Mersenne Primes - Maple Help

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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

(1)
> 

27−1

127

(2)

The top level isprime command determines if a given number is prime:

> 

isprime⁡27−1

true

(3)

The IsMersenne command checks if a positive integer, n, is a Mersenne exponent, where 2^n-1 is a Mersenne prime:

> 

22−1

3

(4)
> 

IsMersenne⁡2

true

(5)
> 

211−1

2047

(6)
> 

IsMersenne⁡11

false

(7)
> 

ifactor⁡211−1

23⁢89

(8)

There are 49 known Mersenne Primes.

> 

interface⁡rtablesize=52:

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DataSeries⁡seq⁡IthMersenne⁡i,i=1..49,labels=seq⁡1..49

Warning, the rankings of the 45th to 51st Mersenne primes are provisional, since it has not been determined that there do not exist more Mersenne primes between 44th and 51st

DataSeries⁡235713171931618910712752160712792203228132174253442396899941112131993721701232094449786243110503132049216091756839859433125778713982692976221302137769725931346691720996011240365832596495130402457325826573715666742643801431126095788516174207281,labels=1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,datatype=anything

(9)
> 

See Also

NumberTheory