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pondzo
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just a quick question. why is two prime if its has factors, (1+i) and (1-i)?
pondzo said:just a quick question. why is two prime if its has factors, (1+i) and (1-i)?
mrnike992 said:I'd also like to point out that if we include prime numbers, then we could (correct me if I'm mistaken) also include [itex] (1 + i^5)(1- i^5) [/itex] and so on, leaving us with an infinite number of factors, which is impractical, so we eliminate the obvious and infinite possibilities, to leave us with only natural numbers.
pondzo said:Then shouldn't the 'ultimate goal' be to find a formula that produces all primes in Z(i) and not Z? and furthermore, would a search for such a formula for all primes in Z be futile, as the sequence of primes 2,3,5,7,11,13... should be the sequence Z[itex]\bigcap[/itex]Z(i), namely 3, 7, 11, 19... (but then i guess this gets back to what you said about whether you are talking of primes in Z or in Z(i) or which ever ring).
pondzo said:Then shouldn't the 'ultimate goal' be to find a formula that produces all primes in Z(i) and not Z? and furthermore, would a search for such a formula for all primes in Z be futile, as the sequence of primes 2,3,5,7,11,13... should be the sequence Z[itex]\cap[/itex]Z(i), namely 3, 7, 11, 19... (but then i guess this gets back to what you said about whether you are talking of primes in Z or in Z(i) or which ever ring).
pondzo said:ahhh i see, why do you think this was the orginal definition? wouldn't it makes sense to include the complex numbers? so gaussian primes are then considered the 'primes'.
Two is a prime number because it can only be divided evenly by itself and one. It has no other factors besides one and itself, making it a prime number.
The only factors of two are one and two. This is because two is a prime number, meaning it can only be divided evenly by itself and one.
A prime number is a number that is only divisible by one and itself. To determine if a number is prime, you can try dividing it by every number from one to the number itself. If it can only be divided evenly by one and itself, then it is a prime number.
Exploring factors of numbers can help us understand the properties and patterns of numbers. It also allows us to identify prime numbers, which have important applications in mathematics and cryptography.
Yes, most numbers have more than two factors. Only prime numbers have exactly two factors (one and itself). Numbers with more than two factors are called composite numbers.