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NumberTheory

  

IsMersenne

  

test whether a number is a Mersenne number

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

IsMersenne(n)

Parameters

n

-

positive integer

Description

• 

The IsMersenne(n) command returns true if 2n1 is prime, false if 2n1 is not prime, and FAIL if the status is unknown.

• 

Cases where the status is unknown will generally take an extremely long time to return an answer.

• 

If 2n1 is prime, then it is said to be a Mersenne prime.

• 

There are currently 49 known Mersenne primes.

• 

For every composite number m, 2m1 is a not a prime.

Examples

withNumberTheory:

IsMersenne2

true

(1)

IsMersenne336458

false

(2)

isprime60298361

true

(3)

IsMersenne60298361

FAIL

(4)

IsMersenne60298362

false

(5)

The Tabulate command can be used to display Mersenne primes in a grid. The following table highlights any Mersenne primes with a pink background.

Vr,c→DocumentTools:-TabulateMatrixr,c,i,j→c*i1+j,fillcolor=T,i,j→`if`IsMersennec*i1+j,Pink,White:

V10,10

Tabulate

(6)

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

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

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71

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73

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75

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77

78

79

80

81

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

97

98

99

100

 

Note that V(r, c) can be modified to show tables for various values of r and c.

Compatibility

• 

The NumberTheory[IsMersenne] command was introduced in Maple 2016.

• 

For more information on Maple 2016 changes, see Updates in Maple 2016.

See Also

NumberTheory

NumberTheory[IthMersenne]