prove that if p1, p2, ....... pn are distinct prime numbers with p1 = 2 and n > 1, then p1, p2,........pn +1 can be written in the form 4k + 3 for some integer k

Hint: I know that every odd integer can be written as 4k + 3 for an integer k

Try to write 5 as 4k+3, for some integer k....(Smirk)

And the first claim's false, too: $\displaystyle 2\cdot 3=6$ cannot be written as 4k+3 for no integer k.