Find the smallest prime that is the fifth term of an increasing [arithmetic sequence](https://artofproblemsolving.com/wiki/index.php/Arithmetic_sequence), all four preceding terms also being [prime](https://artofproblemsolving.com/wiki/index.php/Prime_number).
Obviously, all of the terms must be [odd](https://artofproblemsolving.com/wiki/index.php/Odd). The common difference between the terms cannot be $2$ or $4$, since otherwise there would be a number in the sequence that is divisible by $3$. However, if the common difference is $6$, we find that $5,11,17,23$, and $29$ form an [arithmetic sequence](https://artofproblemsolving.com/wiki/index.php/Arithmetic_sequence). Thus, the answer is $029$.