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137,413

137,413 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.).

137,413 (one hundred thirty-seven thousand four hundred thirteen) is an odd 6-digit number. It is a prime number — divisible only by 1 and itself. Written other ways, in hexadecimal, 0x218C5.

Arithmetic Number Cube-Free Deficient Number Odious Number Pernicious Number Prime Pythagorean Prime Recamán's Sequence Squarefree

Interestingness

Properties

Parity
Odd
Digit count
6
Digit sum
19
Digit product
252
Digital root
1
Palindrome
No
Bit width
18 bits
Reversed
314,731
Recamán's sequence
a(37,630) = 137,413
Square (n²)
18,882,332,569
Cube (n³)
2,594,677,965,303,997
Divisor count
2
σ(n) — sum of divisors
137,414
φ(n) — Euler's totient
137,412

Primality

137,413 is prime. It has exactly two divisors: 1 and itself.

Divisors & multiples

All divisors (2)
1 · 137413
Aliquot sum (sum of proper divisors): 1
Factor pairs (a × b = 137,413)
1 × 137413
First multiples
137,413 · 274,826 (double) · 412,239 · 549,652 · 687,065 · 824,478 · 961,891 · 1,099,304 · 1,236,717 · 1,374,130

Sums & aliquot sequence

As a sum of two squares: 143² + 342²
As consecutive integers: 68,706 + 68,707

Continued fraction of √n

√137,413 = [370; (1, 2, 3, 1, 19, 1, 4, 1, 2, 2, 2, 1, 1, 1, 1, 2, 2, 1, 2, 1, 13, 3, 1, 6, …)]

Representations

In words
one hundred thirty-seven thousand four hundred thirteen
Ordinal
137413th
Binary
100001100011000101
Octal
414305
Hexadecimal
0x218C5
Base64
AhjF
One's complement
4,294,829,882 (32-bit)
Scientific notation
1.37413 × 10⁵
As a duration
137,413 s = 1 day, 14 hours, 10 minutes, 13 seconds
In other bases
ternary (3) 20222111101
quaternary (4) 201203011
quinary (5) 13344123
senary (6) 2540101
septenary (7) 1111423
nonary (9) 228441
undecimal (11) 94271
duodecimal (12) 67631
tridecimal (13) 4a713
tetradecimal (14) 38113
pentadecimal (15) 2aaad

As an angle

137,413° = 381 × 360° + 253°
253° ≈ 4.416 rad
Compass bearing: WSW (west-southwest)

Historical numeral systems

Babylonian (base 60)
𒌋𒌋𒌋𒁹𒁹𒁹𒁹𒁹𒁹𒁹𒁹 𒌋 𒌋𒁹𒁹𒁹
Egyptian hieroglyphic
𓆐𓂍𓂍𓂍𓆼𓆼𓆼𓆼𓆼𓆼𓆼𓍢𓍢𓍢𓍢𓎆𓏺𓏺𓏺
Greek (Milesian)
͵ρλζυιγʹ
Mayan (base 20)
𝋱·𝋣·𝋪·𝋭
Chinese
一十三萬七千四百一十三
Chinese (financial)
壹拾參萬柒仟肆佰壹拾參
In other modern scripts
Eastern Arabic ١٣٧٤١٣ Devanagari १३७४१३ Bengali ১৩৭৪১৩ Tamil ௧௩௭௪௧௩ Thai ๑๓๗๔๑๓ Tibetan ༡༣༧༤༡༣ Khmer ១៣៧៤១៣ Lao ໑໓໗໔໑໓ Burmese ၁၃၇၄၁၃

Also seen as

Prime neighborhood

Adjacent primes:

Unicode codepoint
𡣅
CJK Unified Ideograph-218C5
U+218C5
Other letter (Lo)

UTF-8 encoding: F0 A1 A3 85 (4 bytes).

Hex color
#0218C5
RGB(2, 24, 197)
IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.2.24.197.

Address
0.2.24.197
Class
reserved
IPv4-mapped IPv6
::ffff:0.2.24.197

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 137,413 and was likely granted around 1872.

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

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.