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First proof that infinitely many prime numbers come in pairs
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Philip Chee
May 14, 2013, 3:50:28 PM5/14/13
to
[[
It�s a result only a mathematician could love. Researchers hoping to get
�2� as the answer for a long-sought proof involving pairs of prime
numbers are celebrating the fact that a mathematician has wrestled the
value down from infinity to 70 million.
�That�s only [a factor of] 35 million away� from the target, quips Dan
Goldston, an analytic number theorist at San Jose State University in
California who was not involved in the work. �Every step down is a step
towards the ultimate answer.�
]]
<http://www.nature.com/news/first-proof-that-infinitely-many-prime-numbers-come-in-pairs-1.12989>
Phil
--
Philip Chee <phi...@aleytys.pc.my>, <phili...@gmail.com>
http://flashblock.mozdev.org/ http://xsidebar.mozdev.org
Guard us from the she-wolf and the wolf, and guard us from the thief,
oh Night, and so be good for us to pass.
It�s a result only a mathematician could love. Researchers hoping to get
�2� as the answer for a long-sought proof involving pairs of prime
numbers are celebrating the fact that a mathematician has wrestled the
value down from infinity to 70 million.
�That�s only [a factor of] 35 million away� from the target, quips Dan
Goldston, an analytic number theorist at San Jose State University in
California who was not involved in the work. �Every step down is a step
towards the ultimate answer.�
]]
<http://www.nature.com/news/first-proof-that-infinitely-many-prime-numbers-come-in-pairs-1.12989>
Phil
--
Philip Chee <phi...@aleytys.pc.my>, <phili...@gmail.com>
http://flashblock.mozdev.org/ http://xsidebar.mozdev.org
Guard us from the she-wolf and the wolf, and guard us from the thief,
oh Night, and so be good for us to pass.
David Dyer-Bennet
May 14, 2013, 4:57:27 PM5/14/13
to
Philip Chee <phi...@aleytys.pc.my> writes:
> [[
> It’s a result only a mathematician could love. Researchers hoping to get
> ‘2’ as the answer for a long-sought proof involving pairs of prime
> towards the ultimate answer.”
> ]]
>
> <http://www.nature.com/news/first-proof-that-infinitely-many-prime-numbers-come-in-pairs-1.12989>
That seems like such a weird limit. I haven't tried to find and study
the proof, I'm kind of out of date (not having paid much attention since
college; and never took number theory come to think of it, one of my few
regrets of that type). I hope for him, and maybe for mathematics in
general, that it holds up. But my intuition says that's such a weird
limit, it doesn't feel like it has enough "special properties" to be
right. (Math results aren't based on intuition, of course; though early
stages in reaching results often are.)
--
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> [[
> It’s a result only a mathematician could love. Researchers hoping to get
> ‘2’ as the answer for a long-sought proof involving pairs of prime
> numbers are celebrating the fact that a mathematician has wrestled the
> value down from infinity to 70 million.
>
> “That’s only [a factor of] 35 million away” from the target, quips Dan
> value down from infinity to 70 million.
>
> Goldston, an analytic number theorist at San Jose State University in
> California who was not involved in the work. “Every step down is a step
> towards the ultimate answer.”
> ]]
>
> <http://www.nature.com/news/first-proof-that-infinitely-many-prime-numbers-come-in-pairs-1.12989>
That seems like such a weird limit. I haven't tried to find and study
the proof, I'm kind of out of date (not having paid much attention since
college; and never took number theory come to think of it, one of my few
regrets of that type). I hope for him, and maybe for mathematics in
general, that it holds up. But my intuition says that's such a weird
limit, it doesn't feel like it has enough "special properties" to be
right. (Math results aren't based on intuition, of course; though early
stages in reaching results often are.)
--
Googleproofaddress(account:dd-b provider:dd-b domain:net)
Snapshots: http://dd-b.net/dd-b/SnapshotAlbum/data/
Photos: http://dd-b.net/photography/gallery/
Dragaera: http://dragaera.info
Keith F. Lynch
May 14, 2013, 7:55:55 PM5/14/13
to
>> It\342\200\231s a result only a mathematician could love.
And an apostrophe only a UTF-8 fanatic could love. :-)
>> Researchers hoping to get \342\200\2302\342\200\231 as the answer
> That seems like such a weird limit.
Look up Graham's number. And Skewes' number. First-cut upper bounds
are often large and arbitrary, and are soon reduced.
> I haven't tried to find and study the proof, ...
I have. (Tried to, I mean.) But it doesn't seem to be available
anywhere yet.
> I'm kind of out of date (not having paid much attention since
> college; and never took number theory come to think of it, one of my
> few regrets of that type).
It's not too late. The numbers are all still there to be studied. :-)
Save your regrets for things it's too late to do (or undo).
To bring you up to date, three recent (21st century) prime number
results are:
* Arbitrarily long arithmetic sequences of primes exist. If you want
to find a million primes that are equally spaced, you can (given
sufficient computer power -- the current record is just 26). (Note
that these aren't necessarily *consecutive* primes).
* There is no minimum ratio between consecutive primes. If you want to
find a prime that's larger than the previous by just one part in a
million, or one part in a trillion, you can.
* There is a claimed proof of the abc conjecture.
There's still no proof or disproof for the Riemann hypothesis.
Or of the Goldbach conjeture.
> I hope for him, and maybe for mathematics in general, that it
> holds up.
Likewise. It is of course far too early to tell.
> But my intuition says that's such a weird limit, it doesn't feel
> like it has enough "special properties" to be right.
Nobody is claiming, and I'm sure nobody believes, that that's *the*
limit, i.e. that there are infinitely many primes that differ from
an adjacent prime by exactly 70 million, but only finitely many that
differ by any smaller number.
If this proof turns out to be correct, I'd bet my life savings that
within a few years someone will knock the limit down to some much
smaller number, probably one that's equally nice and round, perhaps
1000. And that by the end of the century it will be reduced to 4, or
perhaps even 2. (I don't think anyone seriously doubts that the twin
prime conjecture is true.)
Speaking of the twin prime conjecture, a few years ago I made what may
be the geekiest Wikipedia edit ever: I happened to notice that the the
8th digit of the twin prime constant given on the twin prime conjecture
page was wrong, so I corrected it.
--
Keith F. Lynch - http://keithlynch.net/
Please see http://keithlynch.net/email.html before emailing me.
And an apostrophe only a UTF-8 fanatic could love. :-)
>> Researchers hoping to get \342\200\2302\342\200\231 as the answer
>> for a long-sought proof involving pairs of prime numbers are
>> celebrating the fact that a mathematician has wrestled the value
>> down from infinity to 70 million.
And that 2 didn't even need to be quoted.
>> celebrating the fact that a mathematician has wrestled the value
>> down from infinity to 70 million.
> That seems like such a weird limit.
are often large and arbitrary, and are soon reduced.
> I haven't tried to find and study the proof, ...
I have. (Tried to, I mean.) But it doesn't seem to be available
anywhere yet.
> I'm kind of out of date (not having paid much attention since
> college; and never took number theory come to think of it, one of my
> few regrets of that type).
Save your regrets for things it's too late to do (or undo).
To bring you up to date, three recent (21st century) prime number
results are:
* Arbitrarily long arithmetic sequences of primes exist. If you want
to find a million primes that are equally spaced, you can (given
sufficient computer power -- the current record is just 26). (Note
that these aren't necessarily *consecutive* primes).
* There is no minimum ratio between consecutive primes. If you want to
find a prime that's larger than the previous by just one part in a
million, or one part in a trillion, you can.
* There is a claimed proof of the abc conjecture.
There's still no proof or disproof for the Riemann hypothesis.
Or of the Goldbach conjeture.
> I hope for him, and maybe for mathematics in general, that it
> holds up.
> But my intuition says that's such a weird limit, it doesn't feel
> like it has enough "special properties" to be right.
limit, i.e. that there are infinitely many primes that differ from
an adjacent prime by exactly 70 million, but only finitely many that
differ by any smaller number.
If this proof turns out to be correct, I'd bet my life savings that
within a few years someone will knock the limit down to some much
smaller number, probably one that's equally nice and round, perhaps
1000. And that by the end of the century it will be reduced to 4, or
perhaps even 2. (I don't think anyone seriously doubts that the twin
prime conjecture is true.)
Speaking of the twin prime conjecture, a few years ago I made what may
be the geekiest Wikipedia edit ever: I happened to notice that the the
8th digit of the twin prime constant given on the twin prime conjecture
page was wrong, so I corrected it.
--
Keith F. Lynch - http://keithlynch.net/
Please see http://keithlynch.net/email.html before emailing me.
Paul Dormer
May 15, 2013, 7:05:00 AM5/15/13
to
In article <kmuiub$ogu$1...@reader1.panix.com>, k...@KeithLynch.net (Keith F.
Lynch) wrote:
>
> And that 2 didn't even need to be quoted.
It wasn't quoted, it was underlined here.
>
> And that 2 didn't even need to be quoted.
Keith F. Lynch
May 17, 2013, 11:17:15 PM5/17/13
to
Keith F. Lynch <k...@KeithLynch.net> wrote:
> To bring you up to date, three recent (21st century) prime number
> results are: ...
> To bring you up to date, three recent (21st century) prime number
And one more, just announced: An alleged proof that every odd
number greater than 5 is the sum of three primes.
This was announced within a day of the proof that infinitenly many
primes differ from another prime by not more than 70 million.
This led Adam Goucher to conjecture, in
http://cp4space.wordpress.com/2013/05/15/simultaneous-proofs/
There are infinitely many pairs of exciting proofs published within
70000000 milliseconds of each other.
Keith F. Lynch
Jun 26, 2013, 8:11:17 PM6/26/13
to
Keith F. Lynch <k...@KeithLynch.net> wrote:
> David Dyer-Bennet <dd...@dd-b.net> wrote:
>> But my intuition says that's such a weird limit, it doesn't feel
>> like it has enough "special properties" to be right.
> Nobody is claiming, and I'm sure nobody believes, that that's *the*
> limit, i.e. that there are infinitely many primes that differ from
> an adjacent prime by exactly 70 million, but only finitely many that
> differ by any smaller number.
> If this proof turns out to be correct, I'd bet my life savings that
> within a few years someone will knock the limit down to some much
> smaller number, probably one that's equally nice and round, perhaps
> 1000. And that by the end of the century it will be reduced to 4,
> or perhaps even 2. (I don't think anyone seriously doubts that the
> twin prime conjecture is true.)
As usual, I was right. Except I underestimated how long it would take
>> But my intuition says that's such a weird limit, it doesn't feel
>> like it has enough "special properties" to be right.
> Nobody is claiming, and I'm sure nobody believes, that that's *the*
> limit, i.e. that there are infinitely many primes that differ from
> an adjacent prime by exactly 70 million, but only finitely many that
> differ by any smaller number.
> If this proof turns out to be correct, I'd bet my life savings that
> within a few years someone will knock the limit down to some much
> smaller number, probably one that's equally nice and round, perhaps
> 1000. And that by the end of the century it will be reduced to 4,
> or perhaps even 2. (I don't think anyone seriously doubts that the
> twin prime conjecture is true.)
for that upper bound to drop. The current upper bound is about 12,000.
See
http://michaelnielsen.org/polymath1/index.php?title=Bounded_gaps_between_primes
for a list of successive upper bounds.
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