Number 1
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Full Definition: A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number.
Quote: RomesGiven the definition of a prime number is: "A prime number (or a prime) is a natural number greater than 1..." then no, 1 is not a prime number by definition. Therefor it's also not the first prime number.
Full Definition: A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number.
Why is that better than this definition?: "A prime number is generally defined to be any positive number that has exactly two distinct positive integer divisors (the divisors being 1 and the number itself)"?
Because my definition is from Google/Wikipedia (which is more exact than Encyclopedia Britannica).Quote: AyecarumbaWhy is that better than this definition?: "A prime number is generally defined to be any positive number that has exactly two distinct positive integer divisors (the divisors being 1 and the number itself)"?
Doesn't matter, 1 isn't prime under any of those definitions. 1 has exactly one distinct integer factor, not two.Quote: AyecarumbaWhy is that better than this definition?: "A prime number is generally defined to be any positive number that has exactly two distinct positive integer divisors (the divisors being 1 and the number itself)"?
Also, there's a big difference between questioning whether a premise is true under a definition, and questioning the validity of the definition. Under the definition of prime, the number 1 is not prime. Neither is the letter R. Similarly, under the definition of "vowel", neither 1 nor R are vowels.[1]
If you want to question the validity of the definition of prime, you'll need to explain why -- but expect to be refuted by literally thousands of years of mathematical thought.
[1]The definition of vowel is a sound made only by the vocal cords, that is, without the tongue touching the teeth, palate or lips. Try making an "R" sound without your tongue touching your teeth. It sounds pretty funny.
No it's not -- Euclid's Elements was written about 2300 years ago.Quote: AyecarumbaI wouldn't go so far as to say "thousands of years". 1 as a prime appeared in scholarly texts as recently as 1999. Excluding it from the list of primes in order to fit the use of prime factorization is a relatively recent innovation (like since the mid 1970's).
Try this, 'which was cuter, her boobs or her buns?'
I'm trying to be 'more inclusive' in the question, I have fallen short, again ;-)
Post as is, I may edit later....
Quote: teliotThe fundamental theorem of arithmetic states that every positive energy is a unique product of primes. That would be out the window if one was a prime. This question about one is not really open to debate period anymore then the atomic formula for various molecules is open to debate. Primes are atoms.
Looks like you got snagged by autocorrect. But it is kind of cool to think of integers as energies.
https://youtu.be/NRE3UcKNYoE
Warning -- do not keep badgering teliot. He is liable to snap in two or three more posts.
I like this analogy...
https://www.quora.com/Why-is-1-not-a-prime-number-1Quote: https://www.quora.com/Why-is-1-not-a-prime-number-1Let us say, there is a tournament in which there are 10 teams and everyday, any two teams are selected by lottery and they play each other. The tournament lasts for a month and after a month some teams have played 1 match, some have played 2 matches or more and some didn't get a chance to play any.
Now, let us say, there is a category for undefeated teams throughout the tournaments, and another category for defeated ones but, since there might be few teams which didn't even play, should they be considered undefeated or defeated? So, the rule is added that these categories will be applicable to the teams who have played at least one match.
Similar, is the concept of prime numbers. Prime numbers, as a concept, are a special type of natural numbers which are not products of other natural numbers. Example - 6 is not prime number since it is product of 3 and 2. By this logic 1 automatically becomes prime since it is the smallest natural number. So, should it be considered prime number or not? Why not state the rule to be applicable after the smallest natural number. That is why 1 is not a Prime Number.
