2016 (number)

← 2015 2016 2017 →
List of numbers Integers ← 0 1k 2k 3k 4k 5k 6k 7k 8k 9k →
Cardinal	two thousand sixteen
Ordinal	2016th (two thousand sixteenth)
Factorization	25 × 32 × 7
Divisors	1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 32, 36, 42, 48, 56, 63, 72, 84, 96, 112, 126, 144, 168, 224, 252, 288, 336, 504, 672, 1008, 2016
Greek numeral	,ΒΙϚ´
Roman numeral	MMXVI, mmxvi
Binary	111111000002
Ternary	22022003
Senary	132006
Octal	37408
Duodecimal	120012
Hexadecimal	7E016

2016 is the natural number following 2015 and preceding 2017.

Mathematics

2016 is the second-smallest Erdős–Nicolas number after 24. ^[1] 2016 is a triangular number. 2016 has a total of 36 divisors. ^[2]

Other properties

• ${\displaystyle 2^{11}-2^{5}=2048-32=2016}$ (the difference between powers of two),
• ${\displaystyle 8!=20\times 2016=40320}$ (or eight factorial),
• ${\displaystyle {{2016^{17}+1} \over 2017}}$ is prime (since 2017 is similarly prime, 2016¹⁷ + 1 is a semiprime). ^[3]

${\displaystyle 2016\times 2+1=4033=37\times 109}$ is a strong pseudoprime to base 2; ^[4] aside from 2016, only five other numbers below 10,000 share this property (1023, 1638, 2340, 4160, and 7920).

References

1. Sloane, N. J. A. (ed.). "SequenceA194472(Erdős-Nicolas numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
2. Sloane, N. J. A. (ed.). "SequenceA000217(Triangular numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
3. Sloane, N. J. A. (ed.). "SequenceA104494(Positive integers n such that n^17 + 1 is semiprime (A001358).)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-02-27.
4. Sloane, N. J. A. (ed.). "SequenceA001262(Strong pseudoprimes to base 2.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-02-27.