Mersenne prime
Number theory
A prime of the form 2ⁿ − 1 for some integer n.
What is usually left out
If 2ⁿ − 1 is prime then n must itself be prime, but the converse fails — 2¹¹ − 1 = 2047 = 23 × 89. Mersenne primes dominate the record books because the Lucas–Lehmer test decides their primality far faster than general methods, not because they are unusually common. Whether infinitely many exist is open.
Related terms
In the atlas
- Mersenne prime — Number theory, open