Leonard Euler discovered many years ago that

$\frac π 4 = \frac 3 4 \cdot \frac 5 4 \cdot \frac 7 8 \cdot \frac {11} {12} \cdot \frac {13} {12} \cdots$ 

where the numerators on the right-hand side are the *odd* prime numbers and each denominator (on both sides) is the multiple of 4 nearest to the corresponding numerator. Pretty fascinating if you ask me.