nextprime

The term "nextprime" in computer science and mathematics typically refers to a function or algorithm that, given an integer n, returns the smallest prime number strictly greater than n. This operation is fundamental in various areas, including cryptography, number theory algorithms, and certain optimization problems.

The implementation of a nextprime function usually involves two main steps: checking if the input number n+1 is prime, and if not, incrementing the number and checking again until a prime is found. Primality testing itself can be done through various methods, from simple trial division for smaller numbers to more sophisticated probabilistic tests like the Miller-Rabin test for larger inputs. The efficiency of the nextprime function is largely determined by the efficiency of its underlying primality test and the distribution of prime numbers.

For instance, if the input is 7, the nextprime function would first check 8 (not prime), then 9 (not prime), then 10 (not prime), and finally 11 (which is prime). Therefore, nextprime(7) would return 11. The concept is straightforward but its practical application relies on efficient computational methods for handling potentially large numbers.