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Number

31

31 is a prime, odd, a calendar year.

Arithmetic Number Binary Palindrome Chen Prime Deficient Number Emirp Happy Number Mersenne Prime Odious Number Pernicious Number Prime Recamán's Sequence Self Number Sexy Prime Squarefree Twin Prime Year

Historical context — 31 AD

Calendar year

AD 31 (XXXI) was a common year starting on Monday of the Julian calendar.

Excerpt from Wikipedia (en) ↗ · Licensed CC BY-SA 4.0 · English fallback Read the full article on Wikipedia →

Notable events — 31 BC

Sep 2 Octavian's fleet defeats Antony and Cleopatra at Actium.

Events compiled from Wikipedia ↗ · Licensed CC BY-SA 4.0

Year facts

Year type: Common year
Standard 365-day year; not divisible by 4 (or divisible by 100 but not 400).
Days in year: 365
ISO weeks: 52
Started on: Wednesday
January 1, 31
Ended on: Wednesday
December 31, 31
Friday the 13ths: 1
One Friday the 13th this year.
Decade: 30s
30–39
Century: 1st century
1–100
Millennium: 1st millennium
1–1000
Years ago: 1,995
1995 years before 2026.

In other calendars

Hebrew: 3791 / 3792 AM
Rosh Hashanah falls in September/October.
Chinese: Year of the zodiac:Metal zodiac:Rabbit
Sexagenary cycle position 28 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 574 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Ethiopian: 23 / 24 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): -47 / -48 Saka
Indian national calendar; year starts in March.

Properties

Parity: Odd
Digit count: 2
Digit sum: 4
Digit product: 3
Digital root: 4
Palindrome: No
Bit width: 5 bits
Reversed: 13
Recamán's sequence: a(54) = 31
Square (n²): 961
Cube (n³): 29,791
Divisor count: 2
σ(n) — sum of divisors: 32
φ(n) — Euler's totient: 30

Primality

31 is prime. It has exactly two divisors: 1 and itself.

Divisors & multiples

All divisors (2)

1 · 31

Aliquot sum (sum of proper divisors): 1

Factor pairs (a × b = 31)

1 × 31

First multiples

31 · 62 (double) · 93 · 124 · 155 · 186 · 217 · 248 · 279 · 310

Sums & aliquot sequence

As consecutive integers: 15 + 16

Representations

In words: thirty-one
Ordinal: 31st
Roman numeral: XXXI
Binary: 11111
Octal: 37
Hexadecimal: 0x1F
Base64: Hw==
One's complement: 224 (8-bit)
Scientific notation: 3.1 × 10¹

In other bases

ternary (3) 1011

quaternary (4) 133

quinary (5) 111

senary (6) 51

septenary (7) 43

nonary (9) 34

undecimal (11) 29

duodecimal (12) 27

tridecimal (13) 25

tetradecimal (14) 23

pentadecimal (15) 21

Palindromic in base 2, base 5

Historical numeral systems

Babylonian (base 60): 𒌋𒌋𒌋𒁹
Egyptian hieroglyphic: 𓎆𓎆𓎆𓏺
Greek (Milesian): λαʹ
Mayan (base 20): 𝋡·𝋫
Chinese: 三十一
Chinese (financial): 參拾壹

In other modern scripts

Eastern Arabic ٣١ Devanagari ३१ Bengali ৩১ Tamil ௩௧ Thai ๓๑ Tibetan ༣༡ Khmer ៣១ Lao ໓໑ Burmese ၃၁

Digit at this position in famous constants

π — Pi (π): Digit 31 = 9
e — Euler's number (e): Digit 31 = 2
φ — Golden ratio (φ): Digit 31 = 5
√2 — Pythagoras's (√2): Digit 31 = 9
ln 2 — Natural log of 2: Digit 31 = 8
γ — Euler-Mascheroni (γ): Digit 31 = 2

Also seen as

Prime neighborhood

Adjacent primes:

Previous prime: 29 (gap of 2)
Next prime: 37 (gap of 6)

Pair status: twin with 29, sexy with 37.

ASCII character

As an ASCII codepoint, 31 is control character (0x1F). ASCII control character.

Hex color

#00001F

RGB(0, 0, 31)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.0.31.

Address: 0.0.0.31
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.0.31

Unspecified address (0.0.0.0/8) — "this network" placeholder.