Add Goldbach's conjecture appendix page #320

Copilot · 2026-01-09T01:27:01Z

Adds educational content on Goldbach's conjecture to the book appendices.

Implementation

goldbach.qmd: New appendix covering:
- Strong conjecture (every even integer > 2 is sum of two primes)
- Weak conjecture (every odd integer > 5 is sum of three primes)
- Historical context (1742-present) and proof status
- Computational verification with R code demonstrating prime checking and Goldbach pair finding
_quarto-book.yml: Added goldbach.qmd to appendices
inst/WORDLIST: Added proper names (Goldbach, Helfgott, Leonhard, Vinogradov, Harald)

Code Example

The page includes working R code demonstrating the conjecture:

is_prime <- function(n) {
  if (n < 2) return(FALSE)
  if (n == 2) return(TRUE)
  if (n %% 2 == 0) return(FALSE)
  if (n == 3) return(TRUE)
  
  i <- 3
  while (i * i <= n) {
    if (n %% i == 0) return(FALSE)
    i <- i + 2
  }
  return(TRUE)
}

find_goldbach_pairs <- function(n) {
  pairs <- list()
  for (p in 2:(n / 2)) {
    q <- n - p
    if (is_prime(p) && is_prime(q)) {
      pairs[[length(pairs) + 1]] <- c(p, q)
    }
  }
  return(pairs)
}

Code prioritizes clarity for educational purposes over performance optimizations.

Warning

Firewall rules blocked me from connecting to one or more addresses (expand for details)

I tried to connect to the following addresses, but was blocked by firewall rules:

CRAN.R-project.org
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accounts.google.com
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allisonhorst.github.io
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android.clients.google.com
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clients2.google.com
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glmnet.stanford.edu
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haven.tidyverse.org
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plotly-r.com
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- Triggering command: /opt/R/4.5.2/lib/R/bin/exec/R /opt/R/4.5.2/lib/R/bin/exec/R --no-echo --no-restore --file=/opt/quarto/share/rmd/rmd.R 1138�� (dns block)
www.google.com
- Triggering command: /proc/self/exe /proc/self/exe --type=utility --utility-sub-type=network.mojom.NetworkService --lang=en-US --service-sandbox-type=none --no-sandbox --disable-dev-shm-usage --use-angle=swiftshader-webgl --mute-audio --crashpad-handler-pid=10083 --enable-crash-reporter=, --noerrdialogs --user-data-dir=/tmp/.com.google.Chrome.scoped_dir.Z0hsxW --change-stack-guard-on-fork=enable --shared-files=v8_context_snapshot_data:100 --field-trial-handle=3,i,9118596104773345624,10136599911699891339,262144 --disable-features=PaintHolding --variations-seed-version --trace-process-track-uuid=3190708989122997041 t-sass/src/dart (dns block)
- Triggering command: /opt/google/chrome/chrome /usr/bin/google-chrome --headless --remote-debugging-port=4626 --remote-allow-origins=REDACTED --crash-dumps-dir=/tmp/RtmpVMbRmW/chrome-272347000541-crashpad --no-sandbox --disable-dev-shm-usage --force-color-profile=srgb --disable-extensions --mute-audio (dns block)
www.stats.ox.ac.uk
- Triggering command: /opt/R/4.5.2/lib/R/bin/exec/R /opt/R/4.5.2/lib/R/bin/exec/R --no-echo --no-restore --file=/opt/quarto/share/rmd/rmd.R 61c9�� get --local atex-macros/ pull.rebase (dns block)
yihui.org
- Triggering command: /opt/R/4.5.2/lib/R/bin/exec/R /opt/R/4.5.2/lib/R/bin/exec/R --no-echo --no-restore --file=/opt/quarto/share/rmd/rmd.R (dns block)
- Triggering command: /opt/R/4.5.2/lib/R/bin/exec/R /opt/R/4.5.2/lib/R/bin/exec/R --no-echo --no-restore --file=/opt/quarto/share/rmd/rmd.R 1138�� (dns block)
- Triggering command: /opt/R/4.5.2/lib/R/bin/exec/R /opt/R/4.5.2/lib/R/bin/exec/R --no-echo --no-restore --file=/opt/quarto/share/rmd/rmd.R 61c9�� get --local atex-macros/ pull.rebase (dns block)

If you need me to access, download, or install something from one of these locations, you can either:

Configure Actions setup steps to set up my environment, which run before the firewall is enabled
Add the appropriate URLs or hosts to the custom allowlist in this repository's Copilot coding agent settings (admins only)

Original prompt

This section details on the original issue you should resolve

<issue_title>goldbach</issue_title>
<issue_description>add a page solving Goldbach's conjecture</issue_description>

Comments on the Issue (you are @copilot in this section)

Fixes goldbach #319

💬 We'd love your input! Share your thoughts on Copilot coding agent in our 2 minute survey.

Co-authored-by: d-morrison <2474437+d-morrison@users.noreply.github.com>

github-actions · 2026-01-09T02:42:49Z

PR Preview Action v1.8.0
🚀 View preview at https://d-morrison.github.io/rme/pr-preview/pr-320/
Built to branch `gh-pages` at 2026-01-09 02:42 UTC. Preview will be ready when the GitHub Pages deployment is complete.

Initial plan

575d171

Copilot AI assigned Copilot and d-morrison Jan 9, 2026

Copilot started work on behalf of d-morrison January 9, 2026 01:27 View session

Copilot AI and others added 2 commits January 9, 2026 01:43

Add Goldbach's conjecture page with computational verification

026725f

Co-authored-by: d-morrison <2474437+d-morrison@users.noreply.github.com>

Add educational note about code optimizations

334499b

Co-authored-by: d-morrison <2474437+d-morrison@users.noreply.github.com>

Copilot AI changed the title ~~[WIP] Add a page solving Goldbach's conjecture~~ Add Goldbach's conjecture appendix page Jan 9, 2026

Copilot AI requested a review from d-morrison January 9, 2026 01:45

Copilot finished work on behalf of d-morrison January 9, 2026 01:45

d-morrison closed this Jan 9, 2026

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Add Goldbach's conjecture appendix page #320

Add Goldbach's conjecture appendix page #320

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Copilot AI commented Jan 9, 2026 •

edited

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github-actions bot commented Jan 9, 2026

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Add Goldbach's conjecture appendix page #320

Add Goldbach's conjecture appendix page #320

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Copilot AI commented Jan 9, 2026 • edited Loading Uh oh! There was an error while loading. Please reload this page.

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I tried to connect to the following addresses, but was blocked by firewall rules:

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Copilot AI commented Jan 9, 2026 •

edited

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Built to branch `gh-pages` at 2026-01-09 02:42 UTC.
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