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Number

10,039

10,039 is a prime, odd.

10,039 (ten thousand thirty-nine) is an odd 5-digit number. It is a prime number — divisible only by 1 and itself. Written other ways, in hexadecimal, 0x2737.

Arithmetic Number Chen Prime Cube-Free Deficient Number Emirp Happy Number Odious Number Prime Recamán's Sequence Squarefree Twin Prime

Interestingness

Properties

Parity
Odd
Digit count
5
Digit sum
13
Digit product
0
Digital root
4
Palindrome
No
Bit width
14 bits
Reversed
93,001
Recamán's sequence
a(4,865) = 10,039
Square (n²)
100,781,521
Cube (n³)
1,011,745,689,319
Divisor count
2
σ(n) — sum of divisors
10,040
φ(n) — Euler's totient
10,038

Primality

10,039 is prime. It has exactly two divisors: 1 and itself.

Divisors & multiples

All divisors (2)
1 · 10039
Aliquot sum (sum of proper divisors): 1
Factor pairs (a × b = 10,039)
1 × 10039
First multiples
10,039 · 20,078 (double) · 30,117 · 40,156 · 50,195 · 60,234 · 70,273 · 80,312 · 90,351 · 100,390

Sums & aliquot sequence

As consecutive integers: 5,019 + 5,020

Continued fraction of √n

√10,039 = [100; (5, 7, 1, 1, 32, 1, 6, 2, 4, 1, 2, 21, 1, 10, 5, 1, 1, 1, 2, 1, 2, 1, 66, 15, …)]

Period length 56 — the block in parentheses repeats forever.

Representations

In words
ten thousand thirty-nine
Ordinal
10039th
Binary
10011100110111
Octal
23467
Hexadecimal
0x2737
Base64
Jzc=
One's complement
55,496 (16-bit)
Scientific notation
1.0039 × 10⁴
As a duration
10,039 s = 2 hours, 47 minutes, 19 seconds
In other bases
ternary (3) 111202211
quaternary (4) 2130313
quinary (5) 310124
senary (6) 114251
septenary (7) 41161
nonary (9) 14684
undecimal (11) 75a7
duodecimal (12) 5987
tridecimal (13) 4753
tetradecimal (14) 3931
pentadecimal (15) 2e94

As an angle

10,039° = 27 × 360° + 319°
319° ≈ 5.568 rad
Compass bearing: NW (northwest)

Historical numeral systems

Babylonian (base 60)
𒁹𒁹 𒌋𒌋𒌋𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹 𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹
Egyptian hieroglyphic
𓂍𓎆𓎆𓎆𓏺𓏺𓏺𓏺𓏺𓏺𓏺𓏺𓏺
Greek (Milesian)
͵ιλθʹ
Mayan (base 20)
𝋡·𝋥·𝋡·𝋳
Chinese
一萬零三十九
Chinese (financial)
壹萬零參拾玖
In other modern scripts
Eastern Arabic ١٠٠٣٩ Devanagari १००३९ Bengali ১০০৩৯ Tamil ௧௦௦௩௯ Thai ๑๐๐๓๙ Tibetan ༡༠༠༣༩ Khmer ១០០៣៩ Lao ໑໐໐໓໙ Burmese ၁၀၀၃၉

Digit at this position in famous constants

π — Pi (π)
Digit 10,039 = 4
e — Euler's number (e)
Digit 10,039 = 7
φ — Golden ratio (φ)
Digit 10,039 = 7
√2 — Pythagoras's (√2)
Digit 10,039 = 7
ln 2 — Natural log of 2
Digit 10,039 = 0
γ — Euler-Mascheroni (γ)
Digit 10,039 = 0

Also seen as

Prime neighborhood

Adjacent primes:

  • Previous prime: 10,037 (gap of 2)
  • Next prime: 10,061 (gap of 22)

Pair status: twin with 10037.

Unicode codepoint
Eight Pointed Rectilinear Black Star
U+2737
Other symbol (So)

UTF-8 encoding: E2 9C B7 (3 bytes).

Hex color
#002737
RGB(0, 39, 55)
IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.39.55.

Address
0.0.39.55
Class
reserved
IPv4-mapped IPv6
::ffff:0.0.39.55

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

Musical pitch

Heard as a frequency, 10,039 Hz is closest to:

  • Concert pitch (A4 = 440 Hz): D♯9 (9956.1 Hz, +14¢)
  • Scientific pitch (C4 = 256 Hz): E9 (10321.3 Hz, -48¢ — about midway to D♯9)
  • Baroque pitch (A4 = 415 Hz): E9 (9948.8 Hz, +16¢)
Position in π

The digit sequence 10039 first appears in π at position 42,809 of the decimal expansion (the 42,809ordinal-suffix:th digit after the integer 3).

Search range: the first 1,000,000 fractional digits of π. Any 6-digit-or-shorter string is virtually guaranteed to appear in there — the more interesting signal is the position.

Related reading

  • Prime numbers — The building blocks of arithmetic: what primes are, why they matter, and how we find them.
  • Egyptian hieroglyphic numerals — Seven hieroglyphs for every power of ten, from a single stroke to a million.