H. J. Woodall
Encyclopedia
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. "These tables collected from scattered sources the known prime factor
s for the bases 2 and 10 and also presented the authors' results of thirty years' work with these and the other bases."
Since 1925 many people have worked on filling in these tables. It is likely that this project is the longest, ongoing computational project in history. Derrick Henry Lehmer
, a well known mathematician who died in 1991 was for many years a leader of these efforts. Professor Lehmer was a mathematician who was at the forefront of computing as modern electronic computers became a reality. He was also known as the inventor of some ingenious pre-electronic computing devices specifically designed for factoring numbers. These devices are currently in storage at the Computer Museum in Boston.
A generalized Woodall number
is defined to be a number of the form
where n + 2 > b; if a prime can be written in this form, it is then called a generalized Woodall prime.
In 1925 Lt.-Col. Allan 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...
and Woodall gathered together all that was known about the primality and factorization of such numbers and published a small book of tables. "These tables collected from scattered sources the known prime factor
Prime factor
In number theory, the prime factors of a positive integer are the prime numbers that divide that integer exactly, without leaving a remainder. The process of finding these numbers is called integer factorization, or prime factorization. A prime factor can be visualized by understanding Euclid's...
s for the bases 2 and 10 and also presented the authors' results of thirty years' work with these and the other bases."
Since 1925 many people have worked on filling in these tables. It is likely that this project is the longest, ongoing computational project in history. Derrick Henry Lehmer
Derrick Henry Lehmer
Derrick Henry "Dick" Lehmer was an American mathematician who refined Édouard Lucas' work in the 1930s and devised the Lucas–Lehmer test for Mersenne primes...
, a well known mathematician who died in 1991 was for many years a leader of these efforts. Professor Lehmer was a mathematician who was at the forefront of computing as modern electronic computers became a reality. He was also known as the inventor of some ingenious pre-electronic computing devices specifically designed for factoring numbers. These devices are currently in storage at the Computer Museum in Boston.
A generalized Woodall number
Woodall number
In number theory, a Woodall number is any natural number of the formfor some natural number n. The first few Woodall numbers are:Woodall numbers were first studied by Allan J. C. Cunningham and H. J. Woodall in 1917, inspired by James Cullen's earlier study of the similarly-defined Cullen numbers...
is defined to be a number of the form
- nbn − 1,
where n + 2 > b; if a prime can be written in this form, it is then called a generalized Woodall prime.