Ciro Santilli @cirosantilli 37

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Fandom (website) Updated 2025-07-16

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Puzzle Updated 2025-07-16

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SQL histogram Updated 2025-07-16

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OK, there's a billion questions:

SQL Server
- stackoverflow.com/questions/485409/generating-a-histogram-from-column-values-in-a-database OP did not know the difference between count and histogram :-) But it's the number one Google result.
- stackoverflow.com/questions/19103991/create-range-bins-from-sql-server-table-for-histograms has a minor extra group by twist, but otherwise fine
- stackoverflow.com/questions/16268441/generate-histogram-in-sql-server
SQLite
- stackoverflow.com/questions/67514208/how-to-optimise-creating-histogram-bins-in-sqlite perf only, benchmarking would be needed. SQLite.
- stackoverflow.com/questions/32155449/create-a-histogram-with-a-dynamic-number-of-partitions-in-sqlite variable bin size, same number of entries per bin
- stackoverflow.com/questions/60348109/histogram-for-time-periods-using-sqlite-regular-buckets-1h-wide time
MySQL: stackoverflow.com/questions/1764881/getting-data-for-histogram-plot MySQL appears to extend ROUND to also round by integers: ROUND(numeric_value, -2), but this is not widely portable which is a shame
stackoverflow.com/questions/72367652/populating-empty-bins-in-a-histogram-generated-using-sql specifically asks about empty bins, which is amazing. Amazon Redshift dialect unfortunately, but answer provided works widely, and Redshift was forked from PostgreSQL, so there's hope. Those newb open source server focused projects that don't use AGPL!

Let's try it on SQLite 3.40.1, Ubuntu 23.04. Data setup:

sqlite3 tmp.sqlite 'create table t(x integer)'
sqlite3 tmp.sqlite <<EOF
insert into t values (
  0,
  2,
  2,
  3,

  5,
  6,
  6,
  8,
  9,

  17,
)
EOF
sqlite3 tmp.sqlite 'create index tx on t(x)'

For a bin size of 5 ignoring empty ranges we can:

sqlite3 tmp.sqlite <<EOF
select floor(x/5)*5 as x,
       count(*) as cnt
from t
group by 1
order by 1
EOF

which produces the desired:

0|4
5|5
15|1

And to consider empty ranges we can use SQL genenerate_series + as per stackoverflow.com/questions/72367652/populating-empty-bins-in-a-histogram-generated-using-sql:

sqlite3 tmp.sqlite <<EOF
select x, sum(cnt) from (
  select floor(x/5)*5 as x,
         count(*) as cnt
    from t
    group by 1
  union
  select *, 0 as cnt from generate_series(0, 15, 5)
)
group by x
EOF

which outputs the desired:

0|4
5|5
10|0
15|1

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Yitang Zhang's theorem Updated 2025-07-16

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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: