57 (number)
From Halbeeg, the open encyclopedia · Af-Soomaali
80 languages
57 is a natural number that comes after 56 and before 58. It is an odd number and not a prime number, since it is divisible by 3 and 19. Therefore, 57 is a composite number.
The divisors of 57 are 1, 3, 19, and 57. The sum of these divisors is 80. Since 57 is the product of exactly two primes (3 × 19), it is called a semiprime. In Roman numerals it is written as LVII.
Mathematical properties
When 57 is written in base 7, it becomes 111, since 49 + 7 + 1 = 57. It is also a Leyland number, meaning it can be obtained from the formula 2^5 + 5^2 = 32 + 25 = 57. The sum of its digits (5 + 7 = 12) is divisible by 3, which explains why 57 itself is divisible by 3.
The Grothendieck prime
The name '57' is known from a famous anecdote about the mathematician Alexander Grothendieck. According to the story, when asked to provide an example of a prime number, he said 57—even though it is a composite number. Since then, mathematicians informally call 57 the 'Grothendieck prime'. The anecdote is used as an illustration of how Grothendieck approached mathematics at a high level of abstraction rather than through specific numerical examples.
Other uses
57 is the atomic number of lanthanum (La), which is the first element of the lanthanide series in the periodic table. 57 is also Colombia's international dialing code. The food company Heinz long used the marketing slogan 'Heinz 57', which made the number a well-known brand identifier.