7 is a Prime Number , Prime(4)
7 = 1 + 23 − 4 + 56 − 78 + 9
7 = 98 − 7 − 6 − 54 − 3 − 21
7 = 4 + 4 − 4 ÷ 4 = 44 ÷ 4 − 4
7 = 0^6 + 1^9 + 2^8 − 3^7 + 4^5 + 5^4 + 6^3 + 7^1 + 8^2 + 9^0
27 - 1 = 127, Prime Number
Sexy Prime (Primes p such that p + 6 is also prime)
Initial member of prime 5-tuples (p, p+4, p+6, p+10, p+12).
For every integer n, n^7 - n is divisible by 7
Number of fractions in Farey series of order 4: 0/1,1/4,1/3,1/2,2/3,3/4,1/1
Number k such that (7*10^k + 71)/3 is prime. ((7*10^7 + 71)/3 = 23333357 is a prime number.)
Numbers k such that (35*10^k - 11)/3 is prime (116666663)
Numbers k such that 2^k + 9 is prime. (137)
Number k such that (13^k - 3^k)/10 is prime.
Number k such that 9^k + 8^(k-1) is prime.
Number that is the sum of 7 positive 11th powers.
Number of prime knots with 7 crossings.
Heegner number d, (the ring of algebraic integers of \( \mathbb {Q} \left[{\sqrt {-d}}\right] \) has unique factorization)
15 = Integer partitions of 7
Björner-Welker sequence: 2^n*(n^2 + n + 2) - 1. n = 1
7 cannot be written as a sum of 3 squares. (Integers that are not a sum of three squares)
Factors: 1, 7
Sqrt(7) = 2 + 1/(1 + 1/(1 + 1/(1 + 1/(4 + 1/(1 + 1/(1 + 1/(1 + 1/(4 + 1/(1 + 1/(1 + 1/(1 + 1/(4 + 1/(1 + 1/(1 + 1/(1 + 1/(4 + 1/(1 + 1/...)))))))))))))))))
Seven
Representations, Binary to Hexadecimal:
111_2
21_3
13_4
12_5
11_6
10_7
7_8
7_9
7_11
7_12
7_13
7_14
7_15
7_16
Undergraduate Texts in Mathematics
Graduate Studies in Mathematics
