number.wiki
Live analysis

138,401

138,401 is a prime, odd.

This number doesn't have a permanent NumberWiki page yet — what you see below is computed live. Pages get added to the permanent index when they're notable (years, primes, curated, etc.).

138,401 (one hundred thirty-eight thousand four hundred one) is an odd 6-digit number. It is a prime number — divisible only by 1 and itself. Written other ways, in hexadecimal, 0x21CA1.

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

Interestingness

Properties

Parity
Odd
Digit count
6
Digit sum
17
Digit product
0
Digital root
8
Palindrome
No
Bit width
18 bits
Reversed
104,831
Recamán's sequence
a(492,025) = 138,401
Square (n²)
19,154,836,801
Cube (n³)
2,651,048,568,095,201
Divisor count
2
σ(n) — sum of divisors
138,402
φ(n) — Euler's totient
138,400

Primality

138,401 is prime. It has exactly two divisors: 1 and itself.

Divisors & multiples

All divisors (2)
1 · 138401
Aliquot sum (sum of proper divisors): 1
Factor pairs (a × b = 138,401)
1 × 138401
First multiples
138,401 · 276,802 (double) · 415,203 · 553,604 · 692,005 · 830,406 · 968,807 · 1,107,208 · 1,245,609 · 1,384,010

Sums & aliquot sequence

As a sum of two squares: 151² + 340²
As consecutive integers: 69,200 + 69,201

Continued fraction of √n

√138,401 = [372; (43, 1, 3, 3, 1, 1, 1, 4, 3, 1, 8, 1, 1, 6, 8, 1, 1, 1, 1, 148, 4, 1, 7, 1, …)]

Representations

In words
one hundred thirty-eight thousand four hundred one
Ordinal
138401st
Binary
100001110010100001
Octal
416241
Hexadecimal
0x21CA1
Base64
Ahyh
One's complement
4,294,828,894 (32-bit)
Scientific notation
1.38401 × 10⁵
As a duration
138,401 s = 1 day, 14 hours, 26 minutes, 41 seconds
In other bases
ternary (3) 21000211222
quaternary (4) 201302201
quinary (5) 13412101
senary (6) 2544425
septenary (7) 1114334
nonary (9) 230758
undecimal (11) 94a8a
duodecimal (12) 68115
tridecimal (13) 4acc3
tetradecimal (14) 3861b
pentadecimal (15) 2b01b

As an angle

138,401° = 384 × 360° + 161°
161° ≈ 2.81 rad
Compass bearing: SSE (south-southeast)

Historical numeral systems

Babylonian (base 60)
𒌋𒌋𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹 𒌋𒌋𒁹𒁹𒁹𒁹𒁹𒁹 𒌋𒌋𒌋𒌋𒁹
Egyptian hieroglyphic
𓆐𓂍𓂍𓂍𓆼𓆼𓆼𓆼𓆼𓆼𓆼𓆼𓍢𓍢𓍢𓍢𓏺
Greek (Milesian)
͵ρληυαʹ
Mayan (base 20)
𝋱·𝋦·𝋠·𝋡
Chinese
一十三萬八千四百零一
Chinese (financial)
壹拾參萬捌仟肆佰零壹
In other modern scripts
Eastern Arabic ١٣٨٤٠١ Devanagari १३८४०१ Bengali ১৩৮৪০১ Tamil ௧௩௮௪௦௧ Thai ๑๓๘๔๐๑ Tibetan ༡༣༨༤༠༡ Khmer ១៣៨៤០១ Lao ໑໓໘໔໐໑ Burmese ၁၃၈၄၀၁

Also seen as

Prime neighborhood

Adjacent primes:

Pair status: twin with 138403.

Unicode codepoint
𡲡
CJK Unified Ideograph-21Ca1
U+21CA1
Other letter (Lo)

UTF-8 encoding: F0 A1 B2 A1 (4 bytes).

Hex color
#021CA1
RGB(2, 28, 161)
IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.2.28.161.

Address
0.2.28.161
Class
reserved
IPv4-mapped IPv6
::ffff:0.2.28.161

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

Possible US patent number

This number falls in the range of US utility patent numbers. If it's a patent, it would be issued as US 138,401 and was likely granted around 1872.

Patent numbers below 100,000 are excluded as too ambiguous; modern numbering currently reaches roughly 12.5 million.

Position in π

The digit sequence 138401 first appears in π at position 459,383 of the decimal expansion (the 459,383ordinal-suffix:rd 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.
  • Mayan numerals — Vigesimal dots-and-bars with a shell zero — one of the earliest true zeros.