6 = 12 + 34 + 56 − 7 − 89
6 = 98 − 7 − 65 + 4 − 3 − 21
6 = 0^1 + 1^8 − 2^7 − 3^9 + 4^5 + 5^6 + 6^2 + 7^4 + 8^0 + 9^3
6 = 1^2 + 1^2 + 2^2
Semiprime (Product of 2 Primes)
Number k such that (2*k)!/k!-1 is prime.
6 (first perfect number) = 1+2+3 = 1x2x3
Six is a number perfect in itself, and not because God created the world in six days; rather the contrary is true: God created the world in six days because this number is perfect, and it would remain perfect, even if the work of the six days did not exist. St. Augustine
Other perfect numbers
28
496
8128
33550336
8589869056
137438691328
2305843008139952128
2658455991569831744654692615953842176
...
6 = (4 + 4)÷ 4 + 4 = 4.4 + 4 ×.4
\( 6^3 = 3^3+4^3+5^3 \)
26 - 1 = 31 = 3 * 3 * 7
6 = 1x2x3 is a triangular number product of 3 consecutive numbers, such as 120, 210, 990, 185136,, 258474216
11 = Integer partitions of 6
a(n) = 3*n*(n + 3)/2. (n = 1)
Number that is the sum of 6 positive 6th powers
Number k such that the Woodall number kx2^k - 1 is prime
Numbers k such that (35*10^k - 11)/3 is prime
Numbers k such that (8*10^k + 49)/3 is prime.
Numbers k such that 2^k + 9 is prime. (73)
Number k such that (k! + 3)/3 is prime
Numbers k such that k^4 + 1 is prime. (1297)
Positive integer n such that n^11 + 1 is semiprime.
Maximal number of pieces obtained by slicing a torus (or a bagel) with n cuts: (n^3 + 3*n^2 + 8*n)/6, n = 2
Numbers of edges of regular polygon constructible with unmarked straightedge and compass.
e^(π sqrt(6))≈2197.9909 is a near-integer
The ring of integers of the associated field Q(sqrt(-3)) has unique factorization.
Six
Sqrt(6) = 2 + 1/(2 + 1/(4 + 1/(2 + 1/(4 + 1/(2 + 1/(4 + 1/(2 + 1/(4 + 1/(2 + 1/(4 + 1/(2 + 1/(4 + 1/(2 + 1/(4 + 1/(2 + 1/(4 + 1/(2 + 1/...)))))))))))))))))
Representations, Binary to Hexadecimal:
110_2
20_3
12_4
11_5
10_6
6_7
6_8
6_9
6_11
6_12
6_13
6_14
6_15
6_16
Undergraduate Texts in Mathematics
Graduate Studies in Mathematics
