Every even # > 2 is the + of 2 Primes. True ??
Thomas Gray
Cy Berman (cybe...@erinet.com) writes:
> Can it be proved that every even number greater than 2 is
> a sum of 2 primes?
Yes while eating my corn flakes this morning, I came upon a truly
remarkable proof. Unfortunately this pace is too small to hold it.
--
What's the difference between DMS and SP1, they're both computers?
- software hacker (1974)
i.sinature
Jim Ward
>> Can it be proved that every even number greater than 2 is
>> a sum of 2 primes?
>Yes while eating my corn flakes this morning, I came upon a truly
>remarkable proof. Unfortunately this pace is too small to hold it.
What kind of corn flakes features math puzzles on the back? (I want a
box) Was there a picture of Goldbach on the front? Was he eating his
Wheaties? There must've been a decoder ring inside, don't forget to
root around for the prize!
Matthew T. Russotto
In article <4pk10j$a...@news.erinet.com>, Cy Berman <cybe...@erinet.com> wrote:
}Can it be proved that every even number greater than 2 is
}a sum of 2 primes?
Probably, but if you figure it out you should try and get a PhD in
Mathematics out of it.
It's a well-known unproven conjecture (Goldbach's Conjecture, I think)
believed to be true.
--
Matthew T. Russotto russ...@pond.com russ...@his.com
"Extremism in defense of liberty is no vice, and moderation in pursuit
of justice is no virtue."
gars...@pipeline.com
In article <4pmiue$f...@wanda.phl.pond.com>, Matthew T. Russotto writes:
>In article <4pk10j$a...@news.erinet.com>, Cy Berman <cybe...@erinet.com>
wrote:
>}Can it be proved that every even number greater than 2 is
>}a sum of 2 primes?
>
>Probably, but if you figure it out you should try and get a PhD in
>Mathematics out of it.
>
>It's a well-known unproven conjecture (Goldbach's Conjecture, I think)
>believed to be true.
Let N be an even number greater than 2. N can be expressed as 2J,
where J is an integer greater than or equal to 2.
If J is prime, then N is obviously the sum of J+J.
If J is not prime, then there must exist some integer x, such that:
J+x AND j-x are BOTH prime.
(Note, when J is prime, x is zero, so the entire conjecture can be
re-expressed as:
In other words: All integers greater than or equal to 2 are either
prime or equidistant from rwo primes.
Granted, I haven't proved a thing. But a restatement should be
worth a Master's at least.
-- Gary Simon
???
It cannot be proved as its not true :)
For example:
54351851846387321657425187487632515465443245468743
78135454651324200651249853247812684321345645654546
26534414423413253441234532341055442526737897821323
34458654234414544512412354452674655749058354422455
74325254254644656548665789781223743240710654232345
41253464546753634564687787453355645434547768734526
42653444453776856775344263354646857587235446123423
54154454564277877246234078509863456745948567322634
84376982639485765345095687028376463746582756435323
48745457544526843242162754235543546457234564573556
546
Cannot be written as the sum of 2 primes. This is the smallest such number.
I hope I didn't mistype this. :)
Sincerely,
Matthew Roozee
mro...@math.uci.edu
Richard Walter
??? <mro...@math.uci.edu> wrote:
>
<Large number snipped>
> Cannot be written as the sum of 2 primes. This is the smallest such number.
>
> Sincerely,
> Matthew Roozee
> mro...@math.uci.edu
Does anyone have a reference of where this is stated / proven?
Thanks,
-Richard Walter
rwa...@auspex.com
Note: I speak for myself, not for Auspex.
===============================================================================
"Disclaimer: This posting represents the poster's views, not those of Auspex"
===============================================================================
Bernie Cosell
russ...@wanda.phl.pond.com (Matthew T. Russotto) wrote:
} In article <4pk10j$a...@news.erinet.com>, Cy Berman <cybe...@erinet.com> wrote:
} }Can it be proved that every even number greater than 2 is
} }a sum of 2 primes?
} Probably, but if you figure it out you should try and get a PhD in
} Mathematics out of it.
Nah... hold out for a Fields medal....
/B\
--
Bernie Cosell Fantasy Farm Fibers
ber...@fantasyfarm.com Pearisburg, VA
--> Too many people, too few sheep <--
matthew conroy
In article <31C0756F...@auspex.com>,
Richard Walter <rwa...@auspex.com> wrote:
>??? <mro...@math.uci.edu> wrote:
>>
> <Large number snipped>
>
>> Cannot be written as the sum of 2 primes. This is the smallest such number.
>>
>
>
I am certain that Mr. Roozee's claim was meant as a joke.
Goldbach's Conjecture is still just a conjecture.
matthew
S. Macaw
> 54351851846387321657425187487632515465443245468743
> 78135454651324200651249853247812684321345645654546
> 26534414423413253441234532341055442526737897821323
> 34458654234414544512412354452674655749058354422455
> 74325254254644656548665789781223743240710654232345
> 41253464546753634564687787453355645434547768734526
> 42653444453776856775344263354646857587235446123423
> 54154454564277877246234078509863456745948567322634
> 84376982639485765345095687028376463746582756435323
> 48745457544526843242162754235543546457234564573556
> 546
>Cannot be written as the sum of 2 primes. This is the smallest such number.
>I hope I didn't mistype this. :)
con...@euclid.Colorado.EDU (matthew conroy) wrote:
>I am certain that Mr. Roozee's claim was meant as a joke.
>Goldbach's Conjecture is still just a conjecture.
>matthew
Mr. "???" contends that this huge number has special properties which would
be difficult to test, while Matthew Conroy believes that the number was
simply made up out of thin air. The number given by Mr. "???" contains 503
digits. They have the following distribution:
0 - 10
1 - 24
2 - 55
3 - 62
4 - 112
5 - 91
6 - 57
7 - 48
8 - 35
9 - 9
Right off the bat, it looks suspiciously like Mr. "???" likes the number 4
and tends to stay away from 9 and 0 when he types numbers at random. The
statistical test for investigating this sort of thing is called the
"Chi-Square Test". I'll see if I can apply it properly here.
I'll ignore the last 3 digits (5,4,6) to simplify things. The last one has
to be even anyway, and therefore complicates things slightly. Out of 500
digits, the expected frequency of appearance of any individual digit would
be 50. Here are the outcomes, expected outcomes, differences, squared
differences, and ratios of squared differences to expected outcomes:
0, 10, 50, -40, 1600, 32
1, 24, 50, -26, 676, 13.52
2, 55, 50, 5, 25, 0.5
3, 62, 50, 12, 144, 2.88
4,111, 50, 61, 3721, 74.42
5, 90, 50, 40, 1600, 32
6, 56, 50, 6, 36, 0.72
7, 48, 50, -2, 4, 0.08
8, 35 50, -15, 225, 4.5
9, 9 50, -41, 1681, 33.62
The total chi-square value is 194.24. Unfortunately, I can't look up the
improbability of such a value, as the tables in my statistics textbook
don't even come close to values that high. Suffice it to say that the value
is extreme and highly improbable. It's clear that the hypothesis must be
rejected that the digits of the large number given by Mr. "???" are
normally distributed and not the product of a bias.
Mike
--
Visit Strawberry Macaw's Puzzle Page at http://pobox.com/~puzzles
Paul Filseth
Cy Berman <cybe...@erinet.com> wrote:
> Can it be proved that every even number greater than 2 is
> a sum of 2 primes?
Matthew Roozee (mro...@math.uci.edu) wrote:
> It cannot be proved as its not true :)
>
> 54351851846387321657425187487632515465443245468743
> <453 more bogus digits snipped>
>
> Cannot be written as the sum of 2 primes. This is the smallest such number.
> I hope I didn't mistype this. :)
Richard Walter <rwa...@auspex.com> wrote:
> Does anyone have a reference of where this is stated / proven?
No. It seems Mr. Roozee was having a bit of fun. He probably
thought the number he made up as he was typing it in was big enough that
no one could call him on it. Of course I have no idea what two primes
add up to his number, or even whether finding such a pair is feasible
given current technology. But they, like the truth, are out there...
ObPuzzle: How do I know?
--
Paul Filseth I promise to be different. I promise to be unique.
p...@lsil.com I promise not to repeat things other people say.
- Steve Martin
Ed Pegg Jr
The distribution of the digits cannot be used to reject this number. I
have a prime number record myself, and the numbers involved would fail.
For jollies ... find 1000 consectutive composites. All of these
composites are less than 50!. The College Journal of Mathematics will
publish the answer soon (as a 'filler' article).
I found this accidently while playing with Maple's Nextprime function.
If anyone ever does find a counterexample to Goldbach's, I imagine it
might also involve an accidental discovery.
--Ed Pegg Jr.
--
__________________________________________________________________________
Ed Pegg Jr xei...@netcom.com
SCLEROTIN and EXTERNAL are phonetic transposals
David G Radcliffe
Paul Filseth (p...@lsil.com) wrote:
: Richard Walter <rwa...@auspex.com> wrote:
: > Does anyone have a reference of where this is stated / proven?
:
: No. It seems Mr. Roozee was having a bit of fun. He probably
: thought the number he made up as he was typing it in was big enough that
: no one could call him on it. Of course I have no idea what two primes
: add up to his number, or even whether finding such a pair is feasible
: given current technology. But they, like the truth, are out there...
:
: ObPuzzle: How do I know?
I don't know how you know this. Goldbach's conjecture has been
verified up to 4 x 10^11; possibly this bound has increased by
an order of magnitude or two in the past few years.
According to Maple, Roozee's number is the sum of the prime 2707
and a "probable prime" q. Unfortunately q-1 is difficult to factor,
so I wasn't able to prove that q is a prime.
ObPuzzle: Why am I wasting my time on this silly problem?
--
David Radcliffe radc...@alpha2.csd.uwm.edu
Abigail
Ed Pegg Jr wrote:
> For jollies ... find 1000 consectutive composites. All of these
> composites are less than 50!. The College Journal of Mathematics will
> publish the answer soon (as a 'filler' article).
Uhm, what's wrong with 2000!+2 .. 2000!+1001 ? Aren't they all composite,
and larger than 50! ? Or am I missing something?
Abigail -- whose very first exercise on the university was to proof that for
any n > 1, there are n consecutive composite numbers.
Paul Filseth
radc...@alpha2.csd.uwm.edu (David G Radcliffe) wrote:
> Paul Filseth (p...@lsil.com) wrote:
> : No. It seems Mr. Roozee was having a bit of fun. He probably
> : thought the number he made up as he was typing it in was big enough that
> : no one could call him on it.
> : ObPuzzle: How do I know?
>
> I don't know how you know this. Goldbach's conjecture has been
> verified up to 4 x 10^11; possibly this bound has increased by
> an order of magnitude or two in the past few years.
>
> According to Maple, Roozee's number is the sum of the prime 2707
> and a "probable prime" q. Unfortunately q-1 is difficult to factor,
> so I wasn't able to prove that q is a prime.
I know Mr. Roozee made up the number basically the same way Mr. Macaw
knew: because of the characteristics of the digits in the number. People
aren't good random number generators. I didn't do anything as fancy as a
chi-squared test; I just noticed that there were an awful lot of digits
that were one more or one less than the previous digit. In any normal
number, these should be about 20% of the total, but in Mr. Roozee's number
they are about 40%. Here is a randomly selected line of Roozee digits.
41253464546753634564687787453355645434547768734526
By rights there should be about 10 digits numerically adjacent to the
previous digit. There are 23. If the number were the solution to some
arbitrary math problem, this is staggeringly unlikely. But if a person
were simply trying to get a lot of random-looking digits down fast on a
keyboard, it's exactly what should be expected.
Lest one think this might just be how it is, given that any
counterexample to Goldbach is already a very unusual number, consider that
the number Mr. Roozee gave will not have any odd statistical properties
to its digits if it is converted to some other number base, say 16.
There is nothing about the Goldbach Conjecture to make one think it would
single out base-10 as its preferred notation.
Abe Rosner
Abigail <abi...@mars.ic.iaf.nl> wrote:
>Ed Pegg Jr wrote:
>> For jollies ... find 1000 consectutive composites. All of these
>> composites are less than 50!. The College Journal of Mathematics will
>> publish the answer soon (as a 'filler' article).
>Uhm, what's wrong with 2000!+2 .. 2000!+1001 ? Aren't they all composite,
>and larger than 50! ? Or am I missing something?
Nothing, yes, and yes.