Mersenne primes have the form 2^{p} − 1 where *p* is a prime. The graph below plots the trend in the size of these numbers based on the ~~50~~ 51 Mersenne primes currently known.

The vertical axis plots the exponents *p*, which are essentially the logs base 2 of the Mersenne primes. The scale is logarithmic, so this plot suggests that the Mersenne primes grow approximately linearly on a double logarithmic scale.

**Update**: A new Mersenne prime was announced December 21, 2018. The graph was updated to include this new data point.

## More on Mersenne primes