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Old 2015-10-13, 16:08   #23
alpertron
 
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Quote:
Originally Posted by R.D. Silverman View Post
This does not adequately describe the procedure. You have added 2, then 4, then 6.
"Do this 30 times" can be taken to mean, "add 2 then 4 then 6" 30 times. The
meaning of the word "this" in your last sentence is not well defined.
So if you see in a passtime magazine the sentence fill in the blanks: 2, 4, 6, xx, xx, xx you would not write 8, 10, 12? Come on Bob.
This was intended for the OP, not for you.

Quote:
Sigh. You are completely missing the point. I am not asking the OP to
supply missing reasoning. I am asking him/her to explain why merely posting
a sequence of numbers without any given reasoning might constitute a proof.
With the sequence of 30 prime numbers, I asked the OP if all the terms in the infinite sequence are prime or not without calculator. Only reasoning. I have to repeat that the OP believes that the original sequence produces always prime numbers, but he is asking a proof from other people. That's why I presented this simple exercise.

Last fiddled with by alpertron on 2015-10-13 at 16:20
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Old 2015-10-13, 16:29   #24
R.D. Silverman
 
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Quote:
Originally Posted by alpertron View Post
So if you see in a passtime magazine the sentence fill in the blanks: 2, 4, 6, xx, xx, xx you would not write 8, 10, 12?
But this is NOT what you wrote. You gave a procedure, "add 2, then 4, then 6.... Repeat 30 times."
Nowhere in your specification of the procedure was there an indication that the addends were supposed
to KEEP increasing.

I am beginning to think that you have trouble writing clear, unambiguous English.

Quote:
Come on Bob.
This was intended for the OP, not for you.
This is a forum one of whose purposes is the discussion of mathematics. We have an obligation
not to create possible confusion among newbies. This requires that we pose our questions with care.



Quote:
With the sequence of 30 prime numbers, I asked the OP if all the terms in the infinite sequence are prime or not without calculator. Only reasoning.
Now I know that you can't write English. "prime or not without calculator" is not a grammatically correct phrase. It is nonsense.

What you mean is "prime or not without doing any calculation". or, "without using a calculator"

And you are missing the verb "determine", as in "determine whether all the terms........."

Learn to proofread what you write!

BTW, the discriminant is -163.
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Old 2015-10-13, 16:48   #25
alpertron
 
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It is clear that I cannot write in perfect English, since this a second language and almost nobody speaks this language near me. But I think that most non-pedantic people can understand what I write. Thanks for the corrections.

Last fiddled with by alpertron on 2015-10-13 at 16:48
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Old 2015-10-13, 17:01   #26
R.D. Silverman
 
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Quote:
Originally Posted by alpertron View Post
It is clear that I cannot write in perfect English, since this a second language and almost nobody speaks this language near me.
Please accept my very sincere apology. I was not aware that you were not a native English speaker. mea culpa.
Your English is very very good for a non-native speaker. Certainly much better than my French!


Quote:
But I think that most non-pedantic people can understand what I write. Thanks for the corrections.
This is the wrong attitude. My writing teachers made it very clear that when one writes, it is NOT the
obligation of the reader to discern what we mean. It is the writer's job to be clear.

Furthermore, the nature of mathematics is that it IS pedantic.
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Old 2015-10-13, 17:25   #27
Uncwilly
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Quote:
Originally Posted by kalikidoom View Post
...(2^(2^(2^n-1)-1)-1)...

I mean... isn't that at least a proof that there's an infinate amout of them?

Try it with how meny primes you like... and with how meny 2^....-1 you like... it always works
Instead of trying it with n = 2, which leads to 3, 7, 127, try it with n = 5, or n = 11, or n = 13, 17, etc.
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Old 2015-10-13, 19:49   #28
Batalov
 
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Quote:
Originally Posted by kalikidoom View Post
...(2^(2^(2^n-1)-1)-1)...

I mean... isn't that at least a proof that there's an infinate amout of them?

Try it with how meny primes you like... and with how meny 2^....-1 you like... it always works
This is not a good sentence or an argument.
First you need to make it understandable.

Compare:
1. "It always works for me to go outside without a jacket when I see sun in the window." Nothing to argue about here. "It always works (for you)." Fine! And no one can say - "wait, what if there is rain later in the day?" You've already answered - "It always works (for you)", whatever it means. Maybe the rain works for you; who are we to judge?..
2. "If I see sun in the window, then there will be no rain today (and therefore I go out without the jacket)."
The latter is in fact an argument - it has a premise and it has a conclusion. It is not a true argument, though, because everyone can point out a lot of cases, when you see the sun in the window and there will be rain one hour later.

Now, compare:
(1) what you wrote is some (charitably speaking) ..."opinion". It is your opinion and it doesn't matter that a) it doesn't mean anything to others, b) it cannot be verified (there is no "if", there is no "then"...) Nothing to discuss there.
(2) We can assume that what you actually wanted to write was "If n is prime, then 2^n-1 is (always) prime". That is in fact an argument - it has a premise and it has a conclusion. It is not a true argument, because n=11 is prime, but 2^n-1 is not prime.
(3) We can only guess that furthermore you wanted to write this: "If n is prime and 2^n-1 is prime, then 2^(2^n-1)-1 is (always) prime". Which however is also false: n=13 is prime and 2^n-1=8191 is prime, but 2^(2^n-1)-1 is composite (because 338193759479 divides it).

So, therefore if you wanted to say "(2)" or "(3)" then what you wanted to say was false; and you cannot use it to build into any theories. (In logic, there is a rule: "from false, anything follows". In other words, when you have a false statement it is as good as no statement at all.)

If you wanted to say "(1)", then it simply is meaningless and cannot be meaningfully discussed.

Last fiddled with by Batalov on 2015-10-13 at 19:51
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Old 2015-10-14, 12:58   #29
R.D. Silverman
 
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Quote:
Originally Posted by Batalov View Post
This is not a good sentence or an argument.
First you need to make it understandable.

Compare:
1. "It always works for me to go outside without a jacket when I see sun in the window." Nothing to argue about here. "It always works (for you)." Fine! And no one can say - "wait, what if there is rain later in the day?" You've already answered - "It always works (for you)", whatever it means. Maybe the rain works for you; who are we to judge?..
Except that he did not say that it always works for him. He did say "it always works" PERIOD.

It would be nice if the OP replied to some of the posts....

Last fiddled with by R.D. Silverman on 2015-10-14 at 12:59
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Old 2015-10-14, 13:20   #30
alpertron
 
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At this point he should feel like a sheep surrounded by wolves. I do not think he wants to continue discussing here.
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Old 2015-10-14, 13:20   #31
LaurV
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Quote:
Originally Posted by R.D. Silverman View Post
It would be nice if the OP replied to some of the posts....
I think he will not. This is deliberately a "stone in the lake thrown" to see how and if the clever people here manage to take it out. As a "proof" (hehe, I like your list!) I will bring the fact that the typos are deliberate, "infinate", "amout", "meny" (repeated). These all are well underlined, and there is no way you miss them; for a non-native speaker, I immediately go to the dictionary if I don't know the spelling. I am sure I do plenty of grammar mistakes, but I try not to do typing mistakes. Sometimes one typo is cleverer than me and it escapes uncorrected, but never so many in a row, unless they are deliberate. I assume the guy is a frequent on the forum, possibly native speaker, trying to hide himself when throwing stones in the lake...
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Old 2015-10-14, 13:58   #32
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Quote:
Originally Posted by alpertron View Post
At this point he should feel like a sheep surrounded by wolves. I do not think he wants to continue discussing here.
Regarding your example, expanding the polynomial x^2 + x + 41.

Is there any way to PROOVE this is prime for
all integers x between 0 and 39 inclusive,
without actually testing or enumerating the range?

In other words, is this interesting fact unique or
the first of a sequence of such polynomials with
all values prime within a significant range?

That would be a nice puzzle to ask in this thread.
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Old 2015-10-14, 14:19   #33
R. Gerbicz
 
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Quote:
Originally Posted by davar55 View Post
Regarding your example, expanding the polynomial x^2 + x + 41.

Is there any way to PROOVE this is prime for
all integers x between 0 and 39 inclusive,
without actually testing or enumerating the range?
Good question, it was an olympiad problem in 1987, see: http://www.artofproblemsolving.com/w...lems/Problem_6
So if we know that the above f(x)=x^2+x+41 is prime for f(0),f(1),f(2),f(3) then we know that it is also prime for f(4),..,f(39).
As I can remember there is a proof that there is only a finitely many such n value for that we can apply the statement, and we know all of them.
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