38 (number)

38 (thirty-eight) is the natural number following 37 and preceding 39.

In mathematics

specifically, the 11th discrete Semiprime,^[1] it being the 7th of the form (2.q).
the first member of the third cluster of two discrete semiprimes 38, 39 the next such cluster is 57, 58.
with an aliquot sum of 22 in an aliquot sequence of five composite numbers (38,22,14,10,8,7,1,0) to the Prime in the 7-aliquot tree. 38 is the first semiprime within a chain of 4 semiprimes in its aliquot sequence (38,22,14,10). The next semiprime with a four semiprime chain is 166.
38! − 1 yields 523022617466601111760007224100074291199999999 which is the 16th factorial prime.^[2]
There is no answer to the equation φ(x) = 38, making 38 a nontotient.^[3]
38 is the sum of the squares of the first three primes.
37 and 38 are the first pair of consecutive positive integers not divisible by any of their digits.
38 is the largest even number which cannot be written as the sum of two odd composite numbers.
The sum of each row of the only non-trivial (order 3) magic hexagon is 38.^[4]

Ishihara test: Most people will see the number 38, but people with red-green color blindness might see 88 instead.

Thirty-eight is also:

The 38th parallel north is the pre-Korean War boundary between North Korea and South Korea.^[5]
The number of slots on an American roulette wheel (0, 00, and 1 through 36; European roulette does not use the 00 slot and has only 37 slots)
The Ishihara test is a color vision test consisting of 38 pseudoisochromatic plates.^[6]
A "38" is often the name for a snub nose .38 caliber revolver.
The 38 class is the most famous class of steam locomotive used in New South Wales
Gerald Ford, 38th President of the United States
Arnold Schwarzenegger, 38th Governor of California, most recent Republican governor of California, and the second governor to be born outside of the United States
Cats have a total of 38 chromosomes in their genome.
Number used by Zane Smith and Front Row Motorsports to win the 2022 NASCAR Camping World Truck Series championship.
The Lucky 38, the casino from Fallout: New Vegas.

^ Sloane, N. J. A. (ed.). "Sequence A001358". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
^ Sloane, N. J. A. (ed.). "Sequence A002982 (Numbers n such that n! - 1 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31.
^ (sequence A005277 in the OEIS)
^ Higgins, Peter (2008). Number Story: From Counting to Cryptography. New York: Copernicus. p. 53. ISBN 978-1-84800-000-1.
^ Fry, Michael (5 August 2013). "National Geographic, Korea, and the 38th Parallel". National Geographic. Archived from the original on February 25, 2021. Retrieved 15 May 2021.
^ Fluck, Daniel (23 March 2010). "Color Blindness Tests". Colblinder. Retrieved 30 November 2022.