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So is it?
Something I have been thinking about lately.
Something I have been thinking about lately.
JasonRox said:There is no formula for finding primes yet? Right?
It´s actually so simple that I can post it here:James R said:Your question doesn't seem to make sense.
Do you mean "Is there a finite number of prime numbers?"
If so, the answer is no. It is easy to prove that there are infinitely many primes.
Formulas in the sense of "prime(n) = ... " or algorithms to determine it (the latter is trivial)? What do you mean by saying they are not usefull? Can you give links or names?jcsd said:There are formulas that explicitly give the nth prime, none of them are that useful though.
Atheist said:Formulas in the sense of "prime(n) = ... " or algorithms to determine it (the latter is trivial)? What do you mean by saying they are not usefull? Can you give links or names?
Atheist said:@StatusX: I don´t really see a problem with my post although I have to admit that I took that out of my head and didn´t bother to look up a more elegant proof somewhere. I will consider rephrasing what I wrote.
Atheist said:>> in other words it has divisors other than 1 and X+1
Not if my list of primes I start with is complete which was the assumtpion I started from. However, I realize how and why my post was misleading and/or improperly written.
shmoe said:Your conclusion in step 3 is false. For example if our list of primes is 2,3,5,7,11, 13, then X+1=3031=59*509, in other words it has divisors other than 1 and X+1. The consequence of how X is made from our list of primes is that X+1 has a prime divisor that is not on our list, and hence we get another prime.
Alkatran said:2*3*5*7*11*13 + 1 = 30 031
Alkatran said:Proof:
All variables are whole numbers here
x*y mod x = 0
y*x mod x = 0
y=z*t
x*z*t mod x = 0
X times any number mod x is 0 thus X times the product of any numbers mod X is 0 thus X times the product of any numbers plus 1 mod x = 1 if X is greater than 1
x*z*t + 1 mod x = 1
x*z*t + 1 mod z = 1
x*z*t + 1 mod t = 1
You can say x is 2, z is 3, and t is 5 if you like.
shmoe said:Yes, I typo'd a zero into oblivion, thanks for the correction.
I don't see how this shows you get 30031 though. It will only show 2*3*5*7*11*13+1 is congruent to 1 mod 2, 3, 5, 7, 11, and 13. There are infinitely many numbers that satisfy this. (even better-there are infinitely many primes which satisfy this)
I'll need to think of how to show it's not divisible by any others...
Alkatran said:The proof shows that
(2*3*5*7*11*13 + 1) mod (2, 3, 5, 7, 11, or 13) = 1
IE that it isn't divisible by any of them.
Alkatran said:I'll need to think of how to show it's not divisible by any others...
ZeAsYn51 said:Saying that you'll run out of primes is like saying that you'll run out of multiples of two, or multiples of seven.
ZeAsYn51 said:I believe that primes are just as infinite as numbers themselves because just as multiples of two and multiples of seven are in the very structure of our number system, so are primes.
ZeAsYn51 said:Well, tell me exactly how any "set" (multiples of two,primes, etc.) of numbers is less than infinite if numbers themselves are infinite? That was my point.
ZeAsYn51 said:Well, tell me exactly how any "set" (multiples of two,primes, etc.) of numbers is less than infinite if numbers themselves are infinite? That was my point.
ZeAsYn51 said:Okay, maybe I didn't use the best wording, but my point is that there is no proof that primes are finite in number and I do not believe there can be such a proof.
ZeAsYn51 said:Okay, Shmoe. I did go back and look at Atheists posts, but I didn't really find anything useful. I was, however, looking at what you just described to me (post #30) earlier today, but I'm not quite sure I understand it. Could you please take a few mins to explain it to me.