Double Mersenne Number

Author

Eric W. Weisstein
November 28, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/IntegerSequences/DoubleMersenneNumber.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/DoubleMersenneNumber.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Code

Enumeration

DoubleMersenne/@Range[10]

Primes

Flatten[Position[DoubleMersenne/@Range[15],_?PrimeQ]]//Timing

Flatten[Position[DoubleMersenneNumber/@Range[20],_?PrimeQ]]//Timing

DoubleMersenneNumber/@{2,3,5,7}

Digits[DoubleMersenneNumber[7]]

Prime Factors

Integers

Do[
Print[{i,FactorInteger[DoubleMersenne[i]]//Timing}],
{i,10}]

Prime (Subscript[M, n])

(Subscript[M, 13])

FactorInteger[DoubleMersenne[13],FactorComplete->False]//Timing

IntegerQ[c=DoubleMersenne[13]/338193759479]

Digits[c]

PrimeQ[c]//Timing

(Subscript[M, 17])

FactorInteger[DoubleMersenne[17],FactorComplete->False]//Timing

IntegerQ[c=DoubleMersenne[17]/231733529]

Digits[c]

PrimeQ[c]//Timing

(Subscript[M, 19])

FactorInteger[DoubleMersenne[19],FactorComplete->False]//Timing

IntegerQ[c=DoubleMersenne[19]/62914441]

Digits[c]

PrimeQ[c]//Timing

(Subscript[M, 31])

DoubleMersenne[31]/295257526626031

FactorInteger[DoubleMersenne[31],FactorComplete->False]//Timing

IntegerQ[DoubleMersenne[31]/295257526626031]