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A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Equivalently, it is a positive integer that has at least one divisor other than 1 and itself. [1][2] Every positive integer is composite, prime, or the unit 1, so the composite numbers are exactly the numbers that are not prime and not a ...
Carmichael number. In number theory, a Carmichael number is a composite number which in modular arithmetic satisfies the congruence relation: for all integers . [1] The relation may also be expressed [2] in the form: for all integers that are relatively prime to . They are infinite in number.
In number theory, a superior highly composite number is a natural number which, in a particular rigorous sense, has many divisors. Particularly, it is defined by a ratio between the number of divisors an integer has and that integer raised to some positive power. For any possible exponent, whichever integer has the greatest ratio is a superior ...
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.
1, 2, 6, 6, 30, 30, 210, 210, 210, 210, 2310, 2310. We see that for composite n every term n# simply duplicates the preceding term (n − 1)#, as given in the definition. In the above example we have 12# = p 5 # = 11# since 12 is a composite number. Primorials are related to the first Chebyshev function, written ϑ(n) or θ(n) according to:
Table of divisors. Plot of the number of divisors of integers from 1 to 1000. Highly composite numbers are in bold and superior highly composite numbers are starred. In the SVG file, hover over a bar to see its statistics. The tables below list all of the divisors of the numbers 1 to 1000. A divisor of an integer n is an integer m, for which n ...
A related concept is that of a largely composite number, a positive integer that has at least as many divisors as all smaller positive integers. The name can be somewhat misleading, as the first two highly composite numbers (1 and 2) are not actually composite numbers; however, all further terms are. Ramanujan wrote a paper on highly composite ...
In mathematics, the sieve of Eratosthenes is an ancient algorithm for finding all prime numbers up to any given limit. It does so by iteratively marking as composite (i.e., not prime) the multiples of each prime, starting with the first prime number, 2. The multiples of a given prime are generated as a sequence of numbers starting from that ...
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