Problem:
Is the following number prime?
5529
Answer:
\begin{array}{l}
 
\begin{array}{l}
 \text{Test for primality}: \\
 \text{is }5529\text{ a }\text{prime number?} \\
\end{array}
 \\
\hline
 
\begin{array}{l}
 \text{Since }\sqrt{5529}\approx 74.3, \text{it }\text{is }\text{sufficient }\text{to }\text{test }\text{5529 }\text{for }\text{divisibility }\text{by }\text{primes }\text{less }\text{than }\text{or }\text{equal }\text{to }74: \\
 \text{Test }\text{primes }\text{up }\text{to }\text{74 }\text{for }\text{factors }\text{of }5529 \\
\end{array}
 \\
 
\begin{array}{l}
 \text{5529 }\text{is }\text{not }\text{divisible }\text{by }2 \text{since }\text{5529 }\text{is }\text{odd }\text{and }2 \text{is }\text{even}: \\
 \text{5529 }\text{is} \text{not }\text{divisible }\text{by} 2 \\
\end{array}
 \\
 
\begin{array}{l}
 \text{The }\text{sum }\text{of }\text{the }\text{digits }\text{of }\text{5529 }\text{is }5+5+2+9=21, \text{which }\text{is }\text{divisible }\text{by }3. \text{This }\text{means }\text{5529 }\text{is }\text{divisible }\text{by }3: \\
 \fbox{$
\begin{array}{ll}
 \text{Answer:} &  \\
 \text{} & 5529\text{ is }\text{not}\text{ a }\text{prime} \text{number} \\
\end{array}
$} \\
\end{array}
 \\
\end{array}

{'source': 'AMPS', 'file': 'amps/mathematica/number_theory/is_prime_w_steps/2192.txt'}