Counting sort initialization of the output array, each take time. Therefore, the time for the whole algorithm is the sum of the times for these steps, . Because it uses arrays of length and , the total space usage of the algorithm is also . For problem instances in which the maximum key value is significantly smaller than the number of items, counting sort can be highly space-efficient, as the only storage it uses other than its input and output arrays is the Count array which uses space . If each item to be sorted is itself an integer, and used as
Integer sequence prime Integer sequence prime In mathematics, an integer sequence prime is a prime number found as a member of an integer sequence. For example, the 8th Delannoy number, 265729, is prime. A challenge in empirical mathematics is to identify large prime values in rapidly growing sequences. A common subclass of integer sequence primes are constant primes, formed by taking a constant real number and considering prefixes of its decimal representation, omitting the decimal point. For example, the first 6 decimal digits of the constant "π", approximately 3.14159265, form the prime number 314159, which is therefore known as a pi-prime . Similarly,