## 1310: Goldbach Conjectures

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Sheikh al-Majaneen
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### 1310: Goldbach Conjectures

Hovertext: The weak twin primes conjecture states that there are infinitely many pairs of primes. The strong twin primes conjecture states that every prime p has a twin prime (p+2), although (p+2) may not look prime at first. The tautological prime conjecture states that the tautological prime conjecture is true.
Last edited by Sheikh al-Majaneen on Mon Dec 30, 2013 5:34 am UTC, edited 7 times in total.

rhomboidal
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### Re: 1310: Goldbach Conjectures

"EVERY ODD NUMBER IS PRIME." I wonder if this is true of people, too.

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### Re: 1310: Goldbach Conjectures

Count me as one of the people who didn't get it, though I did catch that they go from painfully obvious but useless observations to definitive but blatantly made-up statements. I guess the joke is that the "strength" of a conjecture doesn't necessarily entail or imply being correct. (And I do get the jokes in the mouseover.)
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### Re: 1310: Goldbach Conjectures

Gödel, Escher, Bach has a joke about "Goldbach variations" which is somewhat similar to this. For example, "every even number is the difference of two primes".

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### Re: 1310: Goldbach Conjectures

The Weak Gold-Bug Conjecture states that for sufficiently large r, a circle of radius r encloses T where T is pirate treasure.

The Extremely Weak Gold-Bug Conjecture states that pirates used old car tires as currency.
I'm going to step off the LEM now... here we are, Pismo Beach and all the clams we can eat

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ManaUser
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### Re: 1310: Goldbach Conjectures

As I understand it, the terms strong or weak relate to the fact that the strong conjecture, if proven would also prove the weak one, but not the reverse. This pattern holds true on the right side of this comic, but kind of falls apart on the left... I'm not sure if that's part of the joke or what, to be honest.

da Doctah
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### Re: 1310: Goldbach Conjectures

bitwiseshiftleft wrote:Gödel, Escher, Bach has a joke about "Goldbach variations" which is somewhat similar to this. For example, "every even number is the difference of two primes".
I thought it was "every even prime is the sum of two odd numbers".

Farabor
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### Re: 1310: Goldbach Conjectures

I find the comic mildly amusing, but a logical fail, since the logical chain is "stronger being true automatically implies weaker being true".

bondsbw
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### Re: 1310: Goldbach Conjectures

Farabor wrote:I find the comic mildly amusing, but a logical fail, since the logical chain is "stronger being true automatically implies weaker being true".

Actually I think it does if you allow the blasphemy of counting 1 as prime... ok, let's give the comic a bit of leeway there, otherwise I wouldn't have any reason to post the following:

• If there are no numbers greater than 7, then every odd ("1", "3", "5", "7") would be prime.
• if every odd number were prime, then every even number n over 2 would be the sum of two primes, namely (n-1) and "1".
• If every even number over 2 is the sum of two primes, then every odd number n over 5 is the sum of "3" and any even number (which is already the sum of 2 primes).
• Given all those odds over 5 and evens over 2, you can create any number over 7.
• Given that you can create any number over 7, they keep going.

Envelope Generator
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### Re: 1310: Goldbach Conjectures

But you forgot
• Given that there are no numbers greater than 7, every number greater than 7 is the sum of two numbers
I'm going to step off the LEM now... here we are, Pismo Beach and all the clams we can eat

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### Re: 1310: Goldbach Conjectures

You don't need to count 1 as prime, because 4=2+2 and you get the rest of the evens with n-3 and 3.
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edvimsed
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### Re: 1310: Goldbach Conjectures

Up to 1 being prime, the strong twin prime conjecture is the same as the very strong Goldbach conjecture. The proof goes by induction. (Goldbach considered 1 prime, because then 2 = 1+1, so that we don't need the stupid lower bounds on the conjectures.)

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### Re: 1310: Goldbach Conjectures

gmalivuk wrote:You don't need to count 1 as prime, because 4=2+2 and you get the rest of the evens with n-3 and 3.

MDenham
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### Re: 1310: Goldbach Conjectures

Envelope Generator wrote:But you forgot
• Given that there are no numbers greater than 7, every number greater than 7 is the sum of two numbers
And the logical extension of that:
• Given that there are no numbers greater than 7, every number greater than 7 is the sum of of a prime number and a bobcat.

Flumble
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### Re: 1310: Goldbach Conjectures

How could you prove things about numbers greater than 7 when you assume there are no numbers greater than 7?

Actaeus wrote:
gmalivuk wrote:You don't need to count 1 as prime, because 4=2+2 and you get the rest of the evens with n-3 and 3.

There is no 12, for there are no numbers above 7.

dalcde
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### Re: 1310: Goldbach Conjectures

Flumble wrote:How could you prove things about numbers greater than 7 when you assume there are no numbers greater than 7?

It's vacuously true.

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### Re: 1310: Goldbach Conjectures

Once I learned what the Goldbach conjectures were, I thought this was funny.

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### Re: 1310: Goldbach Conjectures

The hovertext missed out the Evil Twin Primes Conjecture...
xtifr wrote:... and orthogon merely sounds undecided.

Klear
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### Re: 1310: Goldbach Conjectures

orthogon wrote:The hovertext missed out the Evil Twin Primes Conjecture...

Every prime has a twin which has a mustache?

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### Re: 1310: Goldbach Conjectures

Flumble wrote:How could you prove things about numbers greater than 7 when you assume there are no numbers greater than 7?

http://xkcd.com/704/
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### All odd numbers are prime.

A bit of math humor that I haven't seen for some years is the list of proofs that "All odd numbers are prime." Each proof showed the way that a member of a specific profession (or other group of people) would prove it.

Thus, the marketer and/or politician would observe that 3 is prime, 5 is prime, 7 is prime, 11 is prime, 13 is prime, 17 is prime, and that should be enough to convince anyone.

The engineer would observe that 3 is prime, 5 is prime, 7 is prime, 9 is prime, 11 is prime; yup, it looks like they're all prime.

The statistician would say that 3 is prime, 5 is prime, 7 is prime, 9 is a sampling error, 11 is prime, 13 is prime; it's obvious that they're all prime.

The Christian theologian would say that 3 is prime; that proves it. (A Muslim would use 5, then they'd debate and kill each other endlessly about which number is the correct proof.)

There were a lot more, but I've forgotten most of them. I wonder if they're collected somewhere on the Web ...

solune
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### Re: All odd numbers are prime.

jc wrote:There were a lot more, but I've forgotten most of them. I wonder if they're collected somewhere on the Web ...

I had the computer scientist: "3 is prime, 5 is prime, 7 is prime, 9 is not prime, 9 is not prime, 9 is not prime ..."

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### Re: 1310: Goldbach Conjectures

A good accountant would be able to claim that 9 is prime for tax purposes.
xtifr wrote:... and orthogon merely sounds undecided.

Carteeg_Struve
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### Re: 1310: Goldbach Conjectures

Klear wrote:
orthogon wrote:The hovertext missed out the Evil Twin Primes Conjecture...

Every prime has a twin which has a mustache?

At least it's not as bad as the Twin Dilemma, where if you move a small planet closer to the sun it will suddenly get heavier, lose momentum, and fall into the star because of... physics.

Flumble
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### Re: All odd numbers are prime.

jc wrote:There were a lot more, but I've forgotten most of them. I wonder if they're collected somewhere on the Web ...

A quick search shows numerous collections, for example http://rationalwiki.org/wiki/Fun:Proof_that_all_odd_numbers_are_prime.

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### Re: 1310: Goldbach Conjectures

Actually by reducto ad absurdum the Tautological Conjecture is true.

It should be referred to as the Tautological Theorem from now on
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### Re: 1310: Goldbach Conjectures

cellocgw
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### Re: 1310: Goldbach Conjectures

Coming next: The XKCD version of the Goldberg Variations?
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### Re: All odd numbers are prime.

Flumble wrote:
jc wrote:There were a lot more, but I've forgotten most of them. I wonder if they're collected somewhere on the Web ...

A quick search shows numerous collections, for example http://rationalwiki.org/wiki/Fun:Proof_that_all_odd_numbers_are_prime.

At some point the jokes start getting tired and obvious, but this one is great:

Right-wing chain email:[1]
A liberal professor at a famous university lectured his class on what numbers were and were not prime. He started out by saying that the odd numbers 3, 5, and 7 were prime, but went on to say that 9 was not. A certain student, disapproving of simply being told by an "expert" what was or was not prime, raised his hand and asked a question.
"You say 9 is not prime, correct?"
"Correct," replied the liberal professor, who did not like being questioned by his students who obviously were nowhere near as smart as he was.
"But 9 is the sum of 7 and 2, is it not?"
"It is" replied the professor.
The student continued "But 7 and 2 are both prime, so how can anything which is the result of adding two similar things together have traits different from those it is the result of without adding new information?"
The professor's jaw dropped at this, and he fled the classroom without a word. The remaining students cheered the logic of the brave student, and his willingness to stand up to liberal indoctrination.
The name of that student: Albert Einstein.

gmalivuk
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### Re: 1310: Goldbach Conjectures

Actaeus wrote:
gmalivuk wrote:You don't need to count 1 as prime, because 4=2+2 and you get the rest of the evens with n-3 and 3.

12>7 and thus doesn't exist, and also 12=9+3.

Remember that we're simply determining whether the stronger conjectures imply the weaker ones. If there are no numbers greater than 7, then 12 doesn't exist. If all odds are prime, then 9 is prime. QED
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ManaUser
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### Re: 1310: Goldbach Conjectures

bondsbw wrote:
• If there are no numbers greater than 7, then every odd ("1", "3", "5", "7") would be prime.
• if every odd number were prime, then every even number n over 2 would be the sum of two primes, namely (n-1) and "1".
• If every even number over 2 is the sum of two primes, then every odd number n over 5 is the sum of "3" and any even number (which is already the sum of 2 primes).
• Given all those odds over 5 and evens over 2, you can create any number over 7.
• Given that you can create any number over 7, they keep going.

And yet, if we accept that each step here works, that must also mean "there are no numbers above 7" proves "numbers just keep going", which can't possibly be right.

MDenham
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### Re: 1310: Goldbach Conjectures

ManaUser wrote:
bondsbw wrote:
• If there are no numbers greater than 7, then every odd ("1", "3", "5", "7") would be prime.
• if every odd number were prime, then every even number n over 2 would be the sum of two primes, namely (n-1) and "1".
• If every even number over 2 is the sum of two primes, then every odd number n over 5 is the sum of "3" and any even number (which is already the sum of 2 primes).
• Given all those odds over 5 and evens over 2, you can create any number over 7.
• Given that you can create any number over 7, they keep going.

And yet, if we accept that each step here works, that must also mean "there are no numbers above 7" proves "numbers just keep going", which can't possibly be right.
They do just keep going, though. 6, 6.6, 6.66, 6.666, 6.6666...

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### Re: 1310: Goldbach Conjectures

We could be using mod 8 arithmetic maybe? i.e. 7+1=0

The numbers just keep going, but going in a circle. ...5,6,7,0,1,2,3,4,5,6,7,0,1,2....
The thing about recursion problems is that they tend to contain other recursion problems.

Farabor
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### Re: 1310: Goldbach Conjectures

bondsbw wrote:
Farabor wrote:I find the comic mildly amusing, but a logical fail, since the logical chain is "stronger being true automatically implies weaker being true".

Actually I think it does if you allow the blasphemy of counting 1 as prime... ok, let's give the comic a bit of leeway there, otherwise I wouldn't have any reason to post the following:

• If there are no numbers greater than 7, then every odd ("1", "3", "5", "7") would be prime.
• if every odd number were prime, then every even number n over 2 would be the sum of two primes, namely (n-1) and "1".
• If every even number over 2 is the sum of two primes, then every odd number n over 5 is the sum of "3" and any even number (which is already the sum of 2 primes).
• Given all those odds over 5 and evens over 2, you can create any number over 7.
• Given that you can create any number over 7, they keep going.

The problem is Extremely strong does not imply extremely weak, in fact it implies the opposite....if there's no numbers over 7, they don't keep going!
(Silly pedant, I know.)

Envelope Generator
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### Re: 1310: Goldbach Conjectures

The extremely strong hypothesis gives the extremely weak one a nice Samuel Beckett feel to it. Numbers keep going, keep going on, call that "going", call that "on", they must go on, they can't go on, they'll go on...
I'm going to step off the LEM now... here we are, Pismo Beach and all the clams we can eat

eSOANEM wrote:If Fonzie's on the order of 100 zeptokelvin, I think he has bigger problems than difracting through doors.

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### Re: 1310: Goldbach Conjectures

Farabor wrote:
bondsbw wrote:
Farabor wrote:I find the comic mildly amusing, but a logical fail, since the logical chain is "stronger being true automatically implies weaker being true".

Actually I think it does if you allow the blasphemy of counting 1 as prime... ok, let's give the comic a bit of leeway there, otherwise I wouldn't have any reason to post the following:

• If there are no numbers greater than 7, then every odd ("1", "3", "5", "7") would be prime.
• if every odd number were prime, then every even number n over 2 would be the sum of two primes, namely (n-1) and "1".
• If every even number over 2 is the sum of two primes, then every odd number n over 5 is the sum of "3" and any even number (which is already the sum of 2 primes).
• Given all those odds over 5 and evens over 2, you can create any number over 7.
• Given that you can create any number over 7, they keep going.

The problem is Extremely strong does not imply extremely weak, in fact it implies the opposite....if there's no numbers over 7, they don't keep going!
(Silly pedant, I know.)

Alice: "Given that you can create any number over 7, they keep going."
Bob: "But that means there are numbers greater than 7!"
Alice: "There are no numbers greater than 7."
Bob: "But that means they don't 'keep going'!"
Alice: "Given that you can create any number over 7, they keep going."
Mallory: "'Try to decrypt these messages,' they said. 'It'll be fun,' they said."

Flumble
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### Re: 1310: Goldbach Conjectures

garaden wrote:Alice: "Given that you can create any number over 7, they keep going."

I can't read "numbers keep going" in any way other than "there is a successor to every number", which means 7 has a successor which is over 7.

garaden wrote:Mallory: "'Try to decrypt these messages,' they said. 'It'll be fun,' they said."

I'm tempted to make an image macro of it. Just because.

jpvlsmv
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### Re: 1310: Goldbach Conjectures

Not to be confused with the [Rube] Goldberg Conjecture, which takes several hundred pages of text to assert that 2 is even.

cellocgw
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### Re: All odd numbers are prime.

Klear wrote:
Flumble wrote:
jc wrote:There were a lot more, but I've forgotten most of them. I wonder if they're collected somewhere on the Web ...

A quick search shows numerous collections, for example http://rationalwiki.org/wiki/Fun:Proof_that_all_odd_numbers_are_prime.

At some point the jokes start getting tired and obvious, but this one is great:

Right-wing chain email:[1]
A liberal professor at a famous university lectured his class on what numbers were and were not prime. He started out by saying that the odd numbers 3, 5, and 7 were prime, but went on to say that 9 was not. A certain student, disapproving of simply being told by an "expert" what was or was not prime, raised his hand and asked a question.
"You say 9 is not prime, correct?"
"Correct," replied the liberal professor, who did not like being questioned by his students who obviously were nowhere near as smart as he was.
"But 9 is the sum of 7 and 2, is it not?"
"It is" replied the professor.
The student continued "But 7 and 2 are both prime, so how can anything which is the result of adding two similar things together have traits different from those it is the result of without adding new information?"
The professor's jaw dropped at this, and he fled the classroom without a word. The remaining students cheered the logic of the brave student, and his willingness to stand up to liberal indoctrination.
The name of that student: Albert Einstein.

somehow I fail to see how including the words "liberal" , "expert" , or "indoctrination" add to this semijoke. Besides which, I rather doubt Einstein would ever have said anything so moronic. Consider, for example, adding NaOH to HCl .
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ucim
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### Re: 1310: Goldbach Conjectures

cellocgw wrote:somehow I fail to see how including the words "liberal" , "expert" , or "indoctrination" add to this semijoke.
It doesn't; what it does do is reference a chain letter that follows this format pretty closely and has been going around to support some political point of view. It's an s/keyboard/leopard for an existing thing.

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