There are infinitely many primes with a neighbor not further apart than 70 million. This was the first such finite bound to be proven, and therefore a major breakthrough.
This implies that for at least one value (or more) below 70 million there are infinitely many repetitions, but we don't know which e.g. we could have infinitely many:or infinitely many:or infinitely many:or infinitely many:but we don't know which of those.
The Prime k-tuple conjecture conjectures that it is all of them.
The algorithmic trick that solves Rubik's Cubes and breaks ciphers by polylog (2022)
Source. Amazing project, that basically makes a more searchable Wayback Machine.
A bit hard to use their data though, partly due to size, but also lack of free to use querrying mechanisms, and how obtuse Amazon S3 is to use.
Notably, aws-cli with an account is the only reliable way, everything else is way too broken, e.g. trying the to check the an index index.commoncrawl.org/CC-MAIN-2023-06/ very often 500s.
But still, their projct is amazing.
The only out-of-the-box search they seem to have is: urlsearch.commoncrawl.org/ for domains/URLs. It is good, but there could be so much more... notably IPs.
Sample sizes can be found at: commoncrawl.org/2023/04/mar-apr-2023-crawl-archive-now-available/
To explore the data, after login:
aws s3 ls s3://commoncrawl/crawl-data/CC-MAIN-2013-20/Copy the toplevel directory only:
aws s3 cp s3://commoncrawl/crawl-data/CC-MAIN-2013-20/ . --recursive --exclude "*/*"Copy some wet/wat files:
aws s3 cp s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368696381249/wat/CC-MAIN-20130516092621-00000-ip-10-60-113-184.ec2.internal.warc.wat.gz .
aws s3 sync s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368696381249/wet/CC-MAIN-20130516092621-00000-ip-10-60-113-184.ec2.internal.warc.wet.gz .Directory structrure:
- cc-index.paths.gz (1K)
- cc-index-table.paths.gz (1K)
- segment.paths.gz (1.7K) Sample lines:
crawl-data/CC-MAIN-2013-20/segments/1368696381249/ crawl-data/CC-MAIN-2013-20/segments/1368696381630/ - index.html (2.3K)
- wat.paths.gz (98K) Sample lines:
crawl-data/CC-MAIN-2013-20/segments/1368696381249/wat/CC-MAIN-20130516092621-00000-ip-10-60-113-184.ec2.internal.warc.wat.gz crawl-data/CC-MAIN-2013-20/segments/1368696381249/wat/CC-MAIN-20130516092621-00001-ip-10-60-113-184.ec2.internal.warc.wat.gz - wet.paths.gz (98K) Sample lines:
crawl-data/CC-MAIN-2013-20/segments/1368696381249/wet/CC-MAIN-20130516092621-00000-ip-10-60-113-184.ec2.internal.warc.wet.gz crawl-data/CC-MAIN-2013-20/segments/1368696381249/wet/CC-MAIN-20130516092621-00001-ip-10-60-113-184.ec2.internal.warc.wet.gz - warc.paths.gz (99K)
crawl-data/CC-MAIN-2013-20/segments/1368696381249/warc/CC-MAIN-20130516092621-00000-ip-10-60-113-184.ec2.internal.warc.gz crawl-data/CC-MAIN-2013-20/segments/1368696381249/warc/CC-MAIN-20130516092621-00001-ip-10-60-113-184.ec2.internal.warc.gz - segments: directgory with actual data
- 1368696381249: one of many segments, any meaning of name?
- CC-MAIN-20130516092621-00000-ip-10-60-113-184.ec2.internal.warc.wet.gz (142M, 334M unzipped)A tiny bit of metadata, and then plaintext content from the website, e.g. the second one:No IP unfortunately.
WARC/1.0 WARC-Type: conversion WARC-Target-URI: http://004eeb5.netsolhost.com/stephensilver.htm WARC-Date: 2013-05-18T08:11:02Z WARC-Record-ID: <urn:uuid:773b31ba-ddc6-47a5-ae24-d08141b9944d> WARC-Refers-To: <urn:uuid:4b1bdbff-4926-4ced-86f6-072f5bb3837a> WARC-Block-Digest: sha1:LQFSCR2LIJQYMPTXRHWU7HAPQTVSYS3A Content-Type: text/plain Content-Length: 12046 Stephen Silver is a journalist and editor who specializes in the areas of politics, pop culture, film and sports. He works as an editor with the North American Publishing Co. and as a film critic with The Trend, a local newspaper in the Philadelphia area. - A lot of JSON metadata and no contents as desired. Contains IP! Some entries however are humongous with a ton of useless data, that's what bloats these so much:Let's beautify one of them to see it better:
WARC/1.0 WARC-Type: metadata WARC-Target-URI: CC-MAIN-20130516092621-00000-ip-10-60-113-184.ec2.internal.warc.gz WARC-Date: 2013-11-22T14:51:12Z WARC-Record-ID: <urn:uuid:ec54e493-8965-41be-b344-07596cc30b3a> WARC-Refers-To: <urn:uuid:cfeff436-7c4c-4119-aaa4-ec2ce27ad3e1> Content-Type: application/json Content-Length: 1180 {"Envelope":{"Format":"WARC","WARC-Header-Length":"274","Block-Digest":"sha1:JCZOI4V3UOTXGIRLFMPLW4J2WPLAKGVR","Actual-Content-Length":"372","WARC-Header-Metadata":{"WARC-Type":"warcinfo","WARC-Filename":"CC-MAIN-20130516092621-00000-ip-10-60-113-184.ec2.internal.warc.gz","WARC-Date":"2013-11-22T14:51:12Z","Content-Length":"372","WARC-Record-ID":"<urn:uuid:cfeff436-7c4c-4119-aaa4-ec2ce27ad3e1>","Content-Type":"application/warc-fields"},"Payload-Metadata":{"Trailing-Slop-Length":"0","Actual-Content-Type":"application/warc-fields","Actual-Content-Length":"372","Headers-Corrupt":true,"WARC-Info-Metadata":{"robots":"classic","software":"Nutch 1.6 (CC)/CC WarcExport 1.0","description":"Wide crawl of the web with URLs provided by Blekko for Spring 2013","hostname":"ip-10-60-113-184.ec2.internal","format":"WARC File Format 1.0","isPartOf":"CC-MAIN-2013-20","operator":"CommonCrawl Admin","publisher":"CommonCrawl"}}},"Container":{"Compressed":true,"Gzip-Metadata":{"Footer-Length":"8","Deflate-Length":"453","Header-Length":"10","Inflated-CRC":"866052549","Inflated-Length":"650"},"Offset":"0","Filename":"CC-MAIN-20130516092621-00000-ip-10-60-113-184.ec2.internal.warc.gz"}} WARC/1.0 WARC-Type: metadata WARC-Target-URI: http://%20jwashington@ap.org/Content/Press-Release/2012/How-AP-reported-in-all-formats-from-tornado-stricken-regions WARC-Date: 2013-05-18T05:48:54Z WARC-Record-ID: <urn:uuid:d519658f-7a63-46c1-849b-4cd92332ddb8> WARC-Refers-To: <urn:uuid:cefd363b-1fec-4590-8305-4c6fab2e095f> Content-Type: application/json Content-Length: 1501 {"Envelope":{"Format":"WARC","WARC-Header-Length":"433","Block-Digest":"sha1:B2B6JDSGWCUQIIUGV54SXEE25RX4SANS","Actual-Content-Length":"302","WARC-Header-Metadata":{"WARC-Type":"request","WARC-Date":"2013-05-18T05:48:54Z","WARC-Warcinfo-ID":"<urn:uuid:cfeff436-7c4c-4119-aaa4-ec2ce27ad3e1>","Content-Length":"302","WARC-Record-ID":"<urn:uuid:cefd363b-1fec-4590-8305-4c6fab2e095f>","WARC-Target-URI":"http://%20jwashington@ap.org/Content/Press-Release/2012/How-AP-reported-in-all-formats-from-tornado-stricken-regions","WARC-IP-Address":"165.1.125.44","Content-Type":"application/http; msgtype=request"},"Payload-Metadata":{"Trailing-Slop-Length":"4","HTTP-Request-Metadata":{"Headers":{"Accept-Language":"en-us,en-gb,en;q=0.7,*;q=0.3","Host":"ap.org","Accept-Encoding":"x-gzip, gzip, deflate","User-Agent":"CCBot/2.0","Accept":"text/html,application/xhtml+xml,application/xml;q=0.9,*/*;q=0.8"},"Headers-Length":"300","Entity-Length":"0","Entity-Trailing-Slop-Bytes":"0","Request-Message":{"Method":"GET","Version":"HTTP/1.0","Path":"/Content/Press-Release/2012/How-AP-reported-in-all-formats-from-tornado-stricken-regions"},"Entity-Digest":"sha1:3I42H3S6NNFQ2MSVX7XZKYAYSCX5QBYJ"},"Actual-Content-Type":"application/http; msgtype=request"}},"Container":{"Compressed":true,"Gzip-Metadata":{"Footer-Length":"8","Deflate-Length":"455","Header-Length":"10","Inflated-CRC":"453539965","Inflated-Length":"739"},"Offset":"453","Filename":"CC-MAIN-20130516092621-00000-ip-10-60-113-184.ec2.internal.warc.gz"}}Fuck no IP addresses either. But other entries do have it, why not this one?{ "Envelope": { "Format": "WARC", "WARC-Header-Length": "274", "Block-Digest": "sha1:JCZOI4V3UOTXGIRLFMPLW4J2WPLAKGVR", "Actual-Content-Length": "372", "WARC-Header-Metadata": { "WARC-Type": "warcinfo", "WARC-Filename": "CC-MAIN-20130516092621-00000-ip-10-60-113-184.ec2.internal.warc.gz", "WARC-Date": "2013-11-22T14:51:12Z", "Content-Length": "372", "WARC-Record-ID": "<urn:uuid:cfeff436-7c4c-4119-aaa4-ec2ce27ad3e1>", "Content-Type": "application/warc-fields" }, "Payload-Metadata": { "Trailing-Slop-Length": "0", "Actual-Content-Type": "application/warc-fields", "Actual-Content-Length": "372", "Headers-Corrupt": true, "WARC-Info-Metadata": { "robots": "classic", "software": "Nutch 1.6 (CC)/CC WarcExport 1.0", "description": "Wide crawl of the web with URLs provided by Blekko for Spring 2013", "hostname": "ip-10-60-113-184.ec2.internal", "format": "WARC File Format 1.0", "isPartOf": "CC-MAIN-2013-20", "operator": "CommonCrawl Admin", "publisher": "CommonCrawl" } } }, "Container": { "Compressed": true, "Gzip-Metadata": { "Footer-Length": "8", "Deflate-Length": "453", "Header-Length": "10", "Inflated-CRC": "866052549", "Inflated-Length": "650" }, "Offset": "0", "Filename": "CC-MAIN-20130516092621-00000-ip-10-60-113-184.ec2.internal.warc.gz" } }The reason these can be huge is theHTML-Metadatasection which contain all outlinks! gist.github.com/Smerity/e750f0ef0ab9aa366558#file-bbc-pretty-wat-L34 CC-MAIN-20130516092621-00000-ip-10-60-113-184.ec2.internal.warc.gz()Obtain:aws s3 cp s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368696381249/warc/CC-MAIN-20130516092621-00000-ip-10-60-113-184.ec2.internal.warc.gz .
- 1368696381249: one of many segments, any meaning of name?
Application of systems of linear equations by 
Ciro Santilli 35 Updated 2025-04-18 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-04-18 +Created 1970-01-01 System of linear equations algorithm by Ciro Santilli 35 Updated 2025-04-18 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-04-18 +Created 1970-01-01You just have to spend a few minutes with students until they complain about the courses or teachers. And you just have to spend a few hours with teachers until they complain about the students or broader system.
University is broken, and everyone knows it. The only question now is finding a viable, "political cash flow positive" path, into something better.
Bibliography:
- academeblog.org/2022/10/05/american-universities-are-going-to-implode/ American Universities Are Going to Implode (2022) by www.linkedin.com/in/jsgabin/
- theimaginativeconservative.org/2020/04/higher-education-implode-alexander-zubatov.html Higher Education Is About to Implode by Alexander Zubatov (2020)
- 2024-05-28 www.theguardian.com/education/article/2024/may/28/i-see-little-point-uk-university-students-on-why-attendance-has-plummeted ‘I see little point’: UK university students on why attendance has plummetedGive it to me, baby. OurBigBook incoming.
"There’s a bit of a feeling that there is just box-ticking going on [among students], and getting a degree at the end of it."
University should focus on inspiring and not on evaluating by Ciro Santilli 35 Updated 2025-04-18 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-04-18 +Created 1970-01-01As of 2020s and much earlier, Ciro Santilli believes that undergrad studies were fundamentally broken (considering the Information Age which completely changed what would be possible) because university had only two goals, with the exception of a few enlightened professors:As a result, most students, who would not go on to do a PhD essentially do a simple trade: all their time, and possibly some money, in exchange for embuing themselves with the incredible name of a respected institution so they can get better jobs later on.
- rank students from worse to best so they can get into PhD programs.For regular jobs grades didn't even matter as much compared the prestige of your university (and therefore, university entry exam grades) and your ability to stand the stress of exams to get minimal passing grade.In particular, being able to rank requires setting the difficulty level at a point where you can see a normal distribution in grades, and not have everyone at either 0 nor 100%.
- get money from the students. Of course, in countries where university is "free", this means reporting how many students you had to some government office so they can give you a corresponding budget. But you still have an incentive to enroll as many as possible.
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