Number Theory: Mersenne Primes
Getting Started
While any command in the package can be referred to using the long form, for example, NumberTheory:-IsMersenne, it is often easier to load the package and then use the short form command names.
restart;
with(NumberTheory):
Examples
Mersenne Primes are prime numbers that are one less than a power of 2. These are of the form: Mn=2n−1, where n is a positive integer. The IthMersenne command returns the exponent for the Ith Mersenne prime number:
IthMersenne⁡4
7
27−1
127
The top level isprime command determines if a given number is prime:
isprime⁡27−1
true
The IsMersenne command checks if a positive integer, n, is a Mersenne exponent, where 2^n-1 is a Mersenne prime:
22−1
3
IsMersenne⁡2
211−1
2047
IsMersenne⁡11
false
ifactor⁡211−1
23⁢89
There are 52 known Mersenne Primes.
interface⁡rtablesize=55:
DataSeries⁡seq⁡IthMersenne⁡i,i=1..52,labels=seq⁡1..52
Warning, the rankings of the 49th to 52nd Mersenne primes are provisional, since it has not been determined that there do not exist more Mersenne primes between 48th and 52nd
122335475136177198319611089111071212713521146071512791622031722811832171942532044232196892299412311213241993725217012623209274449728862432911050330132049312160913275683933859433341257787351398269362976221373021377386972593391346691740209960114124036583422596495143304024574432582657453715666746426438014743112609485788516149742072815077232917518258993352136279841
See Also
NumberTheory
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