The next prime function 
gives the smallest prime
larger than a nonnegative integer 
. The function can be given explicitly
as
 |
where 
is the 
th prime and 
is the prime counting
function. For 
,
2, ... the values are 2, 3, 5, 5, 7, 7, 11, 11, 11, 11, 13, 13, 17, 17, 17, 17, 19,
... (OEIS A151800).
The next prime function is implemented in the Wolfram Language as NextPrime[n].
Finding the next prime after 
gives the smallest 
-digit prime.
For positive integer 
, the first few of these are 2, 11, 101, 1009, 10007, 100003,
1000003, ... (OEIS A003617). The amounts by
which these exceed 
are 1, 1, 1, 9, 7, 3, 3, 19, 7, 7, ... (OEIS A033873).
-Digit Primes for 
." J. Recr. Math. 22, No. 4,
277-279, 1990.Sloane, N. J. A. Sequences