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Number

1,301

1,301 is a prime, odd, a calendar year.

1,301 (one thousand three hundred one) is an odd 4-digit number. It is a prime number — divisible only by 1 and itself. Written other ways, in Roman numerals it is MCCCI and in binary, 10100010101.

Arithmetic Number Centered Square Chen Prime Cousin Prime Cube-Free Deficient Number Emirp Odious Number Pernicious Number Prime Pythagorean Prime Recamán's Sequence Sexy Prime Squarefree Twin Prime Year

Interestingness

12 notable facts · grade A
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Historical context — 1301 AD

Calendar year

Year 1301 (MCCCI) was a common year starting on Sunday of the Julian calendar.

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

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
Saturday
January 1, 1301
Ended on
Saturday
December 31, 1301
Friday the 13ths
1
One Friday the 13th this year.
Decade
1300s
1300–1309
Century
14th century
1301–1400
Millennium
2nd millennium
1001–2000
Years ago
725
725 years before 2026.

In other calendars

Hebrew
5061 / 5062 AM
Rosh Hashanah falls in September/October.
Islamic Hijri
700 / 701 AH
Lunar calendar; year spans differ from Gregorian.
Chinese
Year of the zodiac:Metal zodiac:Ox
Sexagenary cycle position 38 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era
1844 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Persian Solar Hijri
679 / 680 SH
Iranian calendar; Nowruz (new year) falls on the spring equinox.
Ethiopian
1293 / 1294 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka)
1223 / 1222 Saka
Indian national calendar; year starts in March.

Properties

Parity
Odd
Digit count
4
Digit sum
5
Digit product
0
Digital root
5
Palindrome
No
Bit width
11 bits
Reversed
1,031
Recamán's sequence
a(30,446) = 1,301
Square (n²)
1,692,601
Cube (n³)
2,202,073,901
Divisor count
2
σ(n) — sum of divisors
1,302
φ(n) — Euler's totient
1,300

Primality

1,301 is prime. It has exactly two divisors: 1 and itself.

Divisors & multiples

All divisors (2)
1 · 1301
Aliquot sum (sum of proper divisors): 1
Factor pairs (a × b = 1,301)
1 × 1301
First multiples
1,301 · 2,602 (double) · 3,903 · 5,204 · 6,505 · 7,806 · 9,107 · 10,408 · 11,709 · 13,010

Sums & aliquot sequence

As a sum of two squares: 25² + 26²
As consecutive integers: 650 + 651

Continued fraction of √n

√1,301 = [36; (14, 2, 2, 2, 2, 14, 72)]

Period length 7 — the block in parentheses repeats forever.

Representations

In words
one thousand three hundred one
Ordinal
1301st
Roman numeral
MCCCI
Binary
10100010101
Octal
2425
Hexadecimal
0x515
Base64
BRU=
One's complement
64,234 (16-bit)
Scientific notation
1.301 × 10³
As a duration
1,301 s = 21 minutes, 41 seconds
In other bases
ternary (3) 1210012
quaternary (4) 110111
quinary (5) 20201
senary (6) 10005
septenary (7) 3536
nonary (9) 1705
undecimal (11) a83
duodecimal (12) 905
tridecimal (13) 791
tetradecimal (14) 68d
pentadecimal (15) 5bb
Palindromic in base 16

As an angle

1,301° = 3 × 360° + 221°
221° ≈ 3.857 rad
Compass bearing: SW (southwest)

Historical numeral systems

Babylonian (base 60)
𒌋𒌋𒁹 𒌋𒌋𒌋𒌋𒁹
Egyptian hieroglyphic
𓆼𓍢𓍢𓍢𓏺
Greek (Milesian)
͵αταʹ
Mayan (base 20)
𝋣·𝋥·𝋡
Chinese
一千三百零一
Chinese (financial)
壹仟參佰零壹
In other modern scripts
Eastern Arabic ١٣٠١ Devanagari १३०१ Bengali ১৩০১ Tamil ௧௩௦௧ Thai ๑๓๐๑ Tibetan ༡༣༠༡ Khmer ១៣០១ Lao ໑໓໐໑ Burmese ၁၃၀၁

Digit at this position in famous constants

π — Pi (π)
Digit 1,301 = 2
e — Euler's number (e)
Digit 1,301 = 3
φ — Golden ratio (φ)
Digit 1,301 = 0
√2 — Pythagoras's (√2)
Digit 1,301 = 5
ln 2 — Natural log of 2
Digit 1,301 = 0
γ — Euler-Mascheroni (γ)
Digit 1,301 = 7

Also seen as

Prime neighborhood

Adjacent primes:

  • Previous prime: 1,297 (gap of 4)
  • Next prime: 1,303 (gap of 2)

Pair status: twin with 1303, cousin with 1297.

Unicode codepoint
ԕ
Cyrillic Small Letter Lha
U+0515
Lowercase letter (Ll)

UTF-8 encoding: D4 95 (2 bytes).

Hex color
#000515
RGB(0, 5, 21)
IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.5.21.

Address
0.0.5.21
Class
reserved
IPv4-mapped IPv6
::ffff:0.0.5.21

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

Musical pitch

Heard as a frequency, 1,301 Hz is closest to:

  • Concert pitch (A4 = 440 Hz): E6 (1318.5 Hz, -23¢)
  • Scientific pitch (C4 = 256 Hz): E6 (1290.2 Hz, +14¢)
  • Baroque pitch (A4 = 415 Hz): F6 (1317.5 Hz, -22¢)
Position in π

The digit sequence 1301 first appears in π at position 6,320 of the decimal expansion (the 6,320ordinal-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.
  • Mayan numerals — Vigesimal dots-and-bars with a shell zero — one of the earliest true zeros.