Good Prime

A Prime $p_n$ is called ``good'' if

$${p_n}^2>p_{n-i}p_{n+i}$$

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

See also Andrica's Conjecture, Pólya Conjecture

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 Version of the Encyclopedia of Integer Sequences.'' http://www.research.att.com/~njas/sequences/eisonline.html.