Primal Surge | Science News

Support Science Journalism

Science News is a nonprofit.

Support us by subscribing now.


Math Trek

Primal Surge

By
4:40pm, March 1, 2005

What do the following numbers have in common?

3, 7, 31, 127, 8191, 131071, 524287, 2147483647, 2305843009213693951, 618970019642690137449562111, 162259276829213363391578010288127, 170141183460469231731687303715884105727.

Each one is a prime number, evenly divisible only by itself and 1. Each one can also be written in the form a power of 2, less 1: 2p – 1, where p is itself a prime number.

In 1644, French monk and mathematician Marin Mersenne (1588–1648) stated that numbers of the form 2p – 1 are primes only when p has the following and no other values:

p = 2, 3, 5, 7, 13, 17, 19, 31, 67, 127, and 257.

Mersenne himself didn't actually test his assertion for any values greater than p = 19. In fact, it wasn't until 1750 that Leonhard Euler (1707–1783) verified that 231 – 1 (or 2147483

This article is only available to Science News subscribers. Already a subscriber? Log in now. Or subscribe today for full access.

Get Science News headlines by e-mail.

More from Science News

From the Nature Index Paid Content