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Old 2019-04-15, 13:55   #23
retina
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Quote:
Originally Posted by MathDoggy View Post
It is impossible because we constructed an arbitrary number Q which is the product of the finite list of the twin primes and adding 1 to the product
2×3×5×7×11×13+1 = 59×509

And if 2 isn't a twin prime then 3×5+1 = 2×2×2×2

Either way there are always possible divisors that aren't in the original set of primes you multiplied together.

Last fiddled with by retina on 2019-04-15 at 13:55
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Old 2019-04-15, 14:05   #24
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Originally Posted by MathDoggy View Post
It is impossible because we constructed an arbitrary number Q which is the product of the finite list of the twin primes and adding 1 to the product
This is not a reason. You have constructed a number Q which is not divisible by your list of twin primes, and then you assume it must be divisible by a twin prime. You have no justification for the belief that Q must be divisible by a twin prime; in fact, you have constructed Q specifically such that it is NOT divisible by a twin prime, and then you claim a contradiction by just saying Q is divisible by a twin prime.

Your Q is divisible by 2 (do you see why?). All other claims about properties of Q's factors must be proven. Prove your claim.
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Old 2019-04-15, 14:46   #25
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I will try to fix the proof once again
Assume that there exist a finite amount of twin prime numbers.
Then we can construct a list, which in this case will be S, S= A1,A2,A3,A4...An
Let P be the product of all twin prime numbers in S, P= A1*A2*A3*A4..An
Let Q=P+1
If Q is a twin prime number then S is not complete
If Q is composite then some prime factor p divides Q, if this factor p were in our list S then it would divide P, but p divides P+1=Q. If p divides P and Q then p would have to divide the difference of the two numbers, which is (P+1)-P or just 1. Since no twin prime number divides 1, p can not be on the list. This means that at least one twin prime number exists
beyond those in the list.

Last fiddled with by MathDoggy on 2019-04-15 at 15:30
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Old 2019-04-15, 14:55   #26
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Quote:
Originally Posted by MathDoggy View Post
I will try to fix the proof once again
Assume that there exist a finite amount of twin prime numbers.
Then we can construct a list, which in this case will be S, S= A1,A2,A3,A4...An
Let P be the product of all twin prime numbers in S, P= A1*A2*A3*A4..An
Let Q=P+1
If Q is a twin prime number then S is not complete
If Q is composite then some prime factor p divides Q, if this factor p were in our list S then it would divide P, but p divides P+1=Q. If p divides P and Q then p would have to divide the difference of the two numbers which, which is (P+1)-P or just 1. Since no twin prime number divides 1, p can not be on the list. This means that at least one twin prime number exists
beyond those in the list.
Q is divisible by two. See my previous post.

Also, p doesn't have to be a twin prime, it can be some other prime, like 2 for example.

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Old 2019-04-15, 15:03   #27
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Quote:
Originally Posted by MathDoggy View Post
I will try to fix the proof once again ... Since no twin prime number divides 1, p can not be on the list.
Looking good to here.

Quote:
Originally Posted by MathDoggy View Post
This means that at least one twin prime number exists beyond those in the list.
Ooops. This means at least one prime (p) exists beyond those in the list. But why must it be a twin prime?
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Old 2019-04-15, 15:03   #28
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What do I have to fix, retina
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Old 2019-04-15, 15:16   #29
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Quote:
Originally Posted by wblipp View Post
Looking good to here.



Ooops. This means at least one prime (p) exists beyond those in the list. But why must it be a twin prime?
I am thinking
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Old 2019-04-15, 15:43   #30
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Ooops. This means at least one prime (p) exists beyond those in the list. But why must it be a twin prime?[/QUOTE]

There is no such implication
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Old 2019-04-15, 16:02   #31
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Default Another attempt with an alternate method

Just ignore this

Last fiddled with by MathDoggy on 2019-04-15 at 16:13
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Old 2019-04-15, 16:11   #32
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Quote:
Originally Posted by MathDoggy View Post
A factorial number x! of a positive integer is divisible by every integer from 2 to x, inclusive. Hence, x!+1 is either a twin prime number or divisible by a prime larger than x. In either case, for every positive integer x, there is a least one twin prime bigger than x.
The conclusion is that there exist infinitely many twin prime numbers.
How does "divisible by a prime larger than x" show that there is a twin prime bigger than x?

Last fiddled with by CRGreathouse on 2019-04-15 at 16:18
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Old 2019-04-15, 16:22   #33
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Should I quit to try to fix the proof?
It is because nothing is working

Last fiddled with by MathDoggy on 2019-04-15 at 16:23
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