Is this statement true or false ?

Number Theory Level 3

The product of consecutive primes from 2 to any prime plus 1 is a prime.

For example:

1) 2 + 1 = 3

2) 2 x 3 + 1 = 7

3) 2 x 3 x 5+1 = 31

4) 2 x 3 x 5 x 7 +1 = 211

. . and so on...