Design a digital circuit for generating the "next" prime number

The objective is to produce the smallest prime number greater than the value

presented on the inputs. For example, if the value on the inputs is $3$ decimal $(011$

binary$)$ then the output should be the smallest prime number greater than $3,$ which is

$5$ decimal $(101$ binary$).$

Derive Boolean expressions for the output functions of a circuit designed to output

the next prime number working on three bit numbers. For example: if inputs are $011$

the outputs should be $101.$ The circuit should output $0(000$ binary$)$ if the next prime

number can not be represented on three bits.

Please name the inputs as $x,y,z($where $x$ is the most significant bit of the number on

the inputs$)$ and the outputs as $a,b,c($where a is the most significant bit of the

number on the outputs$).$

Type your answer in the text box below.

Show:

$($i$)$ the truth tables, one truth table for each output function, and

$($ii$)$ the simplified expressions $($only$),$ for each output function $($you do not have to

show the simplifications steps$).$

$($Note: when typing Boolean expressions use a single quote character to indicate the

complement, for example, for the minterm $mO$ you would type: $\{$:$x^{\text{'}}{y}^{\text{'}}z)$