# 40,000

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"40k" redirects here. For the tabletop game, see [Warhammer 40,000](/source/Warhammer_40,000). For the isotope 40K, see [Potassium-40](/source/Potassium-40).

**40,000** (**forty thousand**) is the [natural number](/source/Natural_number) that comes after 39,999 and before 40,001. It is the square of 200.

## Selected numbers in the range 40001–49999

### 40001 to 40999

- **40320** = smallest [factorial](/source/Factorial) (8!) that is not a [highly composite number](/source/Highly_composite_number)
- **40425** = [square pyramidal number](/source/Square_pyramidal_number)
- **40585** = largest [factorion](/source/Factorion)[1]
- **40678** = [pentagonal pyramidal number](/source/Pentagonal_pyramidal_number)
- **40755** = the smallest number >1 to be a [Triangular number](/source/Triangular_number), [Pentagonal number](/source/Pentagonal_number), and a [Hexagonal number](/source/Hexagonal_number).[2] Additionally, it's a 390-gonal, 4077-gonal, and 13586-gonal number.[3][4][5]
- **40804** = [palindromic](/source/Palindromic_number) square

### 41000 to 41999

- **41041** = [Carmichael number](/source/Carmichael_number)[6]
- **41472** = 3-[smooth number](/source/Smooth_number), number of reduced trees with 24 nodes[7]
- **41586** = [Large Schröder number](https://oeis.org/A006318)
- **41616** = [triangular square number](/source/Triangular_square_number)[8]
- **41835** = [Motzkin number](/source/Motzkin_number)[9]
- **41841** = 1/41841 = 0.0000239 is a repeating decimal with period 7

### 42000 to 42999

- **42680** = [octahedral number](/source/Octahedral_number)[10]
- **42875** = 353
- **42925** = [square pyramidal number](/source/Square_pyramidal_number)

### 43000 to 43999

- **43261** = [Markov number](/source/Markov_number)[11]
- **43380** = number of nets of a dodecahedron
- **43390** = number of primes \leq 2^{19}.[12]
- **43560** = pentagonal pyramidal number
- **43691** = [Wagstaff prime](/source/Wagstaff_prime)[13]
- **43777** = smallest member of a prime sextuplet

### 44000 to 44999

- **44044** = palindrome of [79](/source/79_(number)) after 6 iterations of the "reverse and add" iterative process[14]
- **44100** = sum of the cubes of the first 20 positive integers [44,100 Hz](/source/44,100_Hz) is a common [sampling frequency](/source/Sampling_frequency) in digital audio (and is the standard for [compact discs](/source/Compact_disc)).
- **44444** = [repdigit](/source/Repdigit)
- **44583** = number of partitions of 41[15]
- **44721** = smallest positive integer such that the expression 1⁄*n* − 1⁄*n* + 2 ≤ 10−9
- **44724** = maximum number of days in which a human being has been verified to live ([Jeanne Calment](/source/Jeanne_Calment)).[16]
- **44944** = palindromic square

### 45000 to 45999

- **45360** = 26th [highly composite number](/source/Highly_composite_number);[17] smallest number with exactly 100 factors (including one and itself)

### 46000 to 46999

- **46080** = [double factorial](/source/Double_factorial) of 12
- **46233** = sum of the first eight factorials
- **46249** = 2nd number that can be written as a^2+b! in 3 ways[18]
- **46368** = [Fibonacci number](/source/Fibonacci_number)[19]
- **46656** = 2162 = 363 = 66, 3-[smooth number](/source/Smooth_number)
- **46657** = Carmichael number[6]
- **46972** = number of [prime knots](/source/Prime_knots) with 14 crossings

### 47000 to 47999

- **47058** = [primary pseudoperfect number](/source/Primary_pseudoperfect_number)[20]
- **47160** = 10-th derivative of xx at x=1[21]
- **47321**/33461 ≈ [√2](/source/Square_root_of_2)

### 48000 to 48999

- **48629** = number of trees with 17 unlabeled nodes[22]
- **48734** = number of 22-bead necklaces (turning over is allowed) where complements are equivalent[23]

### 49000 to 49999

- **49151** = [Woodall number](/source/Woodall_number)[24]
- **49152** = 3-[smooth number](/source/Smooth_number)
- **49726** = pentagonal pyramidal number
- **49940** = number of 21-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed[25]

### Primes

There are 930 prime numbers between 40000 and 50000.

## References

1. ["Sloane's A014080 : Factorions"](https://oeis.org/A014080). *The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-15.

1. ["A046180 - OEIS"](https://oeis.org/A046180). *oeis.org*. Retrieved 2024-12-18.

1. ["Sloane's A002997 : Carmichael numbers"](https://oeis.org/A002997). *The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-15.

1. ["Sloane's A001110 : Square triangular numbers"](https://oeis.org/A001110). *The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-15.

1. ["Sloane's A001006 : Motzkin numbers"](https://oeis.org/A001006). *The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-15.

1. ["Sloane's A005900 : Octahedral numbers"](https://oeis.org/A005900). *The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-15.

1. ["Sloane's A002559 : Markoff (or Markov) numbers"](https://oeis.org/A002559). *The On-Line Encyclopedia of Integer Sequences*. OEIS Foundation. Retrieved 2016-06-15.

1. ["Reversal-Addition Palindrome Test on 79"](http://jasondoucette.com/pal/79)

1. Amzallag, William (22 September 2016). [*The Promise of Immortality*](https://books.google.com/books?id=AQI0DQAAQBAJ&dq=44724+days+old&pg=PA12). Varegus Publishing. p. 12. ISBN 978-2-9558558-1-2. Retrieved September 22, 2016.

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Adapted from the Wikipedia article [40,000](https://en.wikipedia.org/wiki/40%2C000) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/40%2C000?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.