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.
Rare Entries XVII  Miscellaneous (history)
Re: Rare Entries XVII  Miscellaneous (history)
Personal Best  264 Stations in 19 hours 37 minutes.
Bristol City fan through and through  COME ON YOU REDS Andi Weimann is my dad
Bristol City fan through and through  COME ON YOU REDS Andi Weimann is my dad
 The Orange One
 All Zones
 Posts: 2598
 Joined: 18 Jun 2013, 14:23
 Location: Three metres due south of you. Wherever you are.
 Contact:
Re: Rare Entries XVII  Miscellaneous (history)
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!
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.
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.
Re: Rare Entries XVII  Miscellaneous (history)
Thanks for fixing this, by the way.
*insert boasting about notable tube accomplishments here*

 The Twilight Zone
 Posts: 4006
 Joined: 24 Jan 2015, 07:57
 Location: London Waterloo
Re: Rare Entries XVII  Miscellaneous (history)
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)
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
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
Re: Rare Entries XVII  Miscellaneous (history)
OK, using negative number means there are no prime numbers at all!
1x2=2, 1x2=2
1x3=3, 1x3=3
1x5=5, 1x5=5
etc. etc.
1x2=2, 1x2=2
1x3=3, 1x3=3
1x5=5, 1x5=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
Bristol City fan through and through  COME ON YOU REDS Andi Weimann is my dad
 The Orange One
 All Zones
 Posts: 2598
 Joined: 18 Jun 2013, 14:23
 Location: Three metres due south of you. Wherever you are.
 Contact:
Re: Rare Entries XVII  Miscellaneous (history)
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.
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.