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Fastest integer types that are guaranteed to be the fastest integer type available in the implementation, that has at least specified number n of bits. Guaranteed to be specified for at least N=8,16,32,64. Pointer integer types that are guaranteed to be able to hold a pointer. Included only if it is available in the implementation.
The smallest integer m > 1 such that p n # + m is a prime number, where the primorial p n # is the product of the first n prime numbers. A005235 Semiperfect numbers
The width, precision, or bitness [3] of an integral type is the number of bits in its representation. An integral type with n bits can encode 2 n numbers; for example an unsigned type typically represents the non-negative values 0 through 2 n − 1.
C's integer types come in different fixed sizes, capable of representing various ranges of numbers. The type char occupies exactly one byte (the smallest addressable storage unit), which is typically 8 bits wide. (Although char can represent any of C's "basic" characters, a wider type may be required for international character sets.)
Such a number is algebraic and can be expressed as the sum of a rational number and the square root of a rational number. Constructible number: A number representing a length that can be constructed using a compass and straightedge. Constructible numbers form a subfield of the field of algebraic numbers, and include the quadratic surds.
The period of c / k , for c coprime to k, equals the period of 1 / k . If k = 2 a ·5 b n where n > 1 and n is not divisible by 2 or 5, then the length of the transient of 1 / k is max(a, b), and the period equals r, where r is the multiplicative order of 10 mod n, that is the smallest integer such that 10 r ≡ 1 (mod n).
More generally, a positive integer c is the hypotenuse of a primitive Pythagorean triple if and only if each prime factor of c is congruent to 1 modulo 4; that is, each prime factor has the form 4n + 1. In this case, the number of primitive Pythagorean triples (a, b, c) with a < b is 2 k−1, where k is the number of distinct prime factors of c ...
Rather than storing values as a fixed number of bits related to the size of the processor register, these implementations typically use variable-length arrays of digits. Arbitrary precision is used in applications where the speed of arithmetic is not a limiting factor, or where precise results with very large numbers are required.