[[93]] is not prime (composite): [[3]] * [[31]]
Prime neighborhood: [[79]], [[83]], [[89]], [[93]], [[97]], [[101]], [[103]]
Prime gap: 8 (interval [[89]] to [[97]])
Primes up to 93: [[2]], [[3]], [[5]], [[7]], [[11]], [[13]], [[17]], [[19]], [[23]], [[29]], [[31]], [[37]], [[41]], [[43]], [[47]], [[53]], [[59]], [[61]], [[67]], [[71]], [[73]], [[79]], [[83]], [[89]] (24 total).
[[93]] is not a centered hexagonal number.
The closest centered hexagonal numbers are [[91]] (index # [[6]]) and [[127]] (index # [[7]]).
First 20 centered hexagonal numbers: [[1]], [[7]], [[19]], [[37]], [[61]], [[91]], [[127]], [[169]], [[217]], [[271]], [[331]], [[397]], [[469]], [[547]], [[631]], [[721]], [[817]], [[919]], [[1027]], [[1141]].
[[square]]: 8649
[[square root]]: 9.6437
[[cube]]: 804357
[[cube root]]: 4.5307
[[natural log]] (ln): 4.5326
[[base-10 log]] (log10): 1.9685
[[base-2 log]] (log2): 6.5392
https://colinraffel.com/projects/lmd/
The Lakh MIDI dataset is a collection of 176,581 unique MIDI files, 45,129 of which have been matched and aligned to entries in the Million Song Dataset. Its goal is to facilitate large-scale music information retrieval, both symbolic (using the MIDI files alone) and audio content-based (using information extracted from the MIDI files as annotations for the matched audio files).
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I saw this number on the floor on a discarded receipt in the train station: [[3493]]
It’s a multiple of seven. Proof:
349 - 6 = 343 (subtracting double the last digit from the rest of the number)
34 - 6 = 28 (again, reaching a multiple of seven)
Thanks universe for providing a nice example/practice session for a recently learnt divisibility rule :)
On closer inspection, it’s even simpler to verify: 3500 clearly is a multiple of seven, and the number is 3500 - 7.
https://folk.computer/notes/tableshots
The coolest thing I've seen today!