## Common or Garden Letters

Posted by Karl Sharman on June 20, 2011 – 1:00 am

A, B,C,E,G,K,M,Q,S,W

What do these letters have in common…?

Unacceptable answers include:-

1. They are all in capitals

2. They all appear in the alphabet

3. They are in alphabetical order etc etc

June 20th, 2011 at 1:15 am

If you assign numbers to each letter based on the alphabet those letters are 1,2,3,5,7,11,13,17,19,23 so the prime numbers

June 20th, 2011 at 2:19 am

Their position in the alphabet is a prime number.

/Martin

June 20th, 2011 at 8:20 am

fail: 1 is not a prime number

June 20th, 2011 at 11:00 am

^^ Jan’s right.

Let’s say they are all odd numbers then.

June 20th, 2011 at 11:46 am

2 is an odd number?

I think that Karl was unaware that 1 is not a prime number

June 20th, 2011 at 1:08 pm

Karys, if by odd you mean unusual then you would be right. 1 is not truly a prime number and 2 is the only even prime number making it unusual or odd.

1 used to be a prime number back when I learned math.

June 20th, 2011 at 2:13 pm

I’m with Mishu, Martin and John24 – back when I learned math 1 was Prime, and I get the impression that Karl is of the same(ish) era

June 21st, 2011 at 1:43 am

Darn right, I am from a pre-decimal era – when measurments were correctly done in inches, feet and yards, temperatures were farenheit and prime numbers were only divisible by themselves and one. Now, 1 has been kicked out of the elite prime club.

And Jan, with your harsh “fail” comment to drive home my lack of current affairs in the prime numbers world – Fail, at the beginning of a sentence should be started with a capital letter, and I shouldn’t have started this paragraph with a grammatical conjunction…

Meantime, the American Heritage® Dictionary of the English Language, Fourth Edition copyright ©2000 by Houghton Mifflin Company, updated in 2009, published by Houghton Mifflin Company defines a prime number as:

prime number n.

A positive integer not divisible without a remainder by any positive integer other than itself and one.

June 21st, 2011 at 5:25 am

Hi Karl. I’m shocked at how many definitions I found that are consistent with yours, and so imply 1 is a prime.

I’m even more shocked at how many people who having given that definition (which allows 1), then go on to exclude 1 (e.g. by omitting it from a list) without any comment.

John24 observes that 2 being a prime seems odd. It really boils down to how we think. 2 breaks numbers into 2 groups (odd and even), whereas any prime p breaks numbers into p groups (the congruence groups – being defined by the remainder after division by p). We simply don’t seem to have words like “odd” and “even” that we use with the other primes.

June 21st, 2011 at 8:52 am

As I missed the memo about 1 not being a prime number, I googled it and came up with the following link…

http://primes.utm.edu/notes/faq/one.html

June 28th, 2011 at 8:34 am

I have always been taught that 1 is an identity, not a prime.

(I was born in ‘70)

June 28th, 2011 at 4:02 pm

1 is a prime and not one at the same time how cuz it can be

June 29th, 2011 at 4:19 am

Hi hi. The overriding consideration is the usefulness of defining what a prime is. Defining 1 to be a prime is not useful – worse, it’s counter-productive. 1 is neither prime or composite.

June 29th, 2011 at 6:41 am

The answer is Fibonacci

http://en.wikipedia.org/wiki/Fibonacci_number

June 29th, 2011 at 7:12 am

Hi Narendrudu. ??? The Fibonacci sequence starts with (0,1,) 1,2,3,5,8,13,21,34,55. So how does that fit in with 1,2,3,5,7,11,13,17,19,23 ?

July 8th, 2011 at 5:08 am

they have comma(,) in common…

July 8th, 2011 at 7:41 am

hey.

1 is neither prime nor a whole number.

July 8th, 2011 at 8:50 am

Hi Ayush. They do not have a comma in common. The only have a comma separating them.

Hi arjun. 1 is definitely a whole number.

July 10th, 2011 at 8:35 pm

Well, seeing as how 1 isn’t a prime number, you could reword the answer to say they all have only two factors, those being one and themselves.

July 10th, 2011 at 8:43 pm

Hi Dallas. The problem seems to stem from careless definitions of primes – usually given at school. The fact is that any sensible defintion that excludes 1 is OK.

One is that a prime number is any number that can only be divided by two

distinctnumbers, namely 1 and themselves. In the case of 1, there aren’t two distinct numbers that divide it, so it’s not a prime.July 10th, 2011 at 9:02 pm

Ok, yes, but you could still just reword the answer to say that They only have two factors. In the case of 1, 1 is both factors.

July 11th, 2011 at 3:03 am

Hi Dallas, but 1 has 5 factors: 1,1,1,1 and 1; so that’s no good

Personally I think it’s crazy to say that 1 is a factor. With that understanding, a prime is a number that has only one factor – itself. 1 cannot be prime because it has no factors. Sadly that can lead to literary errors: if we have an integer equation like A = B*C, it would be quite likely that you’d say that A has (at least) two factors B and C. But if A turned out to be prime, then you’d have been wrong as A would in fact only have one factor (or perhaps no factors).

July 11th, 2011 at 5:02 am

They way out of this is to say that they are all associated with non-composite numbers.

Taking this a stage further, I can’t help but think of a prime as having no factors. But then 1 would be a prime again. So the use of the word “factors” should be avoided when defining primes – it’s ambiguous.

The fact is that the definition of a prime has is (nowadays) chosen to be a useful one – if that means explicitly excluding 1, then so be it – the definition of a prime doesn’t need to be super slick. So “a prime is a whole number greater than 1, that can only be exactly divided by itself (and 1)”, pretty well covers it.

I don’t even like phrases like “divided by 1″. Division connotes breaking a number into smaller parts whose sizes are > 1. So 6 = 2*3 is fine by me, but 6 = 6*1 doesn’t imply division to my mind.

And, “a composite number is a whole number that isn’t a prime or 1″, is about as straightforward and compact as you can get.

OTOH, defining a composite to be a number that has at least two or more prime factors has many problems. Is 1 a factor? Are the primes distinct? e.g. 4 = 2*2, is only divisible by the prime 2.

July 13th, 2011 at 10:49 am

Stop correcting people, saying whats wrong, saying you don’t know or something that has to relation to this subject. Just try and get the answer.

July 13th, 2011 at 11:08 am

I think I’ve got it – it’s not the answer but.. so what.

All the letters slightly look like each other, if you change a little bit of it.

e.g = B = E(if you add a bit at the end of E).

C = G/Q (again, if you add a bit on to G/Q)…

And so on..

July 13th, 2011 at 11:10 am

Shaz; I think you’re right!

July 13th, 2011 at 11:10 am

i dont know

July 13th, 2011 at 3:18 pm

Hi I. To whom is you comment addressed and how does it have any relation the question?

Hi Shaz and Fiona. The poster explicitly indicated that that type of answer wasn’t welcome.