Colorado Smith’s success with the skull of Duggery had left his confidence at an all-time high. He was ready to brave the defences of the city of Pigtrotl, legendary home of the Oinca kings. The streets of Pigtrotl were rumoured to be studded with diamonds the size of ostrich eggs.
But now, just outside the city, as Smith and Brunnhilde swung from his rawhide whip a thousand feet above a lake infested with giant alligators, Brunnhilde had the sudden worry that the quest was one reckless throw of the dice too many.
Smith brushed aside her doubts. “My pockets are filled with hundreds of Oinca amulets,” he said. “All I have to do is drop the triply sacred number of amulets into the lake. Then the alligators will magically vanish and the treasure will be ours!”
“Good,” said Brunnhilde. “What is the triply sacred number?”
“I am about to work it out. Numbers are sacred to the Oinca if they give rise to primes when 1 is added and subtracted.”
“Like 18?” asked Brunnhilde, anxiously eyeing the whip.
“That’s it, exactly, as both 17 and 19 are prime,” said Smith.
“And triply sacred?”
“The Oinca also revere the number five,” said Smith. “A sacred number that is also sacred on division by five is doubly sacred to them—and if a number is sacred after a further division by five, it is triply sacred. But Oinca counting stops at 3,125, so the triply sacred number can’t be any bigger than that.”
What is the triply sacred number?
Prospect invites you to solve the puzzle and send us the solution. Correct answers will be entered into a draw. Five winners will each receive one copy of the book Taming the Infinite: The Story of Mathematics by Ian Stewart (Quercus, £20). Send answers to email@example.com by 12th September. The winner will be announced in our October issue.