Is 1 a prime number?

Answer 1

By convention, no, although it used to be. It's an arbitrary decision with some mathematical reasons to suggest that it not be considered prime.

From http://mathworld.wolfram.com/PrimeNumber.html

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." With 1 excluded, the smallest prime is therefore 2

Answer 2

Here are some definitions that we use in Abstract Algebra, in a system with addition, multiplication, along with the associative, commutative, and distributive properties, and additive and multiplicative inverses 0 and 1:

We say that any element in the system that has a multiplicative inverse is a unit. With 1 being the multiplicative identity, it is also its own inverse, and therefore is a unit.

Prime - We say that x is prime if it is *not 0*, *not a unit*, and for all a and b, x divides a*b implies x divides a or x divides b.

Irreducible - We say that x is irreducible if it is *not 0*, *not a unit*, and whenever x=a*b, then either a or b is a unit.

As you can see, 1 is a unit, so it can't be prime or irreducible.

OBTW, in the natural numbers and integers, it can be shown that prime and irreducible are coexisting properties; all prime numbers are irreducible, and vice versa.

Answer 3

No.
Smallest prime number is 2.
2 is the only even prime number.
First few prime numbers are:-
2 , 3 , 5 , 7 , 11 , 13 , 17 , 19--------

Answer 4

no, 1 is neither prime nor composite. A prime number has only 2 different factors, one and itself. 1 does not fit that definition.

Answer 5

No, 1 is not a prime number. It is referred to as the "unit".

Answer 6

One is not a prime number

Answer 7

a million isn't top, because of the fact the definition of top is composed of the condition that the variety be extra effective than a million (that regulations out 0 besides) This selection isn't arbitrary. there are a number of desirable and deep theorems approximately top numbers. yet many of the statements of those theorems would would desire to comprise awkward footnotes if a million have been allowed to be top. for occasion, the essential Theorem of arithmetic says that each and every helpful integer could be factored right into a made from primes in precisely one way (no longer counting the order of the climate.) with the point to factor a hundred, one person ought to proceed: a hundred = 2x50=2x2x25=2x2x5x5 yet another person ought to 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 main? you additionally could have a hundred = 2x2x5x5x1 a hundred = 2x2x5x5x1x1 a hundred = 2x2x5x5x1x1x1 etc. the thought would would desire to comprise the footnote ( "apart from components of a million") As for 0, variety concept is a concern with reference to the helpful integers, so 0 purely would not enter into the talk. besides, 0 has numerous components different than itself and a million: 0 = 2x5x7x0 0 = 5x13x89x0x0 by no ability the way a main variety would desire to act!

Answer 8

1 is neither prime nor composite by definition.

Answer 9

1 is neither a prime or composite.......

Answer 10

it is neither prime or composite
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