2006-07-01 22:49:52 · 9 answers · asked by dan m 2 in Science & Mathematics ➔ Mathematics
Suppose we have two numbers, A and B, and their product is C.
So, A*B = C.
Assume that C is a prime number.
Since A and B are also prime numbers, then they must be whole numbers.
Then C has four distinct factors: 1, A, B, and itself
This contradicts with the definition of a prime number, which states that a prime number has exactly two distinct whole number factors, 1 and itself.
Therefore our initial assumption is false, and we can conclude that C is a non-prime number.
QED
2006-07-01 23:02:06 · answer #1 · answered by Pinsir003 3 · 4⤊ 1⤋
I can proof this with the definition of prime numbers
Prime Numbers are number that can only be multiplied by 1 and itself.
The factor that if you multiply a prime by another prime, you would get the multiplication of 1 and the number, and also the prime and the prime again.
For ex:
3 * 3 = 9
9 = 1 * 9 and 3 * 3
2006-07-02 08:11:33 · answer #2 · answered by Sherman81 6 · 0⤊ 0⤋
A prime number(K) is the number wich has just 2 factors ( 1. K)
so when we have 2 prime numbers M,N and multiply them to get a number (A)...
M*N = A ....and we know that A = 1*A
So A will have (1,M,N,A ) as factors so A can not be a Prime number because it will have 4 factors.
NOTE: 1 is not a prime number because it has just one factor.
2006-07-01 23:29:17 · answer #3 · answered by M. Abuhelwa 5 · 0⤊ 0⤋
Yes. Since a prime number is any whole integer that is only divisible by itself or 1, then multiplying two prime numbers will always result in a total that is divisible by the two different prime numbers. The result could therefore not be a prime number.
Unless, of course, one of the prime numbers that you multiplied was the number 1. Then the result *would* be a prime number as defined by "a number divisible only by itself or 1"
2006-07-01 22:54:35 · answer #4 · answered by Anonymous · 0⤊ 0⤋
Easy. A prime number has no factors or than 1 and itself. Since the number resulting from multiplying two primes together must by definition have two factors--the two that were multiplied together--it can not be prime.
2006-07-02 02:06:59 · answer #5 · answered by Anonymous · 0⤊ 0⤋
Note to answerers above:
By the definition of prime number, a prime number must be greater than 1, 1 is _not_ a prime. If primes were defined to include 1, then every statement of every theorem would have to read, "Let p be a prime, p not equal 1, ..."
2006-07-01 23:45:14 · answer #6 · answered by Anonymous · 0⤊ 0⤋
That's wrong!
there is infinte number of primes that result from a prime number plus two which is a prime number
2006-07-02 01:07:03 · answer #7 · answered by mohamed.kapci 3 · 0⤊ 0⤋
That is easy, because the product always has the two prime factors of the beginning.
2006-07-02 11:18:00 · answer #8 · answered by Thermo 6 · 0⤊ 0⤋
1 is a prime number 1x1=1 statement not true
2006-07-01 23:02:50 · answer #9 · answered by james b 2 · 0⤊ 0⤋