The previous prime function 
gives the largest prime
less than 
.
The function can be given explicitly as
 |
where 
is the 
th
prime and 
is the prime counting
function. For 
,
4, ... the values are 2, 3, 3, 5, 5, 7, 7, 7, 7, 11, 11, 13, 13, 13, 13, 17, 17,
19, ... (OEIS A007917).
The previous prime function was implemented in versions of the Wolfram Language prior to 6 as PreviousPrime[n] (after loading the package NumberTheory`NumberTheoryFunctions).
Finding the previous prime before 
gives the largest 
-digit prime. For 
, 2, ..., the first few of these are 7, 97, 997, 9973, 99991,
999983, 9999991, 99999989, ... (OEIS A003618).
The amounts by which these are less than 
are 3, 3, 3, 3, 27, 9, 17, 9, 11, 63, ... (OEIS A033873).
-Digit Primes for 
." J. Recr. Math. 22, No. 4,
277-279, 1990.Ondrejka, R. "Prime Trivia." J. Recr. Math. 14,
No. 4, 285, 1981-1982.Sloane, N. J. A. Sequences