To qualify as a prime, a number must be divisible by 1 and itself, so 1 does not qualify. 2 is the first prime.
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No, one (1) is not a prime number.
A prime number is defined as being a natural number that is evenly divisible by exactly two distinct natural numbers. In the case of the number one, 1 is the only natural number that it can be evenly divided by. Thus, 1 has only one distinct divisor, not the required two necessary to make it a prime number. A numbers having this property is called a "unit".
hope that helps
A prime number is defined as being a natural number that is evenly divisible by exactly two distinct natural numbers. In the case of the number one, 1 is the only natural number that it can be evenly divided by. Thus, 1 has only one distinct divisor, not the required two necessary to make it a prime number. A numbers having this property is called a "unit".
hope that helps
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As everyone says, no, it's not. IMO, the current other answers don't get at the heart of the matter.
If 1 were a prime number, we would constantly be making exceptions for it. For instance, whole numbers can be written as the products of prime numbers: eg. 24 = 2*2*2*3. Moreover this representation is *unique*--if we've written 24 as p1*p2*...*pn, where the pi's are each prime numbers, there must be precisely 4 of them, three of them must be 2's, and the remaining one must be 3. If 1 were prime, we could write 24 = 1*1*2*2*2*3, which breaks this nice elegant property.
Also, "prime" is a concept that's generalized heavily in a branch of advanced math called abstract algebra. For technical reasons that generalize the above consideration, a prime number cannot have another number which, when the pair is multiplied, takes you to 1. For instance, -1 has -1 as its pair, since -1*-1 = 1. 1 also has a pair--itself, since 1*1=1. These numbers are called "units", and are disallowed from being primes even if they otherwise might qualify, because not disqualifying them makes things less elegant.
It's important to note that, for instance, -5 could also be called a prime number. It's usually not, since then you have to keep track of negatives in prime factorizations. But still, the rule I wrote above is actually not valid for negative numbers, since the product of positive primes is necessarily positive, and I was implicitly using the standard terminology of "primes" in the integers as positive numbers.
If 1 were a prime number, we would constantly be making exceptions for it. For instance, whole numbers can be written as the products of prime numbers: eg. 24 = 2*2*2*3. Moreover this representation is *unique*--if we've written 24 as p1*p2*...*pn, where the pi's are each prime numbers, there must be precisely 4 of them, three of them must be 2's, and the remaining one must be 3. If 1 were prime, we could write 24 = 1*1*2*2*2*3, which breaks this nice elegant property.
Also, "prime" is a concept that's generalized heavily in a branch of advanced math called abstract algebra. For technical reasons that generalize the above consideration, a prime number cannot have another number which, when the pair is multiplied, takes you to 1. For instance, -1 has -1 as its pair, since -1*-1 = 1. 1 also has a pair--itself, since 1*1=1. These numbers are called "units", and are disallowed from being primes even if they otherwise might qualify, because not disqualifying them makes things less elegant.
It's important to note that, for instance, -5 could also be called a prime number. It's usually not, since then you have to keep track of negatives in prime factorizations. But still, the rule I wrote above is actually not valid for negative numbers, since the product of positive primes is necessarily positive, and I was implicitly using the standard terminology of "primes" in the integers as positive numbers.
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No it isn't.
Primes are all numbers that are divisible by themselves and 1, namely 2,3,5,7,11 etc.
The numbers 0 and 1 are unique numbers - and the number 1 is not classed as a prime.
Primes are all numbers that are divisible by themselves and 1, namely 2,3,5,7,11 etc.
The numbers 0 and 1 are unique numbers - and the number 1 is not classed as a prime.
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No
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no