8128 AND PERFECT NUMBERS

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The number 8128 is the most notable perfect number.

8128 = 1 + 2 + 4 + 8 + 16 + 32 + 64 + 127 + 254 + 508 + 1016 + 2032 + 4064
  • A perfect number is a positive integer that is equal to the sum of its proper divisors not including the number itself, e.g. 28 is a perfect number because 28 = 1 + 2 + 4 + 7 + 14. The numbers 1, 2, 4, 7, 14 are the divisors of 28 i.e. they can divide 28.
  • First perfect number is 6, i.e. 6 = 1 + 2 + 3.
  • Other examples include 496, 8128 etc.
  • It is not discovered that whether there is any odd perfect number or not. 

8128 is related to the mersenne prime 127

127 = 27 – 1
27 – 1 is prime, then 27 -1 (27 – 1 ) must be a perfect number, i.e.
27 -1 (27 – 1 ) = 8128

  • Prime numbers of the form 2p – 1 are called mersenne primes.
  • Example include 3, 7, 31, 127, 8191, 131071, 524287 etc.
  • Largest known prime number 274207281 – 1 is a Mersenne prime.

Other features of 8128 are :
  • 8128 is 127th triangular number
  • 8128 is 64th hexagonal number
  • 8128 is a harmonic divisor number
  • 8128 is a happy number

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