Is the product for any two prime numbers always odd?

NO!!!

e.g.

'2' & '3' are prime numbers.

There product is 2 x 3 = 6 (Which is even) .

However, all other prime numbers are 'odd'.

Their products are always ODD.

Remember

Even X Even = Even

Even X odd = Even

Odd x Even = Even

Odd X Odd = Odd.