{23}{24} \times \frac{29}{28} \times \frac{31}{32} \times \cdots$$
I've seen this formula on Wikipedia.
The numerators are the odd primes; each denominator is the multiple of four nearest to the numerator.
Thanks.

Let $L(s,\chi)$ be the $L$ function for the non principal modulo $4$ Dirichlet 
character
$$\frac{\pi}{4}=L(1,\chi)=\prod_{p}\frac{p}{p-\chi(p)}=\prod_{p\equiv 1 \text{mod 4}}\frac{p}{p-1}\prod_{p\equiv 3 \text{mod 4}}\frac{p}{p+1}$$
