19 is a Prime Number, Prime(8)
19 = 12 + 34 − 5 + 67 − 89
19 = 98 − 7 + 6 − 54 − 3 − 21
19 = 0^5 + 1^8 − 2^7 − 3^9 + 4^3 + 5^6 + 6^2 + 7^1 + 8^4 + 9^0
19 = 1^2 + 3^2 + 3^2
19! - 18! + 17! - 16! + ... + 1 is prime.
19 = 4! - 3! + 2! - 1!
19 is a twin prime with 17, a cousin prime with 23.
Every natural number is the sum of at most 19 fourth powers
Part of the Cunningham chain of the second kind 19, 37, 73
Keith number or Repfigit (Repetitive Fibonacci-like digit)
Number of fractions in Farey series of order 7: 0/1, 1/7, 1/6, 1/5, 1/4, 2/7, 1/3, 2/5, 3/7, 1/2, 4/7, 3/5, 2/3, 5/7, 3/4, 4/5, 5/6, 6/7, 1/1
19 = (1 + 1) × (11 − 1) − 1
= 22 − 2 − 2/2
= 3 × (3 + 3) + 3/3
= 4 + 4 + 44/4 = = 4!−(4 + 4 ÷ 4) = (4 + 4 − .4) ÷ .4
= 5 × 5 − 5 − 5/5
= 6 + 6 + 6 + 6/6
= 7 + (77 + 7)/7
= 8 + 88/8
= 9 + 9 + 9/9
Number of knapsack partitions of 10
Number of Integer partitions of 19: 490
Heegner number d, (the ring of algebraic integers of \( \mathbb {Q} \left[{\sqrt {-d}}\right] \) has unique factorization)
Prime of the form 2*n^2 + 11.
Mersenne prime 524287 = 2^19 - 1.
Number k such that 4^k + 13 is prime.
Smallest number whose sum of digits is 10.
The ring of integers of the field Q(sqrt(-19)) has unique factorization.
Factors: 1, 19
Representations, Binary to Hexadecimal:
10011_2
201_3
103_4
34_5
31_6
25_7
23_8
21_9
18_11
17_12
16_13
15_14
14_15
13_16
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