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Variants of the Selberg sieve, and bounded intervals containing many primes

Supplementary reference material and source files for the Polymath8b paper (arXiv:1407.4897, Research in the Mathematical Sciences 1:12, 2014).

LaTeX sources, compiled PDFs, and the Mathematica notebooks used for the numerical optimization (degree/monomial optimizers, region plots, variational computations), including the JM, MonomialMultiplier, Variational, and RIMS-submitted-version working directories. 48 files.

Build artifacts (logs, .aux/.bbl, editor backups) and the confidential referee reports are omitted; this is a curated snapshot of the working folder, not a complete mirror. Mathematica .nb files download rather than render in the browser.

Top level

• BddGapsSize6.pdfpdf158 KB
• BddGapsSize6.textex12 KB
• DegreeOptimizer-2014-02-13-BiggerRegion5.nbnb181 KB
• DegreeOptimizer-2014-03-31-AdG1.nbnb185 KB
• DegreeOptimizer-2014-03-31-AdG2.nbnb166 KB
• Mfinder-2014-06-01.nbnb355 KB
• Mfinder-clean.nbnb868 KB
• RegionPlots-BddGapsSize6.nbnb8.0 MB
• asymptotics.textex29 KB
• biblio.textex8 KB
• distribution.textex9 KB
• exponential.textex151 B
• h1-new.textex36 KB
• h1-old.textex35 KB
• h1.textex125 B
• introduction.textex23 KB
• more-sieving.textex23 KB
• newergap.pdfpdf909 KB
• newergap.textex8 KB
• parity.textex8 KB
• remarks.textex10 KB
• sieving.textex42 KB
• subtheorems.textex26 KB
• tuples.textex20 KB
• xyplot.pdfpdf43 KB

JM

• asymptotics-new.textex26 KB
• asymptotics-old.textex27 KB
• introduction-old.textex19 KB
• introduction.textex19 KB
• more-sieving-new.textex22 KB
• more-sieving-old.textex22 KB
• sieving-old.textex40 KB
• sieving.textex41 KB
• subtheorems-old.textex21 KB
• subtheorems.textex22 KB

MonomialMultiplier

• DegreeOptimizer-2014-03-31.nbnb367 KB
• MonomialMultiplier.nbnb53 KB
• MonomialMultiplier05.nbnb244 KB

Variational

• variational.pdfpdf163 KB
• variational.textex14 KB

rims submitted version

• bmc-mathphys.bstbst62 KB
• bmc_article_2col.pdfpdf150 KB
• bmcart-biblio.stysty12 KB
• bmcart.clscls56 KB
• newergap-submitted.pdfpdf934 KB
• newergap-submitted.textex253 KB
• readme.htmlhtml8 KB
• xyplot.pdfpdf43 KB