Next Prime
The next prime function NP(n) gives the smallest prime larger than n. The function can be given explicitly as
| NP(n)=p_(1+pi(n)), |
where p_i is the ith prime and pi(n) is the prime counting function. For n=1, 2, ... the values are 2, 3, 5, 5, 7, 7, 11, 11, 11, 11, 13, 13, 17, 17, 17, 17, 19, ... (OEIS A007918).
The next prime function is implemented in the Wolfram Language as NextPrime [n].
Finding the next prime after 10^(n-1) gives the smallest n-digit prime. For n=1, 2, ..., the first few of these are 2, 11, 101, 1009, 10007, 100003, 1000003, ... (OEIS A003617). The amounts by which these exceed 10^n are 1, 1, 1, 9, 7, 3, 3, 19, 7, 7, ... (OEIS A033873).
See also
Fortunate Prime, Previous Prime, Prime Counting Function, Prime NumberExplore with Wolfram|Alpha
More things to try:
References
O'Hara, F. "The Smallest and Largest N-Digit Primes for N=1(1)150." J. Recr. Math. 22, No. 4, 277-279, 1990.Sloane, N. J. A. Sequences A003617/M2008, A007918, and A033873 in "The On-Line Encyclopedia of Integer Sequences."Referenced on Wolfram|Alpha
Next PrimeCite this as:
Weisstein, Eric W. "Next Prime." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/NextPrime.html