Can Every Integer n > 1 have at Least One Prime Number Between n+1 and n^2?

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SUMMARY

The discussion centers on the conjecture that for every integer n greater than 1, there exists at least one prime number in the interval [n+1, n^2]. Participants reference Bertrand's postulate, which asserts that there is at least one prime in the interval [n, 2n] for all n greater than 2. They also demonstrate that for n greater than 2, the inequality n^2 - n - 1 > n holds true, reinforcing the conjecture. The conclusion drawn is that the conjecture is likely valid based on these mathematical principles.

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  • Understanding of prime numbers and their properties
  • Familiarity with Bertrand's postulate
  • Basic knowledge of inequalities and algebra
  • Experience with mathematical proofs and conjectures
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Myslius
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How do you prove/disprove the following: For any integer n higher then 1, there exists at least one prime number in interval [n+1, n^2]?
 
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Show that n^2-n-1>n for n>2 and apply Bertrand's postulate that there is a prime in [n,2n] for all n>2.
 
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