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gptkbp:instanceOf
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gptkb:Prime_Number
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gptkbp:application
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cryptography
random number generation
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gptkbp:defines
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prime numbers of the form 2^p - 1, where p is a prime
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gptkbp:discoveredBy
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gptkb:Great_Internet_Mersenne_Prime_Search_(GIMPS)
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gptkbp:fifthMersennePrime
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8191
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gptkbp:firstMersennePrime
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3
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gptkbp:firstPerfectNumber
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6
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gptkbp:fourthMersennePrime
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127
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https://www.w3.org/2000/01/rdf-schema#label
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Mersenne primes
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gptkbp:largestKnownMersennePrime
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2^82,589,933-1 (as of 2018)
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gptkbp:namedAfter
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gptkb:Marin_Mersenne
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gptkbp:OEIS
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gptkb:A000668
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gptkbp:openProblem
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Are there infinitely many Mersenne primes?
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gptkbp:property
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If 2^p-1 is prime, then p must be prime
Not all numbers of the form 2^p-1 with p prime are prime
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gptkbp:relationToPerfectNumbers
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Every even perfect number is related to a Mersenne prime
If 2^p-1 is a Mersenne prime, then 2^{p-1}(2^p-1) is a perfect number
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gptkbp:secondMersennePrime
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7
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gptkbp:sequence
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3, 7, 31, 127, 8191, ...
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gptkbp:thirdMersennePrime
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31
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gptkbp:bfsParent
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gptkb:Number_theory
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gptkbp:bfsLayer
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5
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