100 is the sum of the first nine prime numbers, from 2 through 23.[4] It is also divisible by the number of primes below it, 25.[5]
100 cannot be expressed as the difference between any integer and the total of coprimes below it, making it a noncototient.[6]
100 has a reduced totient of 20, and an Euler totient of 40.[7][8] A totient value of 100 is obtained from four numbers: 101, 125, 202, and 250.
100 can be expressed as a sum of some of its divisors, making it a semiperfect number.[9] The geometric mean of its nine divisors is 10.
100 is the sum of the cubes of the first four positive integers (100 = 13 + 23 + 33 + 43).[10] This is related by Nicomachus's theorem to the fact that 100 also equals the square of the sum of the first four positive integers: 100 = 102 = (1 + 2 + 3 + 4)2.[11]
There are exactly 100 prime numbers in base-ten whose digits are in strictly ascending order (e.g. 239, 2357, etc.).[17] The last such prime number is 23456789, which contains eight consecutive integers as digits.
In science
One hundred is the atomic number of fermium, an actinide, and the last of the heavy metals that can be created through neutron bombardment.
On the Celsius scale, 100 degrees is the boiling temperature of pure water at sea level.
The Kármán line lies at an altitude of 100 kilometres (62 mi) above the Earth's sea level and is commonly used to define the boundary between Earth's atmosphere and outer space.
In history
In medieval contexts, it may be described as the short hundred or five score in order to differentiate the English and Germanic use of "hundred" to describe the long hundred[18] of six score or 120.
In religion
There are 100 blasts of the Shofar heard in the service of Rosh Hashana, the Jewish New Year.[19]
A religious Jew is expected to utter at least 100 blessings daily.[20]
^"Sloane's A076980 : Leyland numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-27.
^Sloane, N. J. A. (ed.). "Sequence A059756 (Erdős-Woods numbers: the length of an interval of consecutive integers with property that every element has a factor in common with one of the endpoints)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-11-30.
^"Sloane's A051870 : 18-gonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-27.