37 (number)

37 is the natural number following 36 and preceding 38.

In mathematics

37 is the 12th prime number, and the 3rd isolated prime without a twin prime.
37 is the first irregular prime with irregularity index of 1, where the smallest prime number with an irregularity index of 2 is the thirty-seventh prime number, 157.
The smallest magic square, using only primes and 1, contains 37 as the value of its central cell:
Its magic constant is 37 x 3 = 111, where 3 and 37 are the first and third base-ten unique primes.
37 requires twenty-one steps to return to 1 in the Collatz problem, as do adjacent numbers 36 and 38. The two closest numbers to cycle through the elementary Collatz pathway are 5 and 32, whose sum is 37; also, the trajectories for 3 and 21 both require seven steps to reach 1. On the other hand, the first two integers that return for the Mertens function have a difference of 37, where their product is the twelfth triangular number 78. Meanwhile, their sum is 41, which is the constant term in Euler's lucky numbers that yield prime numbers of the form k² − k + 41, the largest of which is a difference of 78 from the second-largest prime generated by this quadratic polynomial.
In moonshine theory, whereas all p ⩾ 73 are non-supersingular primes, the smallest such prime is 37.
37 is the sixth floor of imaginary parts of non-trivial zeroes in the Riemann zeta function. It is in equivalence with the sum of ceilings of the first two such zeroes, 15 and 22.
The secretary problem is also known as the 37% rule by.

In Artificial Intelligence

Move 37, played by the AI program AlphaGo during the second game of the Google DeepMind Challenge Match against Lee Sedol in March 2016, is considered a landmark moment in the history of artificial intelligence. The move was initially thought to be a mistake by human experts but is now celebrated as a demonstration of machine creativity and deep strategic insight that contributed to AlphaGo's victory.

Decimal properties

For a three-digit number that is divisible by 37, a rule of divisibility is that another divisible by 37 can be generated by transferring first digit onto the end of a number. For example: 37|148 ➜ 37|481 ➜ 37|814. Any multiple of 37 can be mirrored and spaced with a zero each for another multiple of 37. For example, 37 and 703, 74 and 407, and 518 and 80105 are all multiples of 37; any multiple of 37 with a three-digit repdigit inserted generates another multiple of 37.
Every equal-interval number duplicated to a palindrome renders a multiple of both 11 and 111.
In decimal 37 is a permutable prime with 73, which is the twenty-first prime number. By extension, the mirroring of their digits and prime indexes makes 73 the only Sheldon prime.

Geometric properties

There are precisely 37 complex reflection groups.
In three-dimensional space, the most uniform solids are:
In total, these number twenty-one figures, which when including their dual polytopes, the total becomes 6 + 30 + 1 = 37.
The sphere in particular circumscribes all the above regular and semiregular polyhedra ; all of these solids also have unique representations as spherical polyhedra, or spherical tilings.
Image:37-Star-Cluster.png|thumb|right|NGC 2169. It has an asterism in the form of the number 37.

Science

NGC 2169 has an asterism in the form of the number 37, due to its resemblance of the numerals.
The average body temperature of a human in Celsius is 37 degrees.