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• BuzzsawAnn

  

  CHICAGO
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  December 18, 2005
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  Jul 7, 2006, 11:40 am

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      Back to the Mersenne  primes

   Seven is not really a magic number, but does have an uncanny way of appearing in all sorts of odd situations

  There are seven different ways of linking four hexagons together.

  The Mersenne primes are a special type of prime number. The first five are -
  3, 7, 31, 127, 8191
  - and they can be expressed as a power of two minus one -
  2 - 1 = 3
  2 - 1 = 7
  2 - 1 = 31
  2 - 1 = 127
  2 - 1 = 8,191
  ...

  For a mathematician, the equivalent of breaking the 100 metres world record is to find the highest known prime number. Every year or so, someone discovers a higher one and it gets reported in the newspapers. These record-breaking numbers are always Mersenne primes. At the time of writing the highest known prime is 2

  Whenever someone discovers a new Mersenne prime they also automatically discover a new perfect number. (2 - 1) x 2 is the world's largest known perfect number at the time of writing.

  It has been proved that the number of primes is limitless and so records for the highest known prime can go on being broken for ever.

  is the smallest number of integer-sided rectangles that tile a rectangle so that no 2 rectangles share a common length.
  is a Mersenne prime.
  is the unity digit of the number 3³¹.
  = 2³ - 1
  = 1² + 1² + 1² + 2² (sum of 4 squares)
  is the positive solution to: 3x² = 16x + 35

  is a prime number
  7 is a prime number
  73 is a prime number
  739 is a prime number
  7393 is a prime number
  73939 is a prime number
  739391 is a prime number
  7393913 is a prime number
  73939133 is a prime number

  Have we had enough of sevens and the Mersenne prime.