Verify the following statement:
$$\text { ' } 2 ^ { p } - 1 \text { is a prime number for all prime numbers } p \text { less than } 11 \text { '. }$$
Calculate \(23 \times 89\), and hence disprove this statement:
$$\text { ' } 2 ^ { p } - 1 \text { is a prime number for all prime numbers } p ^ { \prime } \text {. }$$