10,000 (ten thousand) is the natural number following 9,999 and preceding 10,001.
Many languages have a specific word for this number: in Ancient Greek it is μύριοι (the etymological root of the word myriad in English), in Aramaic ܪܒܘܬܐ, in Hebrew רבבה [revava], in Chinese 萬/万 (Mandarin wàn, Cantonese maan6, Hokkien bān), in Japanese 万/萬 [man], in Khmer ម៉ឺន [meun], in Korean 만/萬 [man], in Russian тьма [t'ma], in Vietnamese vạn, in Sanskrit अयुत [ayuta], in Thai หมื่น [meun], in Malayalam പതിനായിരം [patinayiram], and in Malagasy alina.[1] In many of these languages, it often denotes a very large but indefinite number.[2]
The classical Greeks used letters of the Greek alphabet to represent Greek numerals: they used a capital letter mu (Μ) to represent ten thousand.[citation needed] This Greek root was used in early versions of the metric system in the form of the decimal prefix myria-.[3]
Depending on the country, the number ten thousand is usually written as 10,000 (including in the UK and US), 10.000, or 10 000.[4]
In scientific notation it is written as 104 or 1 E+4 (equivalently 1 E4) in E notation.
It is the square of 100 and the square root of 100,000,000.
The value of a myriad to the power of itself, 1000010000 = 1040000.
It has a total of 25 divisors, whose geometric mean is a whole number, 100 (the number of primes below this value is 25).[5]
It has a reduced totient of 500, and a totient of 4,000, with a total of 16 integers having a totient value of 10,000.[6][7]
There are a total of 1,229 prime numbers less than ten thousand, a count that is itself prime.[5][8]
A myriagon is a polygon with ten thousand edges and a total of 25 dihedral symmetry groups when including the myriagon itself, alongside 25 cyclic groups as subgroups.[9]
There are 1033 prime numbers between 10000 and 20000, a count that is itself prime. It is 196 prime numbers less than the number of primes between 0 and 10000 (1229, also prime).
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