[math-fun] big prime gaps
The widest prime gap among primes<X (assuming X>100), is claimed in this 40-page paper to exceed C * lnX * lnlnX * lnlnlnlnX / lnlnlnX for some computable positive constant C. This is a major breakthrough but still well short of proving Cramer's conjecture. arxiv.org/abs/1412.5029 Long gaps between primes by Kevin Ford, Ben Green, Sergei Konyagin, James Maynard, Terence Tao April 2015 -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)
The raw form of that formula is intriguing to me. If we represent N as "0", ln N as "1", ln ln N as "2", and so on, then this formula could be represented as "1.2.4/3". The integral of ln N, "1", is N ln N, "0.1". What "signatures" of this kind arise "naturally"? Does "0.2.4/1.3" "mean" anything? Sorry for all the scare quotes; it's quite possible my musings on this have no content whatever! On Wed, Apr 22, 2015 at 6:00 PM, Warren D Smith <warren.wds@gmail.com> wrote:
The widest prime gap among primes<X (assuming X>100), is claimed in this 40-page paper to exceed
C * lnX * lnlnX * lnlnlnlnX / lnlnlnX
for some computable positive constant C. This is a major breakthrough but still well short of proving Cramer's conjecture.
arxiv.org/abs/1412.5029 Long gaps between primes by Kevin Ford, Ben Green, Sergei Konyagin, James Maynard, Terence Tao April 2015
-- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)
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"Scare quotes" is the standard term, but it seems inapt when one is using quotes to say "Hey, I'm being imprecise, but I know I'm being imprecise"; is there a different term one can use here? Perhaps there's a linguistic term for suffixes like "-ish" and "-esque" and for prefatory phrases like "sort of" and "kind of" that could be adapted to serve as a name for this kind of typographical marker of squishiness. Then again, maybe "squish quotes" would do. Jim On Wed, Apr 22, 2015 at 6:38 PM, Allan Wechsler <acwacw@gmail.com> wrote:
The raw form of that formula is intriguing to me. If we represent N as "0", ln N as "1", ln ln N as "2", and so on, then this formula could be represented as "1.2.4/3". The integral of ln N, "1", is N ln N, "0.1". What "signatures" of this kind arise "naturally"? Does "0.2.4/1.3" "mean" anything? Sorry for all the scare quotes; it's quite possible my musings on this have no content whatever!
On Wed, Apr 22, 2015 at 6:00 PM, Warren D Smith <warren.wds@gmail.com> wrote:
The widest prime gap among primes<X (assuming X>100), is claimed in this 40-page paper to exceed
C * lnX * lnlnX * lnlnlnlnX / lnlnlnX
for some computable positive constant C. This is a major breakthrough but still well short of proving Cramer's conjecture.
arxiv.org/abs/1412.5029 Long gaps between primes by Kevin Ford, Ben Green, Sergei Konyagin, James Maynard, Terence Tao April 2015
-- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)
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I prefer to write [0, 1, 1, -1, 1] for x^0 * (log x)^1 * (log log x)^1 * (log log log x)^-1 * (log log log log x)^1. This also has the advantage of allowing component-wise sorting to match asymptotics. Charles Greathouse Analyst/Programmer Case Western Reserve University On Wed, Apr 22, 2015 at 6:38 PM, Allan Wechsler <acwacw@gmail.com> wrote:
The raw form of that formula is intriguing to me. If we represent N as "0", ln N as "1", ln ln N as "2", and so on, then this formula could be represented as "1.2.4/3". The integral of ln N, "1", is N ln N, "0.1". What "signatures" of this kind arise "naturally"? Does "0.2.4/1.3" "mean" anything? Sorry for all the scare quotes; it's quite possible my musings on this have no content whatever!
On Wed, Apr 22, 2015 at 6:00 PM, Warren D Smith <warren.wds@gmail.com> wrote:
The widest prime gap among primes<X (assuming X>100), is claimed in this 40-page paper to exceed
C * lnX * lnlnX * lnlnlnlnX / lnlnlnX
for some computable positive constant C. This is a major breakthrough but still well short of proving Cramer's conjecture.
arxiv.org/abs/1412.5029 Long gaps between primes by Kevin Ford, Ben Green, Sergei Konyagin, James Maynard, Terence Tao April 2015
-- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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participants (4)
-
Allan Wechsler -
Charles Greathouse -
James Propp -
Warren D Smith