- (one, один, aon, un, hvmken, א) The unit, multiplicative identity, and automorphic in any positional number system. 1 = G-d. Also, 1 = 0.99999… The Messier object, M1, is a remnant supernova in the constellation Taurus.
- (two, два, dhá, deux, hokkolen, ב) The oddest prime. the first Sophie Germain prime. A Pell number and highly composite. The first letter in the Torah is bet.
- (three, trois, tuccenen, ג )* A Marsenne Prime and the only prime which is one shy a perfect square. An integer is divisible by three if the sum of its digits is divisible by three. 3 is the base of the ternary system.
- (four, quatre, osten, ד ) The smallest composite number. The smallest noncyclic group has four elements, the Klein fou-group, which is also the name of a cool math band. Every natural number divisible by four is the difference of two squares. There are four matriarchs of Judaism, Sarah, Rebeccah, Leah, and Rachel.
- (five, cinq, cahkepen, ה) A Fermat Prime. No polynomial equation of degree 5 or greater can be solved using a simple formula. The symmetric group, S_{5}, is not solvable. There are five Platonic solids. The Torah cnsists of 5 books.
- (six, six, epaken, ו ) The only number which is both perfect and triangular (which happens to be the result of my first theorem). Shavuot begins on the sixth day of Sivan.
- (seven, sept, kolvpaken, ז) A happy number. There are seven frieze groups. A group of seven objects is a heptad.
- (eight, huit, cenvpaken, ח) A byte is a grouping of eight bits. A Jewish boy undergoes his brit milah on his eighth day.
- (nine, neuf, ostvpaken, ט)The first composite lucky number.The only square prime whose aliquot parts also sum up to a square prime. Nine is an exponential factorial, that is, 9 =3^{21} .
- (ten, dix, palen, י ) The base of our standard numeral system. Ten is bi. A bi-prime, that is, because it is the product of two primes. There ten plagues, ten days of repentance, and ten generations between Adam and Noah.
- (eleven, onze*) To determine if a number is divisible by 11, take the sum of pairs of digits. For example consider 71104. 7 + 11 + 04 = 22, which is 2*11, so 71104 is also divisible by 11.
- (twelve, douze) A superfactorial. Twelve is the answer to the three dimensional Kissing Sphere problem (thus, there are twelve green spheres in my userpic). Twelve is sublime. Jewish girls come of age at 12.
- (thirteen, treize) there are thirteen Archimedian solids. A Jewish boy comes of age at 13,
- (fourteen, quatorze) Discretely bi (prime).
- (fifteen, quinze) The smallest number that can be factored using Shor’s quantum algorithm.
- (sixteen, seize) the only number of the form x^{y}=y^{x} with x and y different integers.
- 17 is the number of wallpaper groups.
- the only number that is twice the sum of its digits
- 19 is the maximum number of 4th powers needed to sum to any number.
- the number of rooted trees with 6 vertices.
- 21 is the smallest number of distinct squares needed to tile a square.
- 22 is the number of partitions of 8.
- 23 is the smallest number of integer-sided boxes that tile a box so that no two boxes share a common length.
- 24 is the largest number divisible by all numbers less than its square root.
- 25 is the smallest square that can be written as a sum of 2 squares.
- 26 is the only number to be directly between a square and a cube.
Most of this is from wikipedia, though at 17 I got impatient and copy/pasted from here
* I either can no longer count in the given language/s or am being lazy about switching to the Hebrew or Russian keyboards. By the by, the languages are: english, russian, irish, french, creek, and hebrew.
The moral of the story is that I’m old today.
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I love your analysis of the numbers 1-26.Very interesting.