Prime Numbers Between Two Quadratics: A Useful Result?

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SUMMARY

The discussion centers on the existence of at least one prime number between the quadratic expressions 16x² + 4x - 1 and 16x² + 8x - 5 for any odd natural number x. The inquiry suggests a potential connection to Andrica's conjecture, which posits that there is always a prime between consecutive squares of integers. The poster expresses skepticism regarding the novelty of this result, indicating that it may already be established in number theory.

PREREQUISITES
  • Understanding of quadratic equations and their properties
  • Familiarity with prime number theory
  • Knowledge of Andrica's conjecture and its implications
  • Basic skills in mathematical proof techniques
NEXT STEPS
  • Research the proof techniques related to Andrica's conjecture
  • Explore the properties of prime numbers in relation to quadratic functions
  • Study existing literature on prime gaps and their mathematical significance
  • Investigate computational methods for identifying primes between quadratic expressions
USEFUL FOR

Mathematicians, number theorists, and students interested in prime number research and quadratic equations.

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Would it be a useful result to know there is at least one prime between
16x^2+4x-1 and 16x^2+8x-5 for any odd natural number x?
 
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