13 is a Prime Number
13 = 1 − 23 + 4 − 56 + 78 + 9
13 = 98 − 7 − 6 − 54 + 3 − 21
13 = 0^6 + 1^7 + 2^9 − 3^8 + 4^2 + 5^5 + 6^1 + 7^4 + 8^3 + 9^0
13 = 2^2 + 3^2
13^2 = 5^2 + 12^2
Number of fractions in Farey series of order 6: 0/1, 1/6, 1/5, 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 5/6, 1/1 13 = (4!×√4 + 4)
Sexy Prime (Primes p such that p + 6 is also prime)
13 is a Wilson prime, since 13^2 divides (13 - 1)! + 1.
Number k such that 9^k + 2 is prime.
Prime of the form 2x^2 + 13y^2.
Prime of the form 2*n^2 + 11.
a(n) = 9^n + 5^n - 1 , n = 1
Centered icosahedral (or cuboctahedral) number, also crystal ball sequence for f.c.c. lattice.
13 = 7^2 - 6^2.
13 = 11 + 1 + 1
= 2 + 22/2
= 3 + 3 × 3 + 3/3
= 4 + 4 + 4 + 4/4 = (4!×√4 + 4)÷ 4 = (4 − .4) ÷ .4 + 4
= (55 + 5 + 5)/5
= 6 + 6 + 6/6
= 7 + 7 − 7/7
= (88 + 8 + 8)/8
= (9 + 99 + 9)/9
Emirp , 31 is also Prime
For every integer n, n^13 - n is divisible by 13
Number of points of norm <= 2^2 in square lattice.
Odd number n such that 3^n+1 is a sum of two squares, 3^13 + 1 = 1594324 = 1262^2 + 20^2
Maximal number of pieces obtained by slicing a torus (or a bagel) with n cuts: (n^3 + 3*n^2 + 8*n)/6, n = 3
Number of Integer partitions of 13: 101
9 Prime Partitions of 13: 2 + 2 + 2 + 2 + 2 + 3 = 2 + 2 + 2 + 2 + 5 = 2 + 2 + 2 + 7 = 2 + 2 + 3 + 3 + 3 = 2 + 3 + 3 + 5 = 2 + 11 = 3 + 3 + 7 = 3 + 5 + 5.
Factors: 1, 13
Thirteen
Representations, Binary to Hexadecimal:
1101_2
111_3
31_4
23_5
21_6
16_7
15_8
14_9
12_11
11_12
10_13
d_14
d_15
d_16
Undergraduate Texts in Mathematics
Graduate Studies in Mathematics
