The sieve in which Eratosthenes separates the prime numbers is infinitely time-consuming. But it does have the slow excitement of hunting an increasingly rare species.

He writes out an open-ended sequence of odd numbers, then crosses out every third number after 3, every fifth after 5, every seventh after 7 and so on. Any number which does not eventually get crossed out is by definition prime, however long it may take to reach it.

The sieve in which Eratosthenes separates the prime numbers is infinitely time-consuming. But it does have the slow excitement of hunting an increasingly rare species.

He writes out an open-ended sequence of odd numbers, then crosses out every third number after 3, every fifth after 5, every seventh after 7 and so on. Any number which does not eventually get crossed out is by definition prime, however long it may take to reach it.

**The sieve of Eratosthenes**

The sieve in which Eratosthenes separates the prime numbers is infinitely time-consuming. But it does have the slow excitement of hunting an increasingly rare species.

He writes out an open-ended sequence of odd numbers, then crosses out every third number after 3, every fifth after 5, every seventh after 7 and so on. Any number which does not eventually get crossed out is by definition prime, however long it may take to reach it.