2007-09-03 07:44:16 · 9 answers · asked by suma p 1 in Science & Mathematics ➔ Mathematics
1's primeness has been debated for a long long time.
Traditionally, yes, it is. It is divisible by itself and 1, only, and therefore fits the generic definition of primeness. It just so happens that 1 is a 1. Its the most trivial prime number ever.
The modern definition, however, requires that a prime be divisible by two distinct integers only... itself and 1. Therefore, primes exclude the integer 1 because it only has one unique factor: 1.
By the modern definition, 1 is neither prime nor composite. Its just the unit number.
I suppose whether or not you included it would depend on the application.
2007-09-03 07:52:29 · answer #1 · answered by Anonymous · 1⤊ 0⤋
No, A more accurate definition of a prime number is a positive integer having exactly one positive divisor other than the number 1. The following is an excerpt from mathworld. Check out their website to get a complete answer as to why it is not prime.
A prime number (or prime integer, often simply called a "prime" for short) is a positive integer that has no positive integer divisors other than 1 and itself. (More concisely, a prime number 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 ), making 24 not a prime number. Positive integers other than 1 which are not prime are called composite numbers.
2007-09-05 22:17:52 · answer #2 · answered by t6917rs 1 · 0⤊ 0⤋
No, 1 is not a prime number because one of the properies of prime numbers states that a number to be prime it should have only 4 factors being the number itself, 1 and the negative of 1 and the number. but 1 has only two factors which are 1 and -1. e.g 2 has 4 factors being: 1, 2, -1 & -2 only or 13 has four factos being 1, 13, -1 & -13. This holds for all prime numbers
2007-09-03 15:27:30 · answer #3 · answered by Masekoane 1 · 0⤊ 0⤋
1 is not a prime number. Although it fits the rule for prime numbers, it is not called a prime number.
definition of prime numbers:
An integer greater than one is called a prime number if its only positive divisors (factors) are one and itself.
2007-09-03 14:53:12 · answer #4 · answered by kaykay4915 3 · 0⤊ 0⤋
No one has yet given the real reason why 1 is not a
prime number. If it were, the unique factorisation
law for integers would be destroyed.
For instance, we know that
10 = 2*5.
That's the only of decomposing 10 into primes.
Suppose 1 were prime.
Then we could write
10 = 2*5 = 2*5*1 = 2*5*1*1, ...
and unique factorisation no longer holds.
2007-09-03 14:57:05 · answer #5 · answered by steiner1745 7 · 0⤊ 0⤋
The number 1 is considered neither prime nor composite but in a class of its own. It is the multiplicative identity, so it is also a unit and a divisor of unity.
2007-09-03 14:52:44 · answer #6 · answered by supensa 6 · 0⤊ 0⤋
! is a prime number.. A prime number is a number whose factor is only 1 and itself.
2007-09-03 14:50:39 · answer #7 · answered by armanomi 2 · 1⤊ 1⤋
if 1 is considered a prime (most don't) it would be a trivial prime number without any interesting property, worth to be disregarded.
2007-09-03 14:50:07 · answer #8 · answered by vlee1225 6 · 0⤊ 0⤋
Definition of a prime number- a number that has only two factors, itself and one. one only has ONE factor, so no. The "itself and one" part kind of works, but it still needs two factors.
2007-09-03 14:51:03 · answer #9 · answered by Tesline T 2 · 0⤊ 0⤋