View Poll Results: Can negative numbers be prime ? | |||

Yes | 2 |
18.18% | |

No | 9 |
81.82% | |

Voters: 11. You may not vote on this poll |

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so now does this means NO wins ?

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Saket
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Ohh, congrs to kshiteej. thanks saswatpadhi for your answer.

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This is just about definitions so the only possible answer can be "no". For a "Yes" answer the definitions must be changed.

http://en.wikipedia.org/wiki/Prime_number states "a prime number (or a prime) is a natural number which has exactly two distinct natural number divisors: 1 and itself"

and http://en.wikipedia.org/wiki/Natural_number states "there are two conventions for the set of natural numbers: it is either the set of positive integers {1, 2, 3, ...} according to the traditional definition or the set of non-negative integers {0, 1, 2, ...}" - so this excludes all negative numbers from the definition of a prime.

and http://en.wikipedia.org/wiki/Divisor states "a divisor of an integer n, also called a factor of n, is an integer which evenly divides n without leaving a remainder."

Also if primes are redefined to include x<0, why is that of any interest? If x is prime then -x is also prime, so adding -2, -3, -5, -7 etc to the list adds no new information. Or you end up with no prime numbers at all, if for example -5 is divisible by -5, -1, 1 and 5, so every prime number by the current definition is not prime because any number x is divisible by +x, -x, +1 and -1. Or you extend the definition to say "exactly four distinct divisors: +/- 1 and +/- itself", in which case you're back to a set of primes where +x and -x are both prime or both not prime and so it has no benefit over the positive numbers only definition as is currently the case.

http://en.wikipedia.org/wiki/Prime_number states "a prime number (or a prime) is a natural number which has exactly two distinct natural number divisors: 1 and itself"

and http://en.wikipedia.org/wiki/Natural_number states "there are two conventions for the set of natural numbers: it is either the set of positive integers {1, 2, 3, ...} according to the traditional definition or the set of non-negative integers {0, 1, 2, ...}" - so this excludes all negative numbers from the definition of a prime.

and http://en.wikipedia.org/wiki/Divisor states "a divisor of an integer n, also called a factor of n, is an integer which evenly divides n without leaving a remainder."

Also if primes are redefined to include x<0, why is that of any interest? If x is prime then -x is also prime, so adding -2, -3, -5, -7 etc to the list adds no new information. Or you end up with no prime numbers at all, if for example -5 is divisible by -5, -1, 1 and 5, so every prime number by the current definition is not prime because any number x is divisible by +x, -x, +1 and -1. Or you extend the definition to say "exactly four distinct divisors: +/- 1 and +/- itself", in which case you're back to a set of primes where +x and -x are both prime or both not prime and so it has no benefit over the positive numbers only definition as is currently the case.

mayjune
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no negative no. cannot be prime... i agree with shabir's points.

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But, I request all members to give a justification for their vote, without which it's meaningless.

If you agree with someone's views like

**xpi0t0s**,

**mayjune**or

**shabbir**(all of them have almost similar reasons, though ); just mention their name .. no need to write the same justification again