Why is 1 not considered a prime number? It meets the requirement of being only divisible by itself and 1.
i dont see any problem with god given axioms espcecially when "god" itself is man made definition.matt grime said:this kind of question, to my mind, fits in with the ones i get asked a lot like: but why do groups satisfy those 4 axioms. it's almost as if people believe that the axioms we choose are somehow god given, carved in some stone and we must make sense of these mysterious rules that came from nowhere when in fact they are man made.
neurocomp2003 said:no its just if 1 was a prime number then every other number would be a composite and prime which would defeat the purpose of calling it a prime list.
includes this condition, thus effecting parsimony.n is prime iff n has exactly two factors
Why?WeeDie said:I think it's kinda stupid not to see 1 as a prime.
From the beginning of the 19th century, I would believe, since that was approximately the time when mathematicians realized the need to take more care in what definitions they chose to use.Daminc said:How long has 1 not been considered a prime?
WeeDie said:arildo: because the characteristic that makes primes interesting is the fact that they are only devisable by themself and 1. The number 1 serves this condition so I see no need to exclude 1 from the definition of primes. In fact, one might get off on a bad start if one were to exclude 1 and graph primes, in order to find connections between primes and other number series.
I assume that was directed at me.matt grime said:that isn't the proper definition of prime, it is your vwersin of the definition. and in any case it is better stated as "has exactrly two positive factors" since this precludes 1 (and even characterizes primes in the integers as well as the naturals).
WeeDie said:I think it's kinda stupid not to see 1 as a prime.
matt grime said:it is better stated as "has exactrly two positive factors" since this precludes 1 (and even characterizes primes in the integers as well as the naturals).
matt grime said:erm yes i did just implicitly state the -7 is a prime in Z, and that is perfectly correct and is what the real definition of prime in an arbitrary ring tells us about primes in Z.
HallsofIvy said:Do you consider the Fundamental Theorem of Arithmetic:
"Every positive integer can be written as a product of powers of primes in exactly one way"
Calling 1 a prime would make it untrue since then we could write 6= 1*2*3 or 6= 12*2*3 or...