Rare Entries XVII - Miscellaneous (history)

Can you identify a station from just a paving slab? Sadly, some people can

Do you think this is too easy or too hard?

Poll ended at 03 Jun 2016, 17:35

Way too easy
0
No votes
Too easy
0
No votes
Just Right
2
100%
Too hard
0
No votes
Way too hard
0
No votes
 
Total votes: 2

User avatar
Tube Geek
The Twilight Zone
Posts: 3609
Joined: 31 Mar 2016, 19:06
Location: BS20 or BS3
Contact:

Re: Rare Entries XVII - Miscellaneous (history)

Post by Tube Geek » 05 Jun 2016, 20:08

But (at the moment) it isn't.

The definition of a prime number is 'a number that has 2 factors - itself and1'. But as for 1, itself and 1 are the same thing, it has only 1 factor, rather than 2. Therefore it is not a prime. :D
Personal Best - 264 Stations in 19 hours 37 minutes.

Bristol City fan through and through - COME ON YOU REDS Andi Weimann is my dad

User avatar
The Orange One
All Zones
Posts: 2597
Joined: 18 Jun 2013, 14:23
Location: Three metres due south of you. Wherever you are.
Contact:

Re: Rare Entries XVII - Miscellaneous (history)

Post by The Orange One » 06 Jun 2016, 01:39

Actually (adapting the definition for rings), an integer p is prime if it satisfies the following:

1) p is not zero
2) p is not a unit - i.e. there is no integer q such that pq=1
3) If p divides ab, then p divides a or p divides b - where a and b are both integers.

A similar concept to primality is irreducibility. An integer p is irreducible if:

1) p is not zero
2) p is not a unit - i.e. there is no integer q such that pq=1
3) If p=ab, with a and b both integers, then either a or b is a unit.

So, under the definition:

• 0 is not prime (it is zero)
• 1 is not prime (it is a unit)
• 2 is prime
• -2 is prime
• 4 is not prime (4 divides 6 x 2 = 12, but does not divide either 6 or 2)

to name a few examples!

In the integers, primes and irreducibles are one and the same. In all rings, p is prime implies p is irreducible, but there are rings where p can be irreducible but not prime!
All London buses: 23 hours 25 minutes (with Adham, David, Josh and Tangy)
Holds some alternative challenge records. Not sure which ones.
20½ Random 15 challenges: 01:58:48 best
That guy who runs those Twitter polls about tube stations and London Boroughs.

User avatar
tractakid
The Twilight Zone
Posts: 3215
Joined: 15 Nov 2011, 20:04
Location: Milton Keynes

Re: Rare Entries XVII - Miscellaneous (history)

Post by tractakid » 06 Jun 2016, 16:41

Thanks for fixing this, by the way.
*insert boasting about notable tube accomplishments here*

A Challenge
The Twilight Zone
Posts: 3998
Joined: 24 Jan 2015, 07:57
Location: London Waterloo

Re: Rare Entries XVII - Miscellaneous (history)

Post by A Challenge » 07 Jun 2016, 18:44

Yet I can find four factors for 2, thereby disrupting the construct of Prime Numbers:

1, 2, -1, -2 (1*2=2 and -1*-2=2)
Tumbleweed and former Nimbleweed Scorekeeper

Winner of Gumbleweeds V, VI + XI, Nimbleweeds I, III - IX + XIV and (joint with GuyBarry) winner of Timesnap

And most importantly, Former leader of Tumbleweed, and first person to 250,000

User avatar
Tube Geek
The Twilight Zone
Posts: 3609
Joined: 31 Mar 2016, 19:06
Location: BS20 or BS3
Contact:

Re: Rare Entries XVII - Miscellaneous (history)

Post by Tube Geek » 07 Jun 2016, 18:56

OK, using negative number means there are no prime numbers at all!

1x2=2, -1x-2=2
1x3=3, -1x-3=3
1x5=5, -1x-5=5
etc. etc.
Personal Best - 264 Stations in 19 hours 37 minutes.

Bristol City fan through and through - COME ON YOU REDS Andi Weimann is my dad

User avatar
The Orange One
All Zones
Posts: 2597
Joined: 18 Jun 2013, 14:23
Location: Three metres due south of you. Wherever you are.
Contact:

Re: Rare Entries XVII - Miscellaneous (history)

Post by The Orange One » 07 Jun 2016, 19:28

No, that two factors rule is rubbish. I've told you, if it's not zero or a unit (1, -1) and the condition holds it's a prime. That's the definition.
All London buses: 23 hours 25 minutes (with Adham, David, Josh and Tangy)
Holds some alternative challenge records. Not sure which ones.
20½ Random 15 challenges: 01:58:48 best
That guy who runs those Twitter polls about tube stations and London Boroughs.

Post Reply