Is 1 a prime number?

Answer 1

The definition of prime number (actually integer) is that it is an integer that has only itself and 1 as divisors. 0 is divisible by ALL numbers, and so is not prime, but attempting to factor it results in an infinite regress, which is not desirable. 1 does seem to meet the definition of prime - it is divisible by itself (1) and 1. However, one of the most useful results of number theory is the unique factorization theorem. It says that every number has a unique factorization. For example,

210 = 10 x 21

But also

210 = 14 x 15

However, 10, 21, and so forth also have factors so when you factor them you eventually get

210 = 2 x 3 x 5 x 7

which is the prime factorization of 210. There is no other way of expressing 210 as a product of primes except for permuting the factors and changing their signs. However, if 1 were a prime, there would be an infinite number of factorizations of 210:

210 = 2 x 3 x 5 x 7 = 1 x 2 x 3 x 5 x 7 = 1 x 1 x 2 x 3 x 5 x 7 = 1 x 1 x 1 x 2 x 3 x 5 x 7 = and so forth.

To preserve unique factorization, 1 is generally not regarded as a prime number. One could also exclude negative numbers from being prime, but a better idea is to say that a prime can exist in a variety of forms such as a and b, as long as the number u such that au = b is a unit, and for the integers, only 1 and -1 are units.

So 1, by definition, is not prime.

Answer 2

in math 1 is not considered as a prime or composit because the definition for prime is any number bigger than 1 that can only be divisible by itself and 1, 1 is already a divisor in the problem so nope

Answer 3

a million isn't top, because of the fact the definition of top includes the situation that the selection be greater effective than a million (that regulations out 0 as nicely) This decision isn't arbitrary. there are various appropriate and deep theorems approximately top numbers. yet lots of the statements of those theorems could could incorporate awkward footnotes if a million have been allowed to be top. as an instance, the standard Theorem of arithmetic says that each and every advantageous integer could be factored right into a made from primes in precisely one way (no longer counting the order of the climate.) in an attempt to ingredient a hundred, one individual might proceed: a hundred = 2x50=2x2x25=2x2x5x5 yet somebody else might proceed a hundred = 10x10 =2x5x2x5 no rely the way you proceed, you will finally end up with the comparable components. yet what if we allowed a million to be a notable? you're able to even have a hundred = 2x2x5x5x1 a hundred = 2x2x5x5x1x1 a hundred = 2x2x5x5x1x1x1 etc. the theorem could could incorporate the footnote ( "aside from components of a million") As for 0, selection thought is a concern touching directly to the advantageous integers, so 0 only would not enter into the dialogue. as nicely, 0 has loads of components different than itself and a million: 0 = 2x5x7x0 0 = 5x13x89x0x0 by no skill the way a notable selection might desire to act!

Answer 4

0 and 1 are neither prime nor composite.

A prime number is devined as any number that can only be multiplied by 1 and itself. But since 1 is only be multiplied by itself, it doesn't actual apply to both rules.

1 is only 1
2 is 1 and 2
3 is 1 and 3
5 is 1 and 5
etc...

Answer 5

NO, it is not. And this is not "a matter of opinion". 1 is not a prime number nor a composite number.

Prime numbers, BY DEFINITION, are positive integers that have TWO DISTINCT factors, namely 1 and itself. Granted 1 is equal to 1 times itself, but it does not have two DISTINCT factors, only one unique factor, which is "1".

A composite number is a positive integer with MORE than two factors. So "1" is not prime nor composite.

Here's a great link that explains other reasons why "1" isn't prime:
http://mathforum.org/library/drmath/view/57058.html

Answer 6

No, to be prime you must have two distinct divisors 1 and another number, which means 1 is not prime because it only has one divisor the number 1

Answer 7

Absolutely not.

The definition of a prime number is that is has exactly 2 factors: 1 and itself.
Since 1 only has one factor, it is NOT prime.

"Most textbooks today call it neither prime nor composite, but older texts generally considered it to be prime. In 1859, Lebesgue stated explicitly that 1 is prime in Exercices d'analyse numérique. It is prime in Primary Elements of Algebra for Common Schools and Academies (1866) by Joseph Ray and Standard Arithmetic (1892) by William J. Milne. A list of primes to 10,006,721 published in 1914 by D. N. Lehmer includes 1. [David Cantrell suggests this is more a historical issue and is inappropriate for this page. He writes, "No high-school students (unless they're doing historical research) are going to encounter a legitimate definition of prime which would include 1." This entry may be removed.]"

It is unbelievable how many people are saying "yes" to this question.

Answer 8

yes. sort of. well, technically, no.
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. so it's not prime or composite. it's just.... one. the loneliest number.

Answer 9

It is not. A prime number is divisible for two numbers: itself and the unit.
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Answer 10

I don't think its a prime number, It doesn't fall under either categories concerning prime numbers.