# Product of all primes less then x

How to prove that $\prod_{p\leqslant{x}}p\leqslant4^{x-1},\ \forall x\geqslant2$,
where product is taken over all prime numbers $p\leqslant{x}$

-
this MO link could help, –  Raymond Manzoni Aug 10 '12 at 18:46