This puzzle seems to be another way of expressing the classic Sieve of Eratosthenes algorithm.

Basically, all the prisoners in prime numbered cells can escape plus the prisoner in cell 1 (which is not considered prime).

That makes 25 + 1 cells that are unlocked after all the officers have completed their rounds. Therefore 26 prisoners escape!

## 26 Prisoners

This puzzle seems to be another way of expressing the classic Sieve of Eratosthenes algorithm.

Basically, all the prisoners in prime numbered cells can escape plus the prisoner in cell 1 (which is not considered prime).

That makes 25 + 1 cells that are unlocked after all the officers have completed their rounds. Therefore 26 prisoners escape!