Property of Mersenne primes
Number Theory
Level
3
What is the digit, in binary , of any Mersenne prime that has at least that many digits in binary?
0
Other!
2
4
5
1
3
6
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
A Mersenne prime is a prime number that can be expressed by the formula 2 n − 1 = x .
In binary, each numerical place can be expressed as 2 n in decimal
Hence, when 2 n − 1 in decimal is represented in binary, it will show a string of 1s all the way down. Hence the answer is 1.