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Every composite number can be written as the product of two or more (not necessarily distinct) primes. [2] For example, the composite number 299 can be written as 13 × 23, and the composite number 360 can be written as 2 3 × 3 2 × 5; furthermore, this representation is unique up to the order of the factors.
81 is: the square of 9 and the second fourth-power of a prime; 3 4. with an aliquot sum of 40; within an aliquot sequence of three composite numbers (81,40,50,43,1,0) to the Prime in the 43-aliquot tree. a perfect totient number like all powers of three. [1] a heptagonal number. [2] an icosioctagonal number. [3] a centered octagonal number. [4 ...
The first highly composite number that is not a Harshad number is 245,044,800; it has a digit sum of 27, which does not divide evenly into 245,044,800. 10 of the first 38 highly composite numbers are superior highly composite numbers .
Such a number is algebraic and can be expressed as the sum of a rational number and the square root of a rational number. Constructible number: A number representing a length that can be constructed using a compass and straightedge. Constructible numbers form a subfield of the field of algebraic numbers, and include the quadratic surds.
Every positive integer greater than 1 is either the product of two or more integer factors greater than 1, in which case it is a composite number, or it is not, in which case it is 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. If one of the factors ...
A composite number n is a strong pseudoprime to at most one quarter of all bases below n; [3] [4] thus, there are no "strong Carmichael numbers", numbers that are strong pseudoprimes to all bases. Thus given a random base, the probability that a number is a strong pseudoprime to that base is less than 1/4, forming the basis of the widely used ...
If n is an odd composite integer that satisfies the above congruence, then n is called an Euler–Jacobi pseudoprime (or, more commonly, an Euler pseudoprime) to base a. As long as a is not a multiple of n (usually 2 ≤ a < n ), then if a and n are not coprime, n is definitely composite, as 1 < gcd ( a , n ) < n is a factor of n .
So if it is unknown whether a number n is prime or composite, we can pick a random number a, calculate the Jacobi symbol ( a / n ) and compare it with Euler's formula; if they differ modulo n, then n is composite; if they have the same residue modulo n for many different values of a, then n is "probably prime".