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m is a divisor of n (also called m divides n, or n is divisible by m) if all prime factors of m have at least the same multiplicity in n. The divisors of n are all products of some or all prime factors of n (including the empty product 1 of no prime factors). The number of divisors can be computed by increasing all multiplicities by 1 and then ...
All prime numbers from 31 to 6,469,693,189 for free download. Lists of Primes at the Prime Pages. The Nth Prime Page Nth prime through n=10^12, pi(x) through x=3*10^13, Random prime in same range. Interface to a list of the first 98 million primes (primes less than 2,000,000,000) Weisstein, Eric W. "Prime Number Sequences". MathWorld.
Table of Gaussian integer factorizations. A Gaussian integer is either the zero, one of the four units (±1, ± i), a Gaussian prime or composite. The article is a table of Gaussian Integers x + iy followed either by an explicit factorization or followed by the label (p) if the integer is a Gaussian prime. The factorizations take the form of an ...
A prime number (or a prime) 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 ...
Every positive integer greater than 1 is either the product of two or more integer factors greater than 1, in which case it is called a composite number, or it is not, in which case it is called a prime number. For example, 15 is a composite number because 15 = 3 · 5, but 7 is a prime number because it cannot be decomposed in this way.
The following is a list of all currently known Mersenne primes and perfect numbers, along with their corresponding exponents p. As of 2023, there are 51 known Mersenne primes (and therefore perfect numbers), the largest 17 of which have been discovered by the distributed computing project Great Internet Mersenne Prime Search, or GIMPS. [2]
A highly composite number is a positive integer that has more divisors than any smaller positive integer. A related concept is that of a largely composite number, a positive integer that has at least as many divisors as any smaller positive integer. The name can be somewhat misleading, as the first two highly composite numbers (1 and 2) are not ...
The following table lists the progression of the largest known prime number in ascending order. [3] Here M p = 2 p − 1 is the Mersenne number with exponent p , where p is a prime number. The longest record-holder known was M 19 = 524,287 , which was the largest known prime for 144 years.