Either this number is a prime number or this number is a composite number
, By using this method, the found number can be assumed as whether this number is a prime number or not.
A simplified version of the method is also taught in the elementary school: Eratosthenes "invented a method of sifting out the composite numbers
, leaving only the primes" (Maletsky et al., 2004), referred to as the Sieve of Eratosthenes.
This conversation raised interesting ideas about factors, an essential idea for understanding prime and composite numbers
, and set the stage for the n ext exploration.
Below is a table of all composite numbers
less than 20 classified into abundant (A),defective (D) and perfect (P).
In this unit we are learning about prime and composite numbers
, so we are doing an investigation called Multiplying Prime Numbers.
have at least two factors which are not itself or 1.
To begin, Juraschek would construct a worksheet to guide Ryan to discover that every composite number
can be expressed as the product of primes.
The number of steps required to X to collapse in a composite number
is called the Smarandache P-persistence of prime X.
Meanwhile, mathematicians developed a version of the number field sieve that can be used for factoring any composite number
One such identification method, proposed by Uriel Feige, Amos fiat and Adi Shamir of the Weizmann Institute of Science in Rehovot, Israel, depends on the observation that while it's relatively easy to determine whether a number is prime (divisible only by itself and 1), finding the factors of a large composite number
is difficult and time-consuming (SN: 3/30/85, p.202).
The number 4,937,775, being a composite number
, can be expressed as the product of prime number: 3 X 5 X 5 X 65,837.
158]) and in factorization of integers (finding which prime numbers when multiplied together produce a given composite number
), the result was a new factoring algorithm.