Prime Numbers

[rockyracoon]

Is 1 a prime number?

Ta :)

[factor-fiction]

No- 2 is the first one. A prime number has two, and only 2 , factors

[factor-fiction]

^ and 1 has only one factor

[factor-fiction]

The first few are 2, 3, 5, 7, 11, 13, 17, 19, 23,....

[Prudie]

No rocky, a prime by definition must have only 2 roots and they must be itself and 1. As I is only divisible by 1, ie only has one factor it's not a prime.

[Prudie]

sorry I typed roots on autopilot and meant to change it. I will be picked up on it I'm sure. I meant only 2 factors.

[Tilly2]

Factor didn't spot your factor error, Prudie. :-)

[rockyracoon]

Many thanks, you've just made my daughter very happy. She sat the UKMT
Intermediate Maths Challenge today and it came up in one of the questions.

Thanks again :)

[factor-fiction]

Maybe factor's trying not to be such a stickler

[Tilly2]

:-) It ain't workin', factor.

[Peter Pedant]

The thing is prime factorisation is unique

2x3 and so on

if you allow one, then you can have 2x3, 2x3x1, 2x3x1x1
which rather wrecks the beauty of unique prime factorisation

so, by cnvention one isnt a prime

Nothing wrong with stickling in the right place FF

[Jackdaw33]

If I remember rightly the correct term for 1 is 'unity'.

[Prudie]

Something I never did as a child - fishing for sticklebacks

[bert_h]

Of course, a prime number is whatever mathematicians find it convenient to define as a prime number. Nature doesn't provide an over-riding answer.

There are some mathematical ideas which cover only the odd prime numbers, and there are others which cover the prime numbers and -1. Neither of them are important enough to re-define 'prime number' and elsewhere say 'the prime numbers and 2', or 'the positive prime numbers'.

Peter P. is at the real crux of the matter with the fact that, should 1 be included as a prime number, it would make it quite awkward to express the unique factorisation theorem - and for no obvious benefit, as I can't think of a single area where 'the prime numbers and 1' would be a useful aggregate concept.

However, in my much-prized copy of Chambers's Shorter Six-Figure Mathematical Tables, authored by L.J. Comrie and dated 1966, Table IX on pages 346-7 'Prime Numbers' starts with 1, not 2 (it goes up 12919).

Congratulations to your daughter.