Mersenne prime
Noun
Meaning
Mersenne prime (plural Mersenne primes)
(number theory) A prime number which is one less than a power of two (i.e., is expressible in the form
2
n
−
1
{\displaystyle 2^{n}-1}
; for example,
31
=
2
5
−
1
{\displaystyle 31=2^{5}-1}
).
Coordinate terms: Fermat prime, Sophie Germain prime
Related terms
Examples
Although it is chronologically the 47th Mersenne prime to be discovered, it is smaller than the largest known at the time, which was the 45th to be discovered.
Euclid also proved a formation rule (IX.36) whereby is an even perfect number whenever is what is now called a Mersenne prime —a prime of the form for prime Much later, Euler proved that all even perfect numbers are of this form.
For example, the 29th Mersenne prime was discovered after the 30th and the 31st.
This was the eighth Mersenne prime discovered at UCLA. citation On April 12, 2009, a GIMPS server log reported that a 47th Mersenne prime had possibly been found.
In modern times, the largest known prime has almost always been a Mersenne prime.
In September 2008, mathematicians at UCLA participating in GIMPS won part of a $100,000 prize from the Electronic Frontier Foundation for their discovery of a very nearly 13-million-digit Mersenne prime.