NEED HELP WITH HOMEWORK No largest prime number

[msminnie]

I am doing a homework assignment for my philosophy class. He wants us to do a simple assignment that verifies the proof that there is no largest prime number. He claims it has to be where someone states to me "there is a largest prime number" I would say that is not true it is infinity and here is why. He told us we can look it up on the internet or ask someone who is a math major or math genious or even another philosopher. This is due tomorrow October 3, 2007 CAN SOMEONE please send me the information that is correct. He claims it is simple and easy and it has a forumula to prove that it can not be done. SOMEONE out there in math land HELP PLEASE you can send me a email directly to min5453@yahoo.com
Thank you so much in advance.

 

[cristo]

There are homework sections in which you should post your questions in future; especially since this is clearly not a physics question! You should also not double (or quadruple) post your questions. Doing this does not make people respond faster. Incidentally, forum rules state that you must show your work before you obtain any help here; it's not our fault that you left your homework to the last minute is it?

Do you have any ideas how to proceed? Try taking the statement and deriving a contradiction.

 

[msminnie]

thanks so much for your help, and for guiding me on the rules here. And the homework was given to us today. I have gotten several formulas off the internet but I know it is not what he is looking for. Also, I know some very smart physics majors who would have no problem answering this question i am sure if I could reach them, so I did not think I needed to limit this question to one section, and because I have never used this site before, I had no idea until you stated here that it does multiply in all areas at once. I thought it went to individual expertise. I do appreciate your feedback even if it was not able to help me with my homework. Sorry for the inconvenience.

 

[cristo]

That's fine. I see that someone's moved your posts now. Have you studied any proof by contradiction? If your teacher says you can find the solution off the internet, then have you tried any google searches?

 

[msminnie]

are all my posts removed, I can see I have probably upset a lot of people "ouch" sorry. I had no idea, I was just looking for homework help lol. Anyway yes I have, I found a bunch of stuff. I went to class today, and brought him what I had found. he said that was way more than I needed it was not that complicated. I asked some of the students how they had found some of there's and they said "asked friends who are math teachers" etc. How my philosophy teacher explained it to me was if you for instance told me there was a largest prime number, I would be able to show you that 1 can not be divded into 1 etc and have a definition of why. I am having trouble finding something really that simple that is the truth, here is the closest I have gotten.

There cannot be a largest prime number.

Why? Because if you made the assumption that you can list all the prime numbers with a finite or including the largest number, than any number great than 1 and not included on the list must divide by a number on the list. Then if you took all the numbers on the list,
Multiplied them together and added one to the total, you will find the resulting number does not divide by any of the numbers on your list, therefore it is prime. But because of
this, your original list is flawed because your list had all the prime numbers listed, so such a starting point cannot exist. Because of that there is no largest prime number.

Example:

Let’s say that 5 was the largest prime number.
2x3x5=30
30+1=31
31 is a prime number so your original formula is in error. If you multiply 2x3x5x31=930
930+1=931 which is prime so once again your original formula is in error.

Therefore you cannot have a starting list that includes the largest prime number, therefore it cannot exist.
I know that is close but I also know it is not exactly on the money as I know my teacher and he lives eats and breaths philosophy and so he has a certain way for EVERYTHING lol.
I do appreciate you taking the time to even talk to me, but I guess I will continue on Google, I am all goggled out lol.

 

[cristo]

Your example is a special case of the proof I'd give. If we assume a finite set of prime numbers, then we can call them p1, p2,..., pn, where pn is the largest prime number. Now construct the number q, say, where q=(p1*p2*p3*...*pn)+1. Now, this is clearly not divisible by any of the prime numbers in our finite set. But a prime number is a number into which no prime numbers divide evenly. So, either q is a prime number, or it has a prime factor that is not in our finite set. Either way, we have a prime number that is not in our set, and so the original statement is false.

 

[msminnie]

Oh my goodness thank you so much Cristo. I will print mine out and then add some of yours. I feel much better about my answer now that yours matches. See it was not such a total loss to send it to physics forum huh? lol

Thanks so much again. You have a great night
Corinne