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)
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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!
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Re: Rare Entries XVII  Miscellaneous (history)
Thanks for fixing this, by the way.
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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)
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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.
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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.
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