# New Scientist Enigma 989 – Prime Progressions

*by Richard England*

#### From New Scientist #2144, 25th July 1998

Harry and Tom have been investigating sets of positive integers that form arithmetic progressions where all the members of the set are prime numbers.

When they looked for a set of five such prime numbers, Harry found the set whose final (largest) prime is the smallest possible for the final prime in such a set. Tom found the set whose final (largest) prime is the next smallest possible.

Exactly the same thing happened when they looked for a set of six such prime numbers, and again when they looked for a set of seven such prime numbers.

What were the smallest and the largest primes in each of the three sets that Tom was able to find?

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