Answer:
25
Step-by-step explanation:
A prime number is a positive integer greater than 1 that cannot be evenly divided by any other numbers except for 1 and itself.
The first few prime numbers are:
- 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, ...
All prime numbers are odd except for 2. Therefore, since p and p + 1 are consecutive integers and both are prime, p must be 2:
[tex]\large\boxed{\boxed{p=2}}[/tex]
If p is 2, then p + 1 must be 3:
[tex]\large\boxed{\boxed{p+1=3}}[/tex]
A composite whole number is a positive integer greater than 1 that has at least one positive factor other than 1 and itself, so it cannot be a prime number.
If the composite whole number is not divisible by p, then it cannot be an even number, as every even number is divisible by 2.
If the composite whole number is not divisible by p + 1, then it cannot be a multiple of 3.
Therefore, the numbers that the composite whole number cannot be are:
Prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, ...
Even numbers: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, ...
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, ...
Therefore, the smallest composite whole number that is not a prime number and is not divisible by 2 or 3 is:
[tex]\huge\boxed{\boxed{25}}[/tex]
