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Curtis Cooper | |
|---|---|
| Nationality | American |
| Alma mater | Iowa State |
| Scientific career | |
| Fields | Mathematics, Computer Science |
| Institutions | Central Missouri |
| Doctoral advisor | Robert Joe Lambert |
Curtis Niles Cooper is an American mathematician who was a professor at the University of Central Missouri, in the Department of Mathematics and Computer Science.
Using software from the GIMPS project, Cooper and Steven Boone found the 43rd known Mersenne prime on their 700 PC cluster on December 15, 2005. The prime, 230,402,457 − 1, is 9,152,052 digits long and is the ninth Mersenne prime for GIMPS. [1]
Cooper and Boone became the first GIMPS contributors to find two primes when they also found the 44th known Mersenne prime, 232,582,657 − 1 (or M32,582,657), which has 9,808,358 digits. This prime was discovered on September 4, 2006, using a PC cluster of over 850 machines. This is the tenth Mersenne prime for GIMPS. [2]
On January 25, 2013, Cooper found his third Mersenne prime of 257,885,161 − 1. [3]
On September 17, 2015, Cooper's computer reported yet another Mersenne prime, 274,207,281 - 1, which was the largest known prime number at 22,338,618 decimal digits. The report was, however, unnoticed until January 7, 2016. [4]
Cooper's own work has mainly been in elementary number theory, especially work related to digital representations of numbers. He collaborated extensively with Robert E. Kennedy. They have worked with Niven numbers, among other results, showing that no 21 consecutive integers can all be Niven numbers, [5] and introduced the notion of tau numbers, numbers whose total number of divisors are itself a divisor of the number. [6] Independent of Kennedy, Cooper has also done work about generalizations of geometric series, and their application to probability. [7]
Cooper is also the editor of the publication Fibonacci Quarterly .
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The Great Internet Mersenne Prime Search (GIMPS) is a collaborative project of volunteers who use freely available software to search for Mersenne prime numbers.
In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form Mn = 2n − 1 for some integer n. They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17th century. If n is a composite number then so is 2n − 1. Therefore, an equivalent definition of the Mersenne primes is that they are the prime numbers of the form Mp = 2p − 1 for some prime p.
A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself. However, 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorized as a product of primes that is unique up to their order.
In number theory, a perfect number is a positive integer that is equal to the sum of its positive proper divisors, that is, divisors excluding the number itself. For instance, 6 has proper divisors 1, 2 and 3, and 1 + 2 + 3 = 6, so 6 is a perfect number. The next perfect number is 28, since 1 + 2 + 4 + 7 + 14 = 28.
George Woltman is the founder of the Great Internet Mersenne Prime Search (GIMPS), a distributed computing project researching Mersenne prime numbers using his software Prime95. He graduated from the Massachusetts Institute of Technology (MIT) with a degree in computer science. He lives in North Carolina. His mathematical libraries created for the GIMPS project are the fastest known for multiplication of large integers, and are used by other distributed computing projects as well, such as Seventeen or Bust.
Prime95, also distributed as the command-line utility mprime for FreeBSD and Linux, is a freeware application written by George Woltman. It is the official client of the Great Internet Mersenne Prime Search (GIMPS), a volunteer computing project dedicated to searching for Mersenne primes. It is also used in overclocking to test for system stability.
61 (sixty-one) is the natural number following 60 and preceding 62.
144 is the natural number following 143 and preceding 145.
In mathematics, a harshad number in a given number base is an integer that is divisible by the sum of its digits when written in that base. Harshad numbers in base n are also known as n-harshad numbers. Harshad numbers were defined by D. R. Kaprekar, a mathematician from India. The word "harshad" comes from the Sanskrit harṣa (joy) + da (give), meaning joy-giver. The term "Niven number" arose from a paper delivered by Ivan M. Niven at a conference on number theory in 1977.
The University of Central Missouri (UCM) is a public university in Warrensburg, Missouri, United States.
100,000 (one hundred thousand) is the natural number following 99,999 and preceding 100,001. In scientific notation, it is written as 105.
The largest known prime number is 282,589,933 − 1, a number which has 24,862,048 digits when written in base 10. It was found via a computer volunteered by Patrick Laroche of the Great Internet Mersenne Prime Search (GIMPS) in 2018.
A refactorable number or tau number is an integer n that is divisible by the count of its divisors, or to put it algebraically, n is such that . The first few refactorable numbers are listed in as
5 (five) is a number, numeral and digit. It is the natural number, and cardinal number, following 4 and preceding 6, and is a prime number.
A megaprime is a prime number with at least one million decimal digits.
43,112,609 is the natural number following 43,112,608 and preceding 43,112,610.