37

is not just a number

37

37 has a unique affinity for the “abstract world” and is characterized by her love for sharing knowledge. She is depicted as a passionate scholar and a devout priestess, but also as an indifferent daughter and friend.

In game background

Kingdom of Math

Statistics, physics, astronomy, engineering… Mathematics finds applications in various scientific fields. Humans naturally believe themselves to be the sole darlings of these concise and lucid numbers. They devote themselves to expelling the Arcanists that symbolize disorder and chaos in number theory, all to preserve the harmony and unity of mathematics.

However, this remains merely a wish.

The realm of pure reason has never truly existed; perpetually hanging above it is the cloud of Gnosis.

Arcanum and rational systems; religious beliefs and scientific proof; the notion that “all things have numbers” and mathematics. They are all like two sides of a ruler, measuring everything in the world. The followers of Pythagoreanism have made significant contributions throughout history, and the theories of fundamental numbers have left an indelible mark on many.

However, the “Storm” swept unrelentingly throughout the world. Mathematics lost its once solid ground, leaving nothing but debris. Then, a pair of tender hands picked it up.

An Unfinished Demonstration

On the Supplementary Calculations of Soul Number 37

I hereby declare to approach this task with impartiality, to eliminate errors and omissions, and to treat each number with fairness, as I uphold the unique guidelines of a Corrector.

1: The smallest irregular prime number
Note: Based on the “Primitive Bernoulli Number” criterion, which is a rational number sequence closely related to number theory.

2: Repeating unit 111 (three consecutive 1s, where 3 is a prime number), 111 = 3 x 37
Note: She avoids the division between “finite” and “infinite.”

3: Any number can be expressed as the sum of at most 37 fifth powers of 5
Note: She is special, possessing multiple possibilities.

4: A regular hexagon
Note: This corresponds to her influence and importance in the School of Apeiron.
…
37 is the third unique prime number in the decimal system and the third isolated prime number without a twin prime. It is the third Cuban prime, the fourth emirp, the fifth lucky prime…

Geometric Problem

37: Oh! Another set of contradictions.
Pandora Wilson: Although I know very little about mathematics, I can sense the disappointment from your tone.
37: Free, selfish, untraceable — traits of irrational numbers. Fortunately, it adheres to coherence and maintains clear boundary criteria…
Pandora Wilson: I hope this won’t affect our conversation.
37: Of course not, addressing various math puzzles is precisely my job; I excel at it.
37: Now, please open up your quadratic surface.
Pandora Wilson: …
Pandora Wilson: Ah — ?
37: Fantastic! In Apeiron, we often engage with spheres and regular polyhedra… Opportunities to study special surfaces are quite rare.
37: Clearly, you don’t belong to real quadratic surfaces, nor do you align with degenerate quadratic surfaces. But it’s alright; I will find a place for you in the geometric classification of three-dimensional Euclidean space.
Pandora Wilson: …Thank you.

In Reverse:1999, 37’s narrative is intricately woven with her distinct worldview and mathematical brilliance, shaping her story in profound ways:

Early Fascination with Mathematics: 37’s upbringing and education fueled a deep fascination with mathematics from an early age. She perceives reality through numerical lenses, assigning meanings to integers, associating irrational numbers with freedom, and seeing prime numbers as playful tricksters.

Unique Perspective: Viewing the world as an intricate mathematical construct, 37 finds joy in seeing patterns where others see randomness. For instance, she finds delight in conceptualizing the year 1999 not just as a point in time, but as a “centered triangular number.”

Emotional Disconnection: Despite her fervent academic pursuits and spiritual dedication, 37 struggles with emotional detachment in her personal relationships. Her immersion in the abstract realm leaves little room for emotional investment in the tangible world and its inhabitants.

Apathy towards Mundane Matters: While her mathematical prowess is undeniable, 37 exhibits little interest in the mundane aspects of daily life. She may admire the placement of objects according to the golden ratio but remains indifferent to their practical significance. Her adherence to the doctrines of her schooling borders on treating them as immutable laws of the universe.

Maternal Influence: A poignant element of 37’s narrative is her relationship with her mother. Reflecting by the coast where her mother’s essence rests, 37 reminisces about the rhythmic waves against her mother’s geometric form, evoking bittersweet memories of her mother’s fleeting presence before departing the realm of the tangible.

The Number 37

Mysterious Number in Numerology:

• 37 is considered one of the most mysterious numbers in numerology.
• It consists of the sum of its factors, which are 3 + 7 = 10 (both odd numbers).
• When squared, these factors result in even numbers: 27 = 9.
• It is also the first triangular prime number after 2, 3, 5, 7, 11, etc.

Prime Factor of Perfect Numbers:

• 37 is a prime factor of the first six perfect numbers: 6, 28, 496, 8128, and 33,550,336.
• A perfect number is the sum of its factors (e.g., 6 = 1 + 2 + 3).

Ulam Number:

• 37 is the 15th prime number and also an Ulam number.
• Ulam numbers avoid prime factorization through their pattern of sums of digits.

Sum of Two Squares:

• 37 can be expressed as the sum of two squares: ⁹² + 1⁶².
• It’s a perfect square that can be factored into prime factors: ³³ × ⁵³.

Decagonal Number:

• 37 is a decagonal number that can be written as the sum of two or more squares (e.g., 9 = ¹² + ²², 16 = ²² + ⁴²).

Harshad Number:

• 37 is a Harshad number, meaning it’s divisible by the sum of its digits (3 + 7 = 10, which is a multiple of 5).

Hexagonal Number:

• It’s the 12th hexagonal number, formed by the product of two opposite-centered hexagons (e.g., 4 × 6 = 24).

Tetraktys of Pythagorean Triplets:

• 37 can be drawn as a Tetraktys (a triangle with the hypotenuse sum equaling the sum of its other two sides) using the first three integers (1, 2, 3) and the fourth integer (4).

Magic Square:

• The smallest magic square using only primes and 1 contains 37 as the value of its central cell.
• Its magic constant is 37 × 3 = 111.

Collatz Problem:

• 37 requires twenty-one steps to return to 1 in the 3x + 1 Collatz problem.
• The sum of the trajectories for 3 and 21 also requires seven steps to reach 1.

Moonshine Theory:

• In moonshine theory, 37 is the smallest non-supersingular prime.

Decimal Properties:

• For a three-digit number divisible by 37, another divisible by 37 can be generated by transferring the first digit to the end (e.g., 37|148 ➜ 37|481 ➜ 37|814).
• Any multiple of 37 can be mirrored and spaced with a zero each for another multiple of 37.

Anyway, just happy birthday to me.