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-11 is a prime number?

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-11 is a prime number? [#permalink]

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New post 12 Aug 2008, 03:42
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Just a quick question.

Can a prime number be negative? e.g. -2, -3, -5, -7, -11, -13 ...?

Thanks.

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Re: -11 is a prime number? [#permalink]

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New post 12 Aug 2008, 04:20
No,

The reason is every prime number is "natural number" and all natural numbers are non-negative.

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Re: -11 is a prime number? [#permalink]

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New post 12 Aug 2008, 04:23
alpha_plus_gamma wrote:
No,

The reason is every prime number is "natural number" and all natural numbers are non-negative.


Thanks alpha,

So what is the definition of natural number? all positive number? need to be integer?

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Re: -11 is a prime number? [#permalink]

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New post 12 Aug 2008, 04:42
judokan wrote:
alpha_plus_gamma wrote:
No,

The reason is every prime number is "natural number" and all natural numbers are non-negative.


Thanks alpha,

So what is the definition of natural number? all positive number? need to be integer?


Set of all Non negative integers {0,1,2...}

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Re: -11 is a prime number? [#permalink]

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New post 12 Aug 2008, 04:56
alpha_plus_gamma wrote:
judokan wrote:
alpha_plus_gamma wrote:
No,

The reason is every prime number is "natural number" and all natural numbers are non-negative.


Thanks alpha,

So what is the definition of natural number? all positive number? need to be integer?


Set of all Non negative integers {0,1,2...}


Actually some branches of math like number theory, combinatorics etc use the definition N={1,2,3....} and some others like set theory, computer science & logic use the definition N= {0,1,2,3,....}.

Since you ask about prime numbers and primes fall under number theory, N={1,2,3..} would be the correct definition.

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Re: -11 is a prime number? [#permalink]

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New post 12 Aug 2008, 06:09
good discussion guys.
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Re: -11 is a prime number? [#permalink]

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New post 12 Aug 2008, 07:13
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Negatives are defined to be non-prime because mathematicians want the Fundamental Theorem of Arithmetic (Unique Factorization into Primes) to be true. With the accepted definition of prime, a number like 45 can be written as a product of primes in one, and only one, way: you need to multiply two 3s and one 5. If we allowed negatives to be prime, we could write 45 as a product of 'primes' in several ways (for example, as (-3)(-3)(5)). Because the Fundamental Theorem of Arithmetic is the foundation of Number Theory, negatives are not considered primes. Incidentally, this is also why 1 is not considered a prime; if 1 were prime, we could write 45 as (3^2)(5), or as (1^(1000))(3^2)(5), or in many other ways, so we wouldn't have unique factorization. When we define primes to be positive integers which have exactly two divisors (1 and themselves), then prime factorizations are unique.
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Re: -11 is a prime number? [#permalink]

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New post 12 Aug 2008, 07:27
IanStewart wrote:
Negatives are defined to be non-prime because mathematicians want the Fundamental Theorem of Arithmetic (Unique Factorization into Primes) to be true. With the accepted definition of prime, a number like 45 can be written as a product of primes in one, and only one, way: you need to multiply two 3s and one 5. If we allowed negatives to be prime, we could write 45 as a product of 'primes' in several ways (for example, as (-3)(-3)(5)). Because the Fundamental Theorem of Arithmetic is the foundation of Number Theory, negatives are not considered primes. Incidentally, this is also why 1 is not considered a prime; if 1 were prime, we could write 45 as (3^2)(5), or as (1^(1000))(3^2)(5), or in many other ways, so we wouldn't have unique factorization. When we define primes to be positive integers which have exactly two divisors (1 and themselves), then prime factorizations are unique.


You are the master!!!
Great information
+1
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Re: -11 is a prime number? [#permalink]

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New post 12 Aug 2008, 07:55
Thanks all for the info.

Could you please confirm my understanding?
(a) 1 is not a prime?
(b) 0^0 = 0?
(c) 0 is even?
(d) 0 is neither negative or positive?
(e) 0 is an integer?

THank again

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Re: -11 is a prime number? [#permalink]

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New post 12 Aug 2008, 08:15
judokan wrote:
Thanks all for the info.

Could you please confirm my understanding?
(a) 1 is not a prime?
(b) 0^0 = 0?
(c) 0 is even?
(d) 0 is neither negative or positive?
(e) 0 is an integer?

THank again


yes to all except 0^0 is undecided in general but acceptable as 1 for GMAT scope. [edited after jallenmorris pointed out that the error]

Last edited by bhushangiri on 12 Aug 2008, 08:43, edited 2 times in total.

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Re: -11 is a prime number? [#permalink]

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New post 12 Aug 2008, 08:29
Isn't there some disagreement in the academic area that 0^0 = 1 ?

bhushangiri wrote:
judokan wrote:
Thanks all for the info.

Could you please confirm my understanding?
(a) 1 is not a prime?
(b) 0^0 = 0?
(c) 0 is even?
(d) 0 is neither negative or positive?
(e) 0 is an integer?

THank again


yes to all

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Re: -11 is a prime number? [#permalink]

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New post 12 Aug 2008, 08:40
Opps i didn't see that. It is taken as 1 in most cases. and can be taken as undefined or indeterminate when considered in calculus studies. Even then, by manipulating the direction of limiting values, you can bring it to 1.


jallenmorris wrote:
Isn't there some disagreement in the academic area that 0^0 = 1 ?

bhushangiri wrote:
judokan wrote:
Thanks all for the info.

Could you please confirm my understanding?
(a) 1 is not a prime?
(b) 0^0 = 0?
(c) 0 is even?
(d) 0 is neither negative or positive?
(e) 0 is an integer?

THank again


yes to all

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Re: -11 is a prime number? [#permalink]

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New post 12 Aug 2008, 08:55
bhushangiri wrote:
Opps i didn't see that. It is taken as 1 in most cases. and can be taken as undefined or indeterminate when considered in calculus studies. Even then, by manipulating the direction of limiting values, you can bring it to 1.


Actually, in calculus, you can make 0^0 'equal' (as a limit) to anything you like. For example:

lim(x->0) x^0 = 1
lim(x->0) 0^x = 0

You will never need to worry about 0^0 on the GMAT- you won't see a question that requires you to know whether this quantity is defined or undefined. As jallenmorris points out, there is no universally accepted rule here anyway.
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Re: -11 is a prime number?   [#permalink] 12 Aug 2008, 08:55
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