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Good Prime


A prime p_n is called "good" if

 p_n^2>p_(n-i)p_(n+i)

for all 1<=i<=n-1 (there is a typo in Guy 1994 in which the is are replaced by 1s). There are infinitely many good primes, and the first few are 5, 11, 17, 29, 37, 41, 53, ... (OEIS A028388).


See also

Andrica's Conjecture, Landau's Problems, Pólya Conjecture

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References

Guy, R. K. "'Good' Primes and the Prime Number Graph." §A14 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 32-33, 1994.Sloane, N. J. A. Sequence A028388 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Good Prime

Cite this as:

Weisstein, Eric W. "Good Prime." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GoodPrime.html

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