Are There Any Even Perfect Numbers Between Two Primes?

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SUMMARY

The discussion centers on identifying even perfect numbers C such that both C-1 and C+1 are prime numbers. The only known even perfect number that satisfies this condition is 6. It is established that all even perfect numbers, except for 6, yield a remainder of 1 when divided by 9. The conversation highlights the challenge of finding additional even perfect numbers, given that only 47 perfect numbers are currently recognized.

PREREQUISITES
  • Understanding of even perfect numbers and their properties
  • Familiarity with prime numbers and their definitions
  • Basic knowledge of modular arithmetic, specifically division and remainders
  • Awareness of the historical context of perfect numbers
NEXT STEPS
  • Research the properties of even perfect numbers in number theory
  • Explore the relationship between perfect numbers and Mersenne primes
  • Study the implications of the Euclid-Euler theorem on perfect numbers
  • Investigate the current status of known perfect numbers and their classifications
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Mathematicians, number theorists, and students interested in the properties of perfect numbers and prime numbers.

K Sengupta
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Determine all possible even perfect number(s) C such that each of C-1 and C+1 is a prime number.
 
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Is it even possible to find ALL of these such numbers when only 47 perfect numbers are known?

Anyway, I say 6. That is all :smile:
 

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