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Given an integer n, choose some integer a coprime to n and calculate a n − 1 modulo n. If the result is different from 1, then n is composite. If it is 1, then n may be prime. If a n −1 (modulo n) is 1 but n is not prime, then n is called a pseudoprime to base a. In practice, if a n −1 (modulo n) is 1, then n is usually prime.
A range check is a check to make sure a number is within a certain range; for example, to ensure that a value about to be assigned to a 16-bit integer is within the capacity of a 16-bit integer (i.e. checking against wrap-around). This is not quite the same as type checking. [how?
The 3-partition problem remains NP-complete even when the integers in S are bounded above by a polynomial in n.In other words, the problem remains NP-complete even when representing the numbers in the input instance in unary. i.e., 3-partition is NP-complete in the strong sense or strongly NP-complete.
The floor of x is also called the integral part, integer part, greatest integer, or entier of x, and was historically denoted [x] (among other notations). [2] However, the same term, integer part, is also used for truncation towards zero, which differs from the floor function for negative numbers. For an integer n, ⌊n⌋ = ⌈n⌉ = n.
In number theory, an n-smooth (or n-friable) number is an integer whose prime factors are all less than or equal to n. [1] [2] For example, a 7-smooth number is a number in which every prime factor is at most 7. Therefore, 49 = 7 2 and 15750 = 2 × 3 2 × 5 3 × 7 are both 7-smooth, while 11 and 702 = 2 × 3 3 × 13 are not 7-smooth.
Prime number: A positive integer with exactly two positive divisors: itself and 1. The primes form an infinite sequence 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, ... Composite number: A positive integer that can be factored into a product of smaller positive integers. Every integer greater than one is either prime or composite.
Integer overflow can be demonstrated through an odometer overflowing, a mechanical version of the phenomenon. All digits are set to the maximum 9 and the next increment of the white digit causes a cascade of carry-over additions setting all digits to 0, but there is no higher digit (1,000,000s digit) to change to a 1, so the counter resets to zero.
For example, in Java, any class that implements the Comparable interface has a compareTo method which either returns a negative integer, zero, or a positive integer, or throws a NullPointerException (if one or both objects are null). Similarly, in the .NET framework, any class that implements the IComparable interface has such a CompareTo method.