why is 1 not a prime number or a campsite number?

Answer 1

Neither 1 nor 0 are prime or composite, because they both are very special in multiplication.

Any number multiplied by 1 is itself, so it is called the multiplicative identity. Besides obviously not having any divisors, its special status as the only multiplicative identity set it apart from other numbers. Another reason, is that many mathematical theorems about prime numbers would be either trivial or unnecessarily cumbersome if 1 was considered a prime.

Zero multiplied by any number is zero, so it is meaningless to think of possible divisors of zero.

Answer 2

A prime number is a positive integer that has exactly two positive integer factors, 1 and itself; therefore, 1 is not considered prime.

A composite number is defined as any number, greater than 1, that is not prime.

Answer 3

Because Prime means it can be divisible by ONLY two numbers that number and it's self, but composit is divisible by MORE than two numbers. So if 1 is not compsit because the factors are 1 and 1,and it's not prime because it's factors are also it's self. If you don't get it the simple way to look at it is to know that 1 is special. I f you still don't get it ask your teacher.

Answer 4

Primes are divisble only by themselves and 1.

so 5 can be divided evenly only by 1 and 5.

If we considered it prime, that means it can only be divided by 1 and 1. But what's to stop us from 1 =1/1/1? or 1=1/1/1/1/1/1/1/1/1/1?

Is one only one? or is it 1*1? or 1*1*1*1*1*1*1*1?

Math likes things exact... and in this case, it's a bit more of a headache, so we just de-classified it and gave it a special property, called the identity. Every well defined operation has one (an identity, that is)!

Answer 5

The number one is far more special than a prime! It is the unit (the building block) of the positive integers, hence the only integer which merits its own existence axiom in Peano's axioms. It is the only multiplicative identity (1.a = a.1 = a for all numbers a). It is the only perfect nth power for all positive integers n. It is the only positive integer with exactly one positive divisor. But it is not a prime. So why not? Below we give four answers, each more technical than its precursor.
Answer One: By definition of prime!
The definition is as follows.
An integer greater than one is called a prime number if its only positive divisors (factors) are one and itself.
Clearly one is left out, but this does not really address the question "why?"
Answer Two: Because of the purpose of primes.
The formal notion of primes was introduced by Euclid in his study of perfect numbers (in his "geometry" classic The Elements). Euclid needed to know when an integer n factored into a product of smaller integers (a nontrivially factorization), hence he was interested in those numbers which did not factor. Using the definition above he proved:
The Fundamental Theorem of Arithmetic
Every positive integer greater than one can be written uniquely as a product of primes, with the prime factors in the product written in order of nondecreasing size.
Here we find the most important use of primes: they are the unique building blocks of the multiplicative group of integers. In discussion of warfare you often hear the phrase "divide and conquer." The same principle holds in mathematics. Many of the properties of an integer can be traced back to the properties of its prime divisors, allowing us to divide the problem (literally) into smaller problems. The number one is useless in this regard because a = 1.a = 1.1.a = ... That is, divisibility by one fails to provide us any information about a.
Answer Three: Because one is a unit.
Don't go feeling sorry for one, it is part of an important class of numbers call the units (or divisors of unity). These are the elements (numbers) which have a multiplicative inverse. For example, in the usual integers there are two units {1, -1}. If we expand our purview to include the Gaussian integers {a+bi | a, b are integers}, then we have four units {1, -1, i, -i}. In some number systems there are infinitely many units.
So indeed there was a time that many folks defined one to be a prime, but it is the importance of units in modern mathematics that causes us to be much more careful with the number one (and with primes).

Answer Four: By the Generalized Definition of Prime.
(See also the technical note in The prime Glossary' definition).
There was a time that many folks defined one to be a prime, but it is the importance of units and primes in modern mathematics that causes us to be much more careful with the number one (and with primes). When we only consider the positive integers, the role of one as a unit is blurred with its role as an identity; however, as we look at other number rings (a technical term for systems in which we can add, subtract and multiply), we see that the class of units is of fundamental importance and they must be found before we can even define the notion of a prime. For example, here is how Borevich and Shafarevich define prime number in their classic text "Number Theory:"

An element p of the ring D, nonzero and not a unit, is called prime if it can not be decomposed into factors p=ab, neither of which is a unit in D.
Sometimes numbers with this property are called irreducible and then the name prime is reserved for those numbers which when they divide a product ab, must divide a or b (these classes are the same for the ordinary integers--but not always in more general systems). Nevertheless, the units are a necessary precursors to the primes, and one falls in the class of units, not primes.

Answer 6

(composite number)
sorry just wanna correct the spelling