Editing Mersenne prime (section)

==Mersenne numbers in nature and elsewhere==
In the mathematical problem [[Tower of Hanoi]], solving a puzzle with an {{math|''n''}}-disc tower requires {{math|''M<sub>n</sub>''}} steps, assuming no mistakes are made.<ref>{{cite book|last=Petković|first=Miodrag|title=Famous Puzzles of Great Mathematicians|year=2009|publisher=AMS Bookstore|isbn=978-0-8218-4814-2|pages=197}}</ref> The number of rice grains on the whole chessboard in the [[wheat and chessboard problem]] is {{math|''M<sub>64</sub>''}}.<ref>{{Cite web |last=Weisstein |first=Eric W. |title=Wheat and Chessboard Problem |url=https://mathworld.wolfram.com/ |access-date=2023-02-11 |website=Mathworld. Wolfram |language=en}}</ref>

The [[asteroid]] with [[minor planet]] number 8191 is named [[8191 Mersenne]] after Marin Mersenne, because 8191 is a Mersenne prime.<ref>{{cite web|author=Alan Chamberlin |url=http://ssd.jpl.nasa.gov/sbdb.cgi?sstr=8191+Mersenne |title=JPL Small-Body Database Browser |publisher=Ssd.jpl.nasa.gov |access-date=2011-05-21}}</ref>

In [[geometry]], an integer [[right triangle]] that is [[Pythagorean triple|primitive]] and has its even leg a power of 2 (&nbsp;{{math|&ge; 4}}&nbsp;) generates a unique right triangle such that its [[inradius]] is always a Mersenne number. For example, if the even leg is {{math|2<sup>''n''&nbsp;+&nbsp;1</sup>}} then because it is primitive it constrains the odd leg to be {{math|4<sup>''n''</sup>&nbsp;−&nbsp;1}}, the [[hypotenuse]] to be {{math|4<sup>''n''</sup>&nbsp;+&nbsp;1}} and its inradius to be {{math|2<sup>''n''</sup>&nbsp;−&nbsp;1}}.<ref>{{cite web |url=http://oeis.org/A016131 |title=OEIS A016131 |publisher=The On-Line Encyclopedia of Integer Sequences}}</ref>