Bertrand's Postulate and Erdős' Proof

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SUMMARY

Bertrand's Postulate asserts that for any integer n, there exists at least one prime number p such that n < p < 2n. Paul Erdős provided a proof of this theorem at a young age, which is documented in his paper available at the provided link. This discussion highlights the significance of Erdős' contribution to number theory and the importance of Bertrand's Postulate in understanding prime distribution.

PREREQUISITES
  • Understanding of prime numbers and their properties
  • Familiarity with basic number theory concepts
  • Knowledge of mathematical proof techniques
  • Ability to read and comprehend mathematical papers
NEXT STEPS
  • Read Erdős' original proof of Bertrand's Postulate
  • Explore the implications of Bertrand's Postulate in number theory
  • Study other proofs of Bertrand's Postulate for comparison
  • Investigate the distribution of prime numbers using computational tools
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Mathematicians, students of number theory, and anyone interested in the properties of prime numbers and mathematical proofs.

Gear300
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Hello.
Is there a quick proof for showing that the next prime is within twice the current prime?

Edit:
Never mind. Erdős had given a proof of this (of Bertrand's postulate to be precise) at a fairly young age.

http://www3.nd.edu/~dgalvin1/pdf/bertrand.pdf
 
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