Cunningham number
Encyclopedia
In mathematics
, specifically in number theory
, a Cunningham number is a certain kind of integer named after English mathematician A. J. C. Cunningham
.
where b and n are integers and b is not already a power of some other number. They are denoted C±(b, n).
Cunningham worked on gathering together all known data on which of these numbers were prime. In 1925 he published tables which summarised his findings with H. J. Woodall
, and much computation has been done in the intervening time to fill these tables.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, specifically in number theory
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
, a Cunningham number is a certain kind of integer named after English mathematician A. J. C. Cunningham
Allan Joseph Champneys Cunningham
The British mathematician Allan Joseph Champneys Cunningham started a military career with the East India Company's Bengal Engineers. During 1871–1881, he was Instructor in Mathematics at the Thomason Civil Engineering College, Roorkee...
.
Definition
Cunningham numbers are a simple type of binomial number, they are of the formwhere b and n are integers and b is not already a power of some other number. They are denoted C±(b, n).
Primality
Establishing whether or not a given Cunningham number is prime has been the main focus of research around this type of number. Two particularly famous families of Cunningham numbers in this respect are the Fermat numbers, which are those of the form C+(2,2m), and the Mersenne numbers, which are of the form C-(2,n).Cunningham worked on gathering together all known data on which of these numbers were prime. In 1925 he published tables which summarised his findings with H. J. Woodall
H. J. Woodall
Herbert J. Woodall was a British mathematician.In 1925 Lt.-Col. Allan J.C. Cunningham and Woodall gathered together all that was known about the primality and factorization of such numbers and published a small book of tables...
, and much computation has been done in the intervening time to fill these tables.