Search results
Results From The WOW.Com Content Network
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 is composite, it can in turn be written as a product of smaller factors, for example 60 = 3 · 20 = 3 · (5 · 4).
[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 unit. [3] [4] E.g., the integer 14 is a composite number because it is the product of the two smaller integers 2 × 7 but the integers 2 and 3 are not because each can only be divided by one and itself ...
If the equality fails to hold true, then n is a composite number and a is a witness for the compositeness, and the test stops. Get back to the step one until the required accuracy is reached. After one or more iterations, if n is not found to be a composite number, then it can be declared probably prime.
Inputs: n: a value to test for primality, n>3; k: a parameter that determines the number of times to test for primality Output: composite if n is composite, otherwise probably prime Repeat k times: Pick a randomly in the range [2, n − 2] If (), then return composite
For other numbers, the algorithm only returns “composite” with no further information. For example, consider n = 341 and a = 2. We have n − 1 = 85 × 4. Then 2 85 mod 341 = 32 and 32 2 mod 341 = 1. This tells us that n is a pseudoprime base 2, but not a strong pseudoprime base 2.
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".
Get AOL Mail for FREE! Manage your email like never before with travel, photo & document views. Personalize your inbox with themes & tabs. You've Got Mail!
Highly composite numbers greater than 6 are also abundant numbers. One need only look at the three largest proper divisors of a particular highly composite number to ascertain this fact. It is false that all highly composite numbers are also Harshad numbers in base 10. The first highly composite number that is not a Harshad number is ...