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 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.

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