Uniqueness of the prime number 2?

Question

I heard Lisa Jardine say, on BBC Radio 4, that 2 is a unique prime number because it is the only even one. Is this not only as significant as saying that 3 is unique because it is the only prime number that is divisible by 3 or that 5 is unique because it is the only prime number that is divisible by 5?

Answer 1

it is very important as this is the only even prime number, so if this multiply any other prime number, the result is an even number too, whereas the other prime number when multiply together , the product is always odd

Answer 2

At one time 1 was considered prime, but mathematicians today use a different definition of prime so that it is not considered prime. By definition: A number is prime if it has exactly TWO factors (1 and itself). By this definition, 1 has only ONE factor and is not prime. (Note: It is also not composite, because composite numbers have MORE than two factors) The formal reason is that lots of other math requires that we don't consider 1 a prime number. One reason is the "Fundamental Theorem of Arithmetic" which says, "Every positive integer can be written uniquely as a product of primes, with the prime factors in the product written in order of nondecreasing size." As you can see, if 1 was considered prime, you could no longer write a number uniquely as a product of primes. Today where were write something like: 30 = 2 x 3 x 5 You'd also have: 30 = 1 x 2 x 3 x 5 30 = 1 x 1 x 2 x 3 x 5 etc. Therefore mathematicians decided to change the definition so that one is not considered prime (or composite).

Answer 3

To say a thing like that is to confirm that the distinction between odd and even is more of a language concept than a numerical concept.

You could also say that it is significant that among all the even numbers, 2 is the only prime one, compared with quite a lot of primes among the odd numbers.

The real anomaly with 2 as a prime is because it is so small. For all other primes P, the number 1 behaves in a certain way relative to it, and the number P-1 behaves in a certain other way. When P is 2, the numbers 1 and P-1 are identical.

Answer 4

When you put it that way, it does sound pretty silly.

However, as math gets more advanced 2 keeps coming up as an exception. For example, I put up a string of challenge questions that wound up with 2 as a special case, because mainly they differentiated between primes congruent to 1 mod 4 and primes congruent to 3 mod 4. (In this case, 2 behaved like the ones congruent to 1 mod 4.)

Answer 5

I agree with a previous answer that 2 although not more important than any other number it is important that it is the only even prime number. Also when we multply 2 with any other prime number then the result is even and not a prime number. You can also use the Seive of Eratosthenes to find prime numbers up to 100. Follow this link http://www.faust.fr.bw.schule.de/mhb/eratosiv.htm

Answer 6

it's unique because all the other prime numbers can't be divided by 2

Answer 7

Two is unique as a prime because it is even. The concept of odd/even is much more commonly used than the concept of prime.

It's not really significant at all. Unless you are looking for stuff to say on a radio station to avoid dead air.

Answer 8

I think she meant it is the oddest prime number being the only even prime number as mentioned ( I think ) by HARDY in discussion with RAMANUJIN

Answer 9

Prime number is that number which can be divided only by "1" or itself. That is, that number can not be factorized further.
Eg.
2 can be divided by '1' & '2' ..................(i)
3 .................. " ....by '1' & '3'...................(ii)
4............... " .........by '1', '2' & '4'
5 ............. " ..........by '1', & '5'..................(iii)
6.............. " ..........by '1', '2', '3' & '6'
7 .............. " .........by '1', & '7'..................(iv)
8 ............... " ........by '1', '2', '4', & '8'
9 .............. " .........by '1', '3' & '9'
10 ............" ..........by '1', '2', '5' & '10' .....(v)
11 ............ " .........by '1' & '11'.................(vi) and so on.........
From the above table you must have seen that the following are the prime numbers.:-
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53...........
are the series of prime numbers, and among them "2" is the only even number. This us the unique feature of '2' stated by Lisa Jardine through BBC radio.

Answer 10

WHY IS THE NUMBER TWO THE ONLY NUMBER THAT WHETHER ADDED TO ITSELF OR MULTIPLIED BY ITSELF, THE ANSWER IS STILL FOUR????