What Are the Possible Sums of Prime Number Pairs?

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SUMMARY

The discussion focuses on identifying the possible sums of prime number pairs, specifically highlighting combinations such as 2+3=5, 2+5=7, and 5+11=16. It establishes that the resulting sequence includes every even number not of the form 2p and every odd number of the form p+2, where p represents a prime number. The conversation also references the Goldbach and Levy conjectures, indicating their relevance to the patterns observed in prime sums.

PREREQUISITES
  • Understanding of prime numbers and their properties
  • Familiarity with basic arithmetic operations
  • Knowledge of the Goldbach conjecture
  • Awareness of the Levy conjecture
NEXT STEPS
  • Research the Goldbach conjecture and its implications on even numbers
  • Explore the Levy conjecture and its relationship with prime sums
  • Investigate the significance of prime number pair sums in number theory
  • Examine patterns in prime numbers and their sums using computational tools
USEFUL FOR

Mathematicians, number theorists, and students interested in prime number properties and conjectures related to prime sums.

Loren Booda
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List all of the possible sums of prime number pairs with each element taken once.

For instance: 2+3=5, 2+5=7, 3+5=8, 2+7=9, 3+7=10, 5+7=12, 5+11=16, 5+13=18 . . .

Can you find significance in this progression? Have you seen this sequence before?
 
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That "sequence" will likely consist of every even number that is not of the form 2p as well as every odd number of the form p+2 (p is a prime number). Are you familiar with the Goldbach and Levy conjectures?

If you have a more specific question than the somewhat open-ended question in the OP, please get straight to the specific question.
 
I'm sorry, I thought I had found a more fundamental pattern.
 

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