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02 Oct 2004, 21:35
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Just wanted 1 clarification from you folks: when u consider prime numbers, do you consider negative numbers also, or only positive?
i have always been in doubt regarding this.
If we consider negative numbers -1 is the only negative prime... its factors being -1 and 1.
All other negative numbers will have atleast 4 factors: for eg, -19 will have factors as: -19, 1, 19, -1.
Is my understanding correct that -1 is a prime number?
Thanks
i have always been in doubt regarding this.
If we consider negative numbers -1 is the only negative prime... its factors being -1 and 1.
All other negative numbers will have atleast 4 factors: for eg, -19 will have factors as: -19, 1, 19, -1.
Is my understanding correct that -1 is a prime number?
Thanks
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02 Oct 2004, 21:45
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Great question, upon some quick browsing, found this info that i think is useful to get a clear understanding..
The reason why 1 is said not to be a prime number is merely convenience. For example, if 1 was prime then the prime factorization of 6 would not be unique since 2 times 3 = 1 times 2 times 3. A number that can be written as a product of prime numbers is composite. Thus there are three types of natural numbers: primes, composites, and 1.
For more info, visit https://www.math.utah.edu/~alfeld/math/prime.html.
Also prime number is defined as: An integer greater than one is called a prime number if its only positive divisors (factors) are one and itself
The reason why 1 is said not to be a prime number is merely convenience. For example, if 1 was prime then the prime factorization of 6 would not be unique since 2 times 3 = 1 times 2 times 3. A number that can be written as a product of prime numbers is composite. Thus there are three types of natural numbers: primes, composites, and 1.
For more info, visit https://www.math.utah.edu/~alfeld/math/prime.html.
Also prime number is defined as: An integer greater than one is called a prime number if its only positive divisors (factors) are one and itself
02 Oct 2004, 22:00
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Venksune,
My question was not whether 1 is a prime number or not, but -1 (minus 1) is a prime or not?
i agree that among the positive numbers, 1 is not prime, and regarding the rest we all know.
My concern is what about negative numbers?
As you said:
So does this mean that the concept of prime and composites apply only to natural numbers (i.e. 1 and onwards) and not to 0 and negative numbers...?
I had a small doubt, because when we say 7 is a prime number we take, only 7 and 1 as factors and not -7 and -1... (just going bit weird
So based on this reasoning is it always safe to assume negative numbers and 0 dont qualify to be called as either prime or composites?
My question was not whether 1 is a prime number or not, but -1 (minus 1) is a prime or not?
i agree that among the positive numbers, 1 is not prime, and regarding the rest we all know.
My concern is what about negative numbers?
As you said:
Quote:
So does this mean that the concept of prime and composites apply only to natural numbers (i.e. 1 and onwards) and not to 0 and negative numbers...?
I had a small doubt, because when we say 7 is a prime number we take, only 7 and 1 as factors and not -7 and -1... (just going bit weird
So based on this reasoning is it always safe to assume negative numbers and 0 dont qualify to be called as either prime or composites?
