A077037 Largest prime < n^3.

7, 23, 61, 113, 211, 337, 509, 727, 997, 1327, 1723, 2179, 2741, 3373, 4093, 4909, 5827, 6857, 7993, 9257, 10639, 12163, 13807, 15619, 17573, 19681, 21943, 24379, 26993, 29789, 32749, 35933, 39301, 42863, 46649, 50651, 54869, 59281, 63997

Offset: 2

Author

Reinhard Zumkeller, Oct 21 2002

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 2..1000

Crossrefs

Cf. A053001, A014220, A000578, A060199.

Programs

Mathematica

PrimePrev[n_]:=Module[{k},k=n-1;While[ !PrimeQ[k],k-- ];k];f[n_]:=n^3;lst={};Do[AppendTo[lst,PrimePrev[f[n]]],{n,5!}];lst (* Vladimir Joseph Stephan Orlovsky, Feb 25 2010 *)
Table[NextPrime[n^3, -1], {n, 2, 40}] (* Robert G. Wilson v, Aug 17 2010 *)

PARI

a(n) = precprime(n^3); \\ Michel Marcus, Jan 14 2023

Python

from sympy import prevprime
def a(n):  return prevprime(n**3)
print([a(n) for n in range(2, 41)]) # Michael S. Branicky, Jul 23 2021

Formula

a(n) > (n-1)^3 for all large n, by Ingham's theorem (see A060199). - Jonathan Sondow, Mar 27 2014