#1
Alright I'm really tired and having a hard time with some (math my worst subject), please help if you can.

8. Does a prime multiplied by a prime ever result in a prime? Does a nonprime multiplied by a nonprime ever result in a prime? Always? Sometimes? Never? Explain your answers

Now for this one I have already checked and have gotten never for both questions, can someone maybe double check me? What I'm having trouble doing, especially right now, is explaining myself.

11. Are there infinitely many natural numbers that are not prime? If so, prove it.

This one is bugging me to for some reason.

Thanks in advance.
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Viking fact no. 3: Vikings drank mead.
Viking fact no. 4: One of your ancestors are likely to have been raped by a viking.
#2
Quote by The Virtuoso


11. Are there infinitely many natural numbers that are not prime? If so, prove it.



There are an infinite number of numbers, so there has to be an infinite number of natural numbers that are not prime

EDIT:

The oldest known proof for the statement that there are infinitely many prime numbers is given by the Greek mathematician Euclid in his Elements (Book IX, Proposition 20). Euclid states the result as "there are more than any given [finite] number of primes", and his proof is essentially the following:

Consider any finite set of primes. Multiply all of them together and add one (see Euclid number). The resulting number is not divisible by any of the primes in the finite set we considered, because dividing by any of these would give a remainder of one. Because all non-prime numbers can be decomposed into a product of underlying primes, then either this resultant number is prime itself, or there is a prime number or prime numbers which the resultant number could be decomposed into but are not in the original finite set of primes. Either way, there is at least one more prime that was not in the finite set we started with. This argument applies no matter what finite set we began with. So there are more primes than any given finite number.

wikipedia beeyotch!
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Last edited by metacarpi at Sep 19, 2007,
#3
Thanks man, that's what I thought but I'm just really tired right now, but the thing is he told us to explain it carefully, so you think you could help me explain why?
Quote by Senor Kristian
Viking fact no. 1: Viking helmets did not have horn.
Viking fact no. 2: Vikings tobogganed on their shields into battle.
Viking fact no. 3: Vikings drank mead.
Viking fact no. 4: One of your ancestors are likely to have been raped by a viking.
#4
8. Prime numbers, by definition, can only be divided by themselves and 1. Therefore, if you multiply a prime number (a) by another prime number (b), not only is the new number divisible by 1 and itself, it is divisible by a and b, therefore is no longer a prime number.

Same goes for non prime multiplied by non prime.
#5
Quote by The Virtuoso

8. Does a prime multiplied by a prime ever result in a prime? Does a nonprime multiplied by a nonprime ever result in a prime? Always? Sometimes? Never? Explain your answers


the idea of a prime number is that it is only divisible by itself and one, thus any multiplication between numbers that arent 1, will result in a "nonprime" number
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#6
Quote by The Virtuoso
Alright I'm really tired and having a hard time with some (math my worst subject), please help if you can.

8. Does a prime multiplied by a prime ever result in a prime? Does a nonprime multiplied by a nonprime ever result in a prime? Always? Sometimes? Never? Explain your answers

Now for this one I have already checked and have gotten never for both questions, can someone maybe double check me? What I'm having trouble doing, especially right now, is explaining myself.

11. Are there infinitely many natural numbers that are not prime? If so, prove it.

This one is bugging me to for some reason.

Thanks in advance.


8. i got never and never
9. what the other guy said, theres an infinite amount of numbers so there has to be infinite not prime numbers
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#7
Thanks guys, yeah I've thought about these but I'm just feeling so woozy right now that I'm confusing myself. Thanks again.
Quote by Senor Kristian
Viking fact no. 1: Viking helmets did not have horn.
Viking fact no. 2: Vikings tobogganed on their shields into battle.
Viking fact no. 3: Vikings drank mead.
Viking fact no. 4: One of your ancestors are likely to have been raped by a viking.
#8
Quote by The Virtuoso
Thanks man, that's what I thought but I'm just really tired right now, but the thing is he told us to explain it carefully, so you think you could help me explain why?


check my edit
Quote by GLP_Arclite
Pooping is well good though, to be fair.


I've got a handle on the fiction.

I'm losing my grip, 'cos I'm losing my fingers.
#9
Quote by The Virtuoso
8. Does a prime multiplied by a prime ever result in a prime? Does a nonprime multiplied by a nonprime ever result in a prime? Always? Sometimes? Never? Explain your answers


well let's say you take two prime numbers, 7 and 17. multiplied, they produce 119. 119 can't be prime because 7x17 are it's factors. any product of any multiplication problem that only involves whole numbers can't be prime . the same rule applies to non prime numbers

EDIT: what they said
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#10
You guys act fast , yet again the pit saves me, kudos.
Quote by Senor Kristian
Viking fact no. 1: Viking helmets did not have horn.
Viking fact no. 2: Vikings tobogganed on their shields into battle.
Viking fact no. 3: Vikings drank mead.
Viking fact no. 4: One of your ancestors are likely to have been raped by a viking.
#11
Quote by The Virtuoso
You guys act fast , yet again the pit saves me, kudos.


It's what we're here for!

Damn, I wish I was on the pit when I was at school.... it seems like nobody on here ever does their own homework!
Quote by GLP_Arclite
Pooping is well good though, to be fair.


I've got a handle on the fiction.

I'm losing my grip, 'cos I'm losing my fingers.
#12
No-one's offered a proper proof for infinite non-primes, so i'll give you a simple one.

The 2 times table. There are infinitely many numbers you can times by two, and none of these numbers will be prime as they are a multiple of two, hence there are inifinitely many non primes.
#13
Wow, thanks guys again, I suck at math compared to you guys...I'll just have to try a little harder next time.

P.S. The Pit is a godsend
Quote by Senor Kristian
Viking fact no. 1: Viking helmets did not have horn.
Viking fact no. 2: Vikings tobogganed on their shields into battle.
Viking fact no. 3: Vikings drank mead.
Viking fact no. 4: One of your ancestors are likely to have been raped by a viking.