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Topic: P=NP Proof Published at CERN
Replies: 141   Last Post: Oct 26, 2015 9:02 PM

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 Guest
Re: P=NP Proof Published at CERN
Posted: May 10, 2009 9:01 PM

The elliptic curve over Q:
E = ellinit(
[1, 0, 0, -35822192130572784206480514296239908919425,
2609719568750620065454923921391767461604324824175741297455625]
)

of conductor
5751679256865023413274743068599885347967822805404077230
= 2 3 5 7 11 13 17 19 23 29 31 37^2 41 43 47 53 59 61
187172595299 7081017707425445923

has torsion group Z/3Z, generated by

tors=[104605984638686332650,84532082161048799807719188075];

Its Mordell-Weil group E(Q) has rank at least 13, with independent
points

[111765301087195517610, 46430435456204326675146597675],
[111116582336682124050, 34996683196066023464195962875],
[111913032824849252130, 49063192420997854527679793475],
[110123909838304503990, 18512376609554805482691445335],
[109146709187032115370, 10506129421757959855129586475],
[110382143345238886970, 22567063509763234684093270475],
[110245179394644403100, 20382223547410442956289336075],
[108522553923729999720, 17018033523451040060797113555],
[108512500742043656106, 17163334387154750309786061867],
[109741057847530716000, 13297340647117901361820923075],
[108902034932485796850, 12260441074498263650721717075],
[110291739877102075140, 21117334974942773428569817185],
[111294342929434080810, 38103895579546047175336101675].

There are at least 1201*2 integer points on this curve. It's 5th known
curve
with torsion Z/Z3 and rank at least 13.

Curves
E1 = [1, 0, 0, -560715933702165990261993692150795879540,
5299428030171662962897867758309003693598430128674403539600]

E2 = [1, 0, 0, -73262771788012628080963454016709537315,
240598790801630018163569184912325717758514948008409652225]

E3 = [1, 0, 0, -7032750154590180472810630714591592198580,
234825110521164672374627005794918283861649641835073217760400]

E4 = [1, 0, 0, -245159698188178088219881294961406816115,
1510191009902655798002552220643158891490617937867360088417]

also have torsion Z/Z3 and rank at least 13. I found curves E1, E2, E3
at 2007,
and curve at 2008 (see http://web.math.hr/~duje/tors/tors.html ).
There are also many integer points on these curves:
at least 890*2 on E1,
at least 1289*2 on E2,
at least 888*2 on E3,
and at least 870*2 on E4.

--Yurij Eroshkin

Martin Musatov wrote:
> An informal and highly experimental, unorthadox proof P=NP has been
> published on CERN preprints.
>
> http://cdsweb.cern.ch/record/1164206/files/s1-ln5758210-9223534-1939656818Hwf-1468147288IdV-15212827115758210PDF_HI0001.pdf
>
> It is mine, and no it is not published anywhere else. My purpose in
> posting it here is for feedback and suggestions on how to strengthen
> it.
>
> I would specifically, as was my intention with this experiment, like
> feedback from anyone interested in the methodology I used and
> suggestion as to how I might go about pursuing a more broadly accepted
> peer-reviewed published proof building on this basic result.
>
> Thank you,
>
> Martin Musatov
> m[dot]mm[at]vzw[dot]blackberry[dot]net.

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