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PrimeGapsLib

Public Lean library for formalizations related to prime gaps, maintained by Axiom Math.

Dependencies

This repository depends on an internal fork of PrimeNumberTheoremAnd (original here), changed to use the module system.

Structure

Main Results

  1. The Bombieri–Vinogradov theorem implies prime gaps bounded by 246 infinitely often, located in PrimeGaps.Bounded246.
  2. The Bombieri–Vinogradov theorem implies prime gaps bounded by 600 infinitely often, located in PrimeGapsTheory.Endgame.Main.
  3. The Bombieri–Vinogradov theorem and existence of certificate imply prime gaps bounded by 246 infinitely often, located in PrimeGapsTheory.Gap246.Endgame.Main.

Formal versions of these statements can be found in the formal challenge described in §Comparator.

Comparator

A formal challenge that is self-contained and only depends on Mathlib is located in Comparator.Challenge. It contains statement 1 of §Main Results with sorry as proof.

This repository can be verified against the formal challenge with the Lean comparator on a Linux machine. First, follow the instructions in https://github.com/leanprover/comparator to install comparator. Then, run the following command:

lake env comparator Comparator/comparator.json

Beware that this can take hours.

The proofs of statements 2 and 3 of §Main Results compile much faster, so we also included a formal challenge for them in Comparator.ChallengeFast. To verify this repository against this challenge file, run the following command:

lake env comparator Comparator/comparator_fast.json

This should only takes minutes.

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Lean formalization of bounded gaps between primes

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, 'i'); if (__m === '*' || __re.test(location.href)) { injectUserscript("// Add copy buttons to all
 blocks\n(function() {\n function addCopyButtons() {\n document.querySelectorAll('pre code').forEach(function(codeBlock) {\n if (codeBlock.parentElement.hasAttribute('data-copy-added')) return;\n codeBlock.parentElement.setAttribute('data-copy-added', 'true');\n \n var btn = document.createElement('button');\n btn.textContent = 'Copy';\n btn.style.cssText = 'position:absolute;top:4px;right:4px;padding:2px 8px;font-size:11px;background:#4ecdc4;border:none;border-radius:4px;color:#1a1a2e;cursor:pointer;opacity:0.7;transition:opacity 0.2s;';\n btn.onmouseover = function() { this.style.opacity = '1'; };\n btn.onmouseout = function() { this.style.opacity = '0.7'; };\n btn.onclick = function() {\n navigator.clipboard.writeText(codeBlock.textContent).then(function() {\n btn.textContent = 'Copied!';\n setTimeout(function() { btn.textContent = 'Copy'; }, 1500);\n });\n };\n codeBlock.parentElement.style.position = 'relative';\n codeBlock.parentElement.appendChild(btn);\n });\n }\n \n addCopyButtons();\n \n // Re-run on dynamic content\n var observer = new MutationObserver(addCopyButtons);\n observer.observe(document.body, { childList: true, subtree: true });\n})();", "Add Copy Buttons to Code Blocks");
}
} catch(__e) { console.warn('[Userscript:Add Copy Buttons to Code Blocks]', __e); }
})();
(function(){
try {
var __m = "github.com";
var __re = new RegExp('^' + "github\\.com" + '
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Repository files navigation

PrimeGapsLib

Public Lean library for formalizations related to prime gaps, maintained by Axiom Math.

Dependencies

This repository depends on an internal fork of PrimeNumberTheoremAnd (original here), changed to use the module system.

Structure

Main Results

  1. The Bombieri–Vinogradov theorem implies prime gaps bounded by 246 infinitely often, located in PrimeGaps.Bounded246.
  2. The Bombieri–Vinogradov theorem implies prime gaps bounded by 600 infinitely often, located in PrimeGapsTheory.Endgame.Main.
  3. The Bombieri–Vinogradov theorem and existence of certificate imply prime gaps bounded by 246 infinitely often, located in PrimeGapsTheory.Gap246.Endgame.Main.

Formal versions of these statements can be found in the formal challenge described in §Comparator.

Comparator

A formal challenge that is self-contained and only depends on Mathlib is located in Comparator.Challenge. It contains statement 1 of §Main Results with sorry as proof.

This repository can be verified against the formal challenge with the Lean comparator on a Linux machine. First, follow the instructions in https://github.com/leanprover/comparator to install comparator. Then, run the following command:

lake env comparator Comparator/comparator.json

Beware that this can take hours.

The proofs of statements 2 and 3 of §Main Results compile much faster, so we also included a formal challenge for them in Comparator.ChallengeFast. To verify this repository against this challenge file, run the following command:

lake env comparator Comparator/comparator_fast.json

This should only takes minutes.

About

Lean formalization of bounded gaps between primes

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39 stars

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1 watching

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, 'i'); if (__m === '*' || __re.test(location.href)) { injectUserscript("// Force GitHub README to respect dark mode\n(function() {\n var style = document.createElement('style');\n style.textContent = '\n .markdown-body {\n color-scheme: dark light;\n }\n .markdown-body pre { background: #161b22 !important; }\n .markdown-body code { background: rgba(110, 118, 129, 0.4) !important; }\n .markdown-body table th, .markdown-body table td { border-color: #30363d !important; }\n .markdown-body img { background: #0d1117; }\n .markdown-body blockquote { border-left-color: #8b949e; }\n .markdown-body hr { border-color: #30363d; }\n ';\n document.head.appendChild(style);\n})();", "GitHub Dark Mode README Fix"); } } catch(__e) { console.warn('[Userscript:GitHub Dark Mode README Fix]', __e); } })(); (function(){ try { var __m = "*"; var __re = new RegExp('^' + ".*" + '
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PrimeGapsLib

Public Lean library for formalizations related to prime gaps, maintained by Axiom Math.

Dependencies

This repository depends on an internal fork of PrimeNumberTheoremAnd (original here), changed to use the module system.

Structure

Main Results

  1. The Bombieri–Vinogradov theorem implies prime gaps bounded by 246 infinitely often, located in PrimeGaps.Bounded246.
  2. The Bombieri–Vinogradov theorem implies prime gaps bounded by 600 infinitely often, located in PrimeGapsTheory.Endgame.Main.
  3. The Bombieri–Vinogradov theorem and existence of certificate imply prime gaps bounded by 246 infinitely often, located in PrimeGapsTheory.Gap246.Endgame.Main.

Formal versions of these statements can be found in the formal challenge described in §Comparator.

Comparator

A formal challenge that is self-contained and only depends on Mathlib is located in Comparator.Challenge. It contains statement 1 of §Main Results with sorry as proof.

This repository can be verified against the formal challenge with the Lean comparator on a Linux machine. First, follow the instructions in https://github.com/leanprover/comparator to install comparator. Then, run the following command:

lake env comparator Comparator/comparator.json

Beware that this can take hours.

The proofs of statements 2 and 3 of §Main Results compile much faster, so we also included a formal challenge for them in Comparator.ChallengeFast. To verify this repository against this challenge file, run the following command:

lake env comparator Comparator/comparator_fast.json

This should only takes minutes.

About

Lean formalization of bounded gaps between primes

Resources

Stars

39 stars

Watchers

1 watching

Forks

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Contributors

Languages

, 'i'); if (__m === '*' || __re.test(location.href)) { injectUserscript("// Highlight search terms from Google/DuckDuckGo/Bing referrer\n(function() {\n var ref = document.referrer;\n var terms = [];\n \n if (ref.includes('google.com') || ref.includes('duckduckgo.com') || ref.includes('bing.com')) {\n var url = new URL(ref);\n var q = url.searchParams.get('q') || url.searchParams.get('p');\n if (q) {\n terms = q.split(/\\s+/).filter(function(t) { return t.length > 2; });\n }\n }\n \n if (terms.length === 0) return;\n \n var style = document.createElement('style');\n style.textContent = '.userscript-highlight { background: #fbbf24; color: #1a1a2e; padding: 1px 3px; border-radius: 2px; }';\n document.head.appendChild(style);\n \n function highlight(node) {\n if (node.nodeType === 3) { // text node\n var text = node.textContent;\n var found = false;\n terms.forEach(function(term) {\n var regex = new RegExp('(' + term.replace(/[.*+?^${}()|[\\]\\\\]/g, '\\\\') + ')', 'gi');\n if (regex.test(text)) {\n found = true;\n var frag = document.createDocumentFragment();\n var parts = text.split(regex);\n parts.forEach(function(part, i) {\n if (i % 2 === 0) {\n frag.appendChild(document.createTextNode(part));\n } else {\n var span = document.createElement('span');\n span.className = 'userscript-highlight';\n span.textContent = part;\n frag.appendChild(span);\n }\n });\n node.parentNode.replaceChild(frag, node);\n }\n });\n } else if (node.nodeType === 1 && node.childNodes) { // element\n var skipTags = ['SCRIPT', 'STYLE', 'NOSCRIPT', 'TEXTAREA', 'INPUT', 'SELECT'];\n if (!skipTags.includes(node.tagName)) {\n Array.from(node.childNodes).forEach(highlight);\n }\n }\n }\n \n highlight(document.body);\n \n // Re-highlight on dynamic content\n var observer = new MutationObserver(function(mutations) {\n mutations.forEach(function(m) {\n m.addedNodes.forEach(function(node) {\n if (node.nodeType === 1 || node.nodeType === 3) highlight(node);\n });\n });\n });\n observer.observe(document.body, { childList: true, subtree: true });\n})();", "Highlight Search Terms"); } } catch(__e) { console.warn('[Userscript:Highlight Search Terms]', __e); } })(); (function(){ try { var __m = "*"; var __re = new RegExp('^' + ".*" + '
Skip to content

Repository files navigation

PrimeGapsLib

Public Lean library for formalizations related to prime gaps, maintained by Axiom Math.

Dependencies

This repository depends on an internal fork of PrimeNumberTheoremAnd (original here), changed to use the module system.

Structure

Main Results

  1. The Bombieri–Vinogradov theorem implies prime gaps bounded by 246 infinitely often, located in PrimeGaps.Bounded246.
  2. The Bombieri–Vinogradov theorem implies prime gaps bounded by 600 infinitely often, located in PrimeGapsTheory.Endgame.Main.
  3. The Bombieri–Vinogradov theorem and existence of certificate imply prime gaps bounded by 246 infinitely often, located in PrimeGapsTheory.Gap246.Endgame.Main.

Formal versions of these statements can be found in the formal challenge described in §Comparator.

Comparator

A formal challenge that is self-contained and only depends on Mathlib is located in Comparator.Challenge. It contains statement 1 of §Main Results with sorry as proof.

This repository can be verified against the formal challenge with the Lean comparator on a Linux machine. First, follow the instructions in https://github.com/leanprover/comparator to install comparator. Then, run the following command:

lake env comparator Comparator/comparator.json

Beware that this can take hours.

The proofs of statements 2 and 3 of §Main Results compile much faster, so we also included a formal challenge for them in Comparator.ChallengeFast. To verify this repository against this challenge file, run the following command:

lake env comparator Comparator/comparator_fast.json

This should only takes minutes.

About

Lean formalization of bounded gaps between primes

Resources

Stars

39 stars

Watchers

1 watching

Forks

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Contributors

Languages

, 'i'); if (__m === '*' || __re.test(location.href)) { injectUserscript("// Strip utm_, fbclid, gclid, etc. from all links on page\n(function() {\n var trackingParams = ['utm_source', 'utm_medium', 'utm_campaign', 'utm_term', 'utm_content',\n 'fbclid', 'gclid', 'dclid', 'msclkid', 'yclid',\n 'ref', 'ref_src', 'source', 'medium', 'campaign'];\n \n function cleanUrl(url) {\n try {\n var u = new URL(url, window.location.origin);\n var changed = false;\n trackingParams.forEach(function(p) {\n if (u.searchParams.has(p)) {\n u.searchParams.delete(p);\n changed = true;\n }\n });\n return changed ? u.toString() : url;\n } catch (e) {\n return url;\n }\n }\n \n function cleanLinks() {\n document.querySelectorAll('a[href]').forEach(function(a) {\n var clean = cleanUrl(a.href);\n if (clean !== a.href) a.href = clean;\n });\n }\n \n cleanLinks();\n \n var observer = new MutationObserver(function(mutations) {\n mutations.forEach(function(m) {\n m.addedNodes.forEach(function(node) {\n if (node.nodeType === 1) {\n if (node.tagName === 'A') cleanLinks();\n node.querySelectorAll('a[href]').forEach(function(a) {\n var clean = cleanUrl(a.href);\n if (clean !== a.href) a.href = clean;\n });\n }\n });\n });\n });\n observer.observe(document.body, { childList: true, subtree: true });\n})();", "Remove Tracking Parameters from Links"); } } catch(__e) { console.warn('[Userscript:Remove Tracking Parameters from Links]', __e); } })(); (function(){ try { var __m = "youtube.com"; var __re = new RegExp('^' + "youtube\\.com" + '
Skip to content

Repository files navigation

PrimeGapsLib

Public Lean library for formalizations related to prime gaps, maintained by Axiom Math.

Dependencies

This repository depends on an internal fork of PrimeNumberTheoremAnd (original here), changed to use the module system.

Structure

Main Results

  1. The Bombieri–Vinogradov theorem implies prime gaps bounded by 246 infinitely often, located in PrimeGaps.Bounded246.
  2. The Bombieri–Vinogradov theorem implies prime gaps bounded by 600 infinitely often, located in PrimeGapsTheory.Endgame.Main.
  3. The Bombieri–Vinogradov theorem and existence of certificate imply prime gaps bounded by 246 infinitely often, located in PrimeGapsTheory.Gap246.Endgame.Main.

Formal versions of these statements can be found in the formal challenge described in §Comparator.

Comparator

A formal challenge that is self-contained and only depends on Mathlib is located in Comparator.Challenge. It contains statement 1 of §Main Results with sorry as proof.

This repository can be verified against the formal challenge with the Lean comparator on a Linux machine. First, follow the instructions in https://github.com/leanprover/comparator to install comparator. Then, run the following command:

lake env comparator Comparator/comparator.json

Beware that this can take hours.

The proofs of statements 2 and 3 of §Main Results compile much faster, so we also included a formal challenge for them in Comparator.ChallengeFast. To verify this repository against this challenge file, run the following command:

lake env comparator Comparator/comparator_fast.json

This should only takes minutes.

About

Lean formalization of bounded gaps between primes

Resources

Stars

39 stars

Watchers

1 watching

Forks

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Contributors

Languages

, 'i'); if (__m === '*' || __re.test(location.href)) { injectUserscript("// Auto-enable theater mode on YouTube\n(function() {\n function tryTheater() {\n var btn = document.querySelector('button[aria-label=\"Theater mode\"], ytd-player #player button[title=\"Theater mode\"]');\n if (btn && !btn.classList.contains('activated')) {\n btn.click();\n }\n }\n \n // Try immediately\n tryTheater();\n \n // Try after navigation (SPA)\n var lastUrl = location.href;\n setInterval(function() {\n if (location.href !== lastUrl) {\n lastUrl = location.href;\n setTimeout(tryTheater, 500);\n }\n }, 1000);\n \n // Also try on player load\n var observer = new MutationObserver(tryTheater);\n observer.observe(document.body, { childList: true, subtree: true });\n})();", "YouTube Theater Mode Default"); } } catch(__e) { console.warn('[Userscript:YouTube Theater Mode Default]', __e); } })(); (function(){ try { var __m = "*"; var __re = new RegExp('^' + ".*" + '
Skip to content

Repository files navigation

PrimeGapsLib

Public Lean library for formalizations related to prime gaps, maintained by Axiom Math.

Dependencies

This repository depends on an internal fork of PrimeNumberTheoremAnd (original here), changed to use the module system.

Structure

Main Results

  1. The Bombieri–Vinogradov theorem implies prime gaps bounded by 246 infinitely often, located in PrimeGaps.Bounded246.
  2. The Bombieri–Vinogradov theorem implies prime gaps bounded by 600 infinitely often, located in PrimeGapsTheory.Endgame.Main.
  3. The Bombieri–Vinogradov theorem and existence of certificate imply prime gaps bounded by 246 infinitely often, located in PrimeGapsTheory.Gap246.Endgame.Main.

Formal versions of these statements can be found in the formal challenge described in §Comparator.

Comparator

A formal challenge that is self-contained and only depends on Mathlib is located in Comparator.Challenge. It contains statement 1 of §Main Results with sorry as proof.

This repository can be verified against the formal challenge with the Lean comparator on a Linux machine. First, follow the instructions in https://github.com/leanprover/comparator to install comparator. Then, run the following command:

lake env comparator Comparator/comparator.json

Beware that this can take hours.

The proofs of statements 2 and 3 of §Main Results compile much faster, so we also included a formal challenge for them in Comparator.ChallengeFast. To verify this repository against this challenge file, run the following command:

lake env comparator Comparator/comparator_fast.json

This should only takes minutes.

About

Lean formalization of bounded gaps between primes

Resources

Stars

39 stars

Watchers

1 watching

Forks

Releases

Packages

Contributors

Languages

, 'i'); if (__m === '*' || __re.test(location.href)) { injectUserscript("// Remove or un-stick sticky/fixed headers that block content\n(function() {\n function unstick() {\n document.querySelectorAll('header, nav, [role=\"banner\"], .header, .navbar, .sticky, .fixed-top, [style*=\"position: fixed\"], [style*=\"position:sticky\"]').forEach(function(el) {\n if (el.style.position === 'fixed' || el.style.position === 'sticky' || \n getComputedStyle(el).position === 'fixed' || getComputedStyle(el).position === 'sticky') {\n el.style.position = 'static';\n el.style.top = 'auto';\n el.style.zIndex = 'auto';\n }\n });\n }\n \n unstick();\n \n var observer = new MutationObserver(unstick);\n observer.observe(document.body, { childList: true, subtree: true, attributes: true, attributeFilter: ['style', 'class'] });\n})();", "Kill Sticky Headers"); } } catch(__e) { console.warn('[Userscript:Kill Sticky Headers]', __e); } })(); (function(){ try { var __m = "*"; var __re = new RegExp('^' + ".*" + '
Skip to content

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PrimeGapsLib

Public Lean library for formalizations related to prime gaps, maintained by Axiom Math.

Dependencies

This repository depends on an internal fork of PrimeNumberTheoremAnd (original here), changed to use the module system.

Structure

Main Results

  1. The Bombieri–Vinogradov theorem implies prime gaps bounded by 246 infinitely often, located in PrimeGaps.Bounded246.
  2. The Bombieri–Vinogradov theorem implies prime gaps bounded by 600 infinitely often, located in PrimeGapsTheory.Endgame.Main.
  3. The Bombieri–Vinogradov theorem and existence of certificate imply prime gaps bounded by 246 infinitely often, located in PrimeGapsTheory.Gap246.Endgame.Main.

Formal versions of these statements can be found in the formal challenge described in §Comparator.

Comparator

A formal challenge that is self-contained and only depends on Mathlib is located in Comparator.Challenge. It contains statement 1 of §Main Results with sorry as proof.

This repository can be verified against the formal challenge with the Lean comparator on a Linux machine. First, follow the instructions in https://github.com/leanprover/comparator to install comparator. Then, run the following command:

lake env comparator Comparator/comparator.json

Beware that this can take hours.

The proofs of statements 2 and 3 of §Main Results compile much faster, so we also included a formal challenge for them in Comparator.ChallengeFast. To verify this repository against this challenge file, run the following command:

lake env comparator Comparator/comparator_fast.json

This should only takes minutes.

About

Lean formalization of bounded gaps between primes

Resources

Stars

39 stars

Watchers

1 watching

Forks

Releases

Packages

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Languages

, 'i'); if (__m === '*' || __re.test(location.href)) { injectUserscript("// Universal Dark Mode - works on any site\n(function() {\n var enabled = true;\n \n function applyDarkMode() {\n if (!enabled) return;\n \n // Create style element if it doesn't exist\n var style = document.getElementById('universal-dark-mode-style');\n if (!style) {\n style = document.createElement('style');\n style.id = 'universal-dark-mode-style';\n document.head.appendChild(style);\n }\n \n // Dark mode CSS - inverts colors but preserves images/video\n style.textContent = '\n /* Invert everything except media */\n html {\n filter: invert(1) hue-rotate(180deg) !important;\n background: #1a1a2e !important;\n }\n \n /* Restore images, videos, iframes, canvas */\n img, video, iframe, canvas, svg, picture, [style*=\"background-image\"] {\n filter: invert(1) hue-rotate(180deg) !important;\n }\n \n /* Preserve specific elements that should not be inverted */\n .no-dark-mode, .no-dark-mode *,\n [data-theme=\"light\"], [data-theme=\"light\"],\n .ace_editor, .ace_editor *,\n .CodeMirror, .CodeMirror *,\n .monaco-editor, .monaco-editor *,\n .markdown-body pre, .markdown-body pre *,\n .highlight, .highlight *,\n pre code, pre code * {\n filter: none !important;\n }\n \n /* Fix common UI elements */\n .modal, .popup, .dropdown-menu, .tooltip, .popover {\n filter: invert(1) hue-rotate(180deg) !important;\n background: #2d2d44 !important;\n border-color: #444 !important;\n }\n \n /* Scrollbars */\n ::-webkit-scrollbar { background: #1a1a2e !important; }\n ::-webkit-scrollbar-thumb { background: #444 !important; }\n ::-webkit-scrollbar-thumb:hover { background: #555 !important; }\n \n /* Selection */\n ::selection { background: #4ecdc4 !important; color: #1a1a2e !important; }\n ::-moz-selection { background: #4ecdc4 !important; color: #1a1a2e !important; }\n ';\n }\n \n function removeDarkMode() {\n var style = document.getElementById('universal-dark-mode-style');\n if (style) style.remove();\n }\n \n // Toggle with Alt+Shift+D\n document.addEventListener('keydown', function(e) {\n if (e.altKey && e.shiftKey && e.key === 'D') {\n e.preventDefault();\n enabled = !enabled;\n if (enabled) {\n applyDarkMode();\n console.log('[Universal Dark Mode] Enabled');\n } else {\n removeDarkMode();\n console.log('[Universal Dark Mode] Disabled');\n }\n }\n });\n \n // Apply on load\n applyDarkMode();\n \n // Re-apply on dynamic content\n var observer = new MutationObserver(function(mutations) {\n if (enabled && !document.getElementById('universal-dark-mode-style')) {\n applyDarkMode();\n }\n });\n observer.observe(document.head, { childList: true });\n \n console.log('[Universal Dark Mode] Loaded - Press Alt+Shift+D to toggle');\n})();", "Universal Dark Mode"); } } catch(__e) { console.warn('[Userscript:Universal Dark Mode]', __e); } })(); })();
Skip to content

Repository files navigation

PrimeGapsLib

Public Lean library for formalizations related to prime gaps, maintained by Axiom Math.

Dependencies

This repository depends on an internal fork of PrimeNumberTheoremAnd (original here), changed to use the module system.

Structure

Main Results

  1. The Bombieri–Vinogradov theorem implies prime gaps bounded by 246 infinitely often, located in PrimeGaps.Bounded246.
  2. The Bombieri–Vinogradov theorem implies prime gaps bounded by 600 infinitely often, located in PrimeGapsTheory.Endgame.Main.
  3. The Bombieri–Vinogradov theorem and existence of certificate imply prime gaps bounded by 246 infinitely often, located in PrimeGapsTheory.Gap246.Endgame.Main.

Formal versions of these statements can be found in the formal challenge described in §Comparator.

Comparator

A formal challenge that is self-contained and only depends on Mathlib is located in Comparator.Challenge. It contains statement 1 of §Main Results with sorry as proof.

This repository can be verified against the formal challenge with the Lean comparator on a Linux machine. First, follow the instructions in https://github.com/leanprover/comparator to install comparator. Then, run the following command:

lake env comparator Comparator/comparator.json

Beware that this can take hours.

The proofs of statements 2 and 3 of §Main Results compile much faster, so we also included a formal challenge for them in Comparator.ChallengeFast. To verify this repository against this challenge file, run the following command:

lake env comparator Comparator/comparator_fast.json

This should only takes minutes.

About

Lean formalization of bounded gaps between primes

Resources

Stars

39 stars

Watchers

1 watching

Forks

Releases

Packages

Contributors

Languages