Question

Find a positive integer n for${\mathbf{Q}}_{\mathbf{n}}\mathbf{=}\mathbf{n}\mathbf{!}\mathbf{+}\mathbf{1}$ is not prime

Short answer

Answer may vary

For example n = 4

Step-by-step solution

Step 1:

${\mathbf{Q}}_{\mathbf{n}}\mathbf{=}\mathbf{n}\mathbf{!}\mathbf{+}\mathbf{1}$

The smallest n - values for which ${\mathbf{Q}}_{\mathbf{n}}$ is not prime is n = 4 (since ${\mathbf{Q}}_{\mathbf{1}}$ = 2 and ${\mathbf{Q}}_{\mathbf{2}}\mathbf{=}\mathbf{3}$and ${\mathbf{Q}}_{\mathbf{3}}\mathbf{=}\mathbf{7}$ is prime).

${\mathbf{Q}}_{\mathbf{4}}\mathbf{=}\mathbf{4}\mathbf{!}\mathbf{+}\mathbf{1}\mathbf{=}\mathbf{24}\mathbf{+}\mathbf{1}\mathbf{=}\mathbf{25}$

Since 25 = 5.5 is not prime.