HI is one (1) a prime number?

Question

a question has been set at our cubs and the chap that set the questions says that one is a prime number however i tought that it has to be a number greater than one ie 2,3,5,7,11,13,17 and so on

Answer 1

No, part of the definition of a prime number is that it is greater than 1.

Answer 2

A prime number (or prime integer, often simply called a "prime" for short) is a positive integer p>1 that has no positive integer divisors other than 1 and p itself. (More concisely, a prime number p is a positive integer having exactly one positive divisor other than 1.) For example, the only divisors of 13 are 1 and 13, making 13 a prime number, while the number 24 has divisors 1, 2, 3, 4, 6, 8, 12, and 24 (corresponding to the factorization 24==2^3.3), making 24 not a prime number. Positive integers other than 1 which are not prime are called composite numbers.

Prime numbers are therefore numbers that cannot be factored or, more precisely, are numbers n whose divisors are trivial and given by exactly 1 and n.

The number 1 is a special case which is considered neither prime nor composite (Wells 1986, p. 31). Although the number 1 used to be considered a prime (Goldbach 1742; Lehmer 1909; Lehmer 1914; Hardy and Wright 1979, p. 11; Gardner 1984, pp. 86-87; Sloane and Plouffe 1995, p. 33; Hardy 1999, p. 46), it requires special treatment in so many definitions and applications involving primes greater than or equal to 2 that it is usually placed into a class of its own. A good reason not to call 1 a prime number is that if 1 were prime, then the statement of the fundamental theorem of arithmetic would have to be modified since "in exactly one way" would be false because any n==n.1. In other words, unique factorization into a product of primes would fail if the primes included 1. A slightly less illuminating but mathematically correct reason is noted by Tietze (1965, p. 2), who states "Why is the number 1 made an exception? This is a problem that schoolboys often argue about, but since it is a question of definition, it is not arguable." As more simply noted by Derbyshire (2004, p. 33), "2 pays its way [as a prime] on balance; 1 doesn't."

Answer 3

1 is not a prime number. It is a "unit" and units are not prime numbers (by definition).

Here is the most recent definition of a prime number:

A number that is not divisible into two other numbers that are neither the original number nor a "unit".
Or, in the words of the "MAthematics Dictionary" (James & James, Van Nostrant Reinhold, 1992):
"any member of an integral domain that is not a unit and can not be written as the product of two members that are not units." Elsewhere, in the defintion, the dictionary specifically states that a prime "is not 0 or 1".

A "unit" is a number for which a multiplicative inverse exists in the domain.

When dealing with "natural numbers" (the positive integers), the only unit is 1 (because 1/1 = 1). Therefore if the only way to divide an integer is to divide by 1, then that integer is prime. For example, the only way you can represent 7 as a product of 2 positive numbers is: 7*1

When dealing with integers (positive and negative) there are two units: +1 and -1 (1/-1 = -1). Under the old definition, 7 would not be a prime number because you could have 7 = (-7)*(-1), neither of which is "itself" or 1.
In the field of integers, there are only two ways to represent 7 as the product of two integers:
(7)*(1)
(-7)*(-1)
both ways involve a unit.

In rational numbers and in real numbers, all numbers (except 0) are units. For example, consider 13: its multiplicative inverse is 1/13 (because 13 * 1/13 = 1) and 1/13 does exist in both fields: rationals and reals. Therefore 13 is a unit: it cannot be prime.
There are infinitely many ways to represent 7 as the product of two rational numbers. For example:
7 = (7/5)*5
However 7/5 is a "unit" because its inverse (5/7) is present in rational and in real numbers.

In complex integers: complex numbers of the form a + bi, where a and b are integers and i is such that i^2 = -1.
5 is not a prime number because it can be represented as the product: (2+i)(2-i) = 4 -2i + 2i - i^2 = 4 -(-1) = 4+1 = 5
and neither (2+i) nor (2-i) are units.

There are only 4 units in complex integers: +1, -1, +i, -i.

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The concept can be extended to other objects. For example polynomials can be prime.

(x^2 - 1) is not prime because it can be written as
(x+1)(x-1).

However, if working in real polynomials (polynomials where the coefficients and the variable can have real values), then the polynomial
(x^2 + 1)
is prime.

In polynomial, any term of degree 0 is a "unit". For example, (4x^2 + 4) is still prime, even though you could write it as
4*(x^2+1).
That is because "4" is a term where x is at degree 0.

However, in complex polynomials, only first degree terms can be prime. Any higher degree term can be reduced to a product of first degree terms:

(x^2 + 1) = (x+i)(x-i)

Answer 4

The smallest prime number is 2.
Therefore 1 is NOT a prime number.

Answer 5

a prime number is a natural number greater than one which has only 2 factors, 1 and itself
ex. 2, 3, 4, 7...

Answer 6

No, the conditions for a prime number is that it is divisible by one and itself (which is different). As there is only one option for division, instead of 2, it cannot count as a prime number.

Answer 7

no as a prime number is a number that only 1 and its self can go into and 1 is 1.

Answer 8

Although technically 1 does fit the definition of a prime number, by convention 1 is *not* considered to be prime.

An updated definition of prime number is "any integer *greater than 1* whose only divisors are 1 and the number itself".

Answer 9

This is one of those questions which has been argued out for centuries.

If you follow the absolute definition of 'prime', then yes, 1 is a prime number. It can only be divided by itself, and by 1. However, various extremely clever mathematicians decided long ago that 1 should be made a special case, and NOT defined as prime. This is because quite a few complicated mathematical theorems fall flat on their face if 1 is classified as prime.

So basically, yes, 1 is a prime number, but mathematicians decided it isn't because it would mean they'd have to work out a whole bunch of stuff all over again, and it was just too difficult!

Answer 10

I think your right because a prime number is any number that has no dividers except itself and one!
I'm not certain though