Prime Numbers
In "The Rich List" last week, a question was to name the prime numbers.
The first to answer, got it wrong by indication the number "1" was a prime number;-
Bu definition, "1" is not a prime number.
So here it goes from a search by Google.
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Prime Numbers
If a number has only two different factors, 1 and itself, then the number is said to be a prime number.
7 is a prime number since it has only two different factors.
Note:
But 1 is not a prime number since it does not have two different factors.
In mathematics, a prime number (or a prime) is a natural number which has exactly two distinct natural number divisors: 1 and itself. An infinitude of prime numbers exists, as demonstrated by Euclid around 300 BC. The first twenty-five prime numbers are:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
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The first to answer, got it wrong by indication the number "1" was a prime number;-
Bu definition, "1" is not a prime number.
So here it goes from a search by Google.
**************************************
Prime Numbers
If a number has only two different factors, 1 and itself, then the number is said to be a prime number.
7 is a prime number since it has only two different factors.
Note:
But 1 is not a prime number since it does not have two different factors.
In mathematics, a prime number (or a prime) is a natural number which has exactly two distinct natural number divisors: 1 and itself. An infinitude of prime numbers exists, as demonstrated by Euclid around 300 BC. The first twenty-five prime numbers are:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
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posted by Friar at Wednesday, December 17, 2008
2 Comments:
Well, I personally think that 1 could be considered as a prime number.
This sound as a crasy idea- it is against all ancient and new proofs.
But let's think about it
The a prime number is a natural number which has exactly two distinct natural number divisors: 1and itself.
Number 1 has two divisors 1 (as a number) and 1 (as a factor)
Using this in some new proofs could bring more crear idea on the prime numbers
Friar is correct.
Number 1 does NOT have "two DISTINCT divisors", so is not a prime.
Also, if 1 were a prime, it would stuff up theorems like the unique-prime-factorisation theorem, which states that every natural number greater than 1 can be written as a unique product of prime numbers.
So convention dictates that 1 is not a prime, hence the wording of the definition of "prime".
It makes sense.
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