Number

420

420 — Cannabis Counterculture

420 is a composite number, even, a calendar year.

Four hundred twenty is widely associated with cannabis culture, originating with a group of California high schoolers in the early 1970s who would meet at 4:20 PM to smoke. It is also the sum of four consecutive primes (101 + 103 + 107 + 109).

Sources https://en.wikipedia.org/wiki/420_(cannabis_culture)

Abundant Number Arithmetic Number Cube-Free Curated Descending Digits Evil Number Harshad / Niven Highly Abundant Practical Number Pronic / Oblong Recamán's Sequence Semiperfect Number Stepped Digits

Interestingness

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10 notable facts · grade A

408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432

less more

Historical context — 420 AD

Calendar year

Year 420 (CDXX) was a leap year starting on Thursday of the Julian calendar.

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

Historical context — 420 BC

Calendar year

Year 420 BC was a year of the pre-Julian Roman calendar.

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

Year facts

Year type: Leap year
Divisible by 4 and not by 100; February has 29 days.
Days in year: 366
ISO weeks: 53
Long year: contains 53 ISO weeks.
Started on: Wednesday
January 1, 420
Ended on: Thursday
December 31, 420
Friday the 13ths: 2
2 Friday the 13ths this year.
Decade: 420s
420–429
Century: 5th century
401–500
Millennium: 1st millennium
1–1000
Years ago: 1,606
1606 years before 2026.

In other calendars

Hebrew: 4180 / 4181 AM
Rosh Hashanah falls in September/October.
Chinese: Year of the zodiac:Metal zodiac:Monkey
Sexagenary cycle position 57 of 60. Lunar new year falls in late January / mid-February.
Buddhist Era: 963 BE
Counted from the parinirvana of the Buddha (Theravada / Thai / Sri Lankan convention).
Ethiopian: 412 / 413 ET
Year boundary at Enkutatash (September 11/12).
Indian National (Saka): 342 / 341 Saka
Indian national calendar; year starts in March.

Cultural significance

Pop culture slang

Cannabis counterculture — "420" as code for marijuana consumption.

Originated with a 1971 group of San Rafael, California high schoolers who met at 4:20 PM.

Wikipedia ↗

Sourced from Wikipedia (Numerology, Chinese numerology, Gematria, and per-culture articles).

Properties

Parity: Even
Digit count: 3
Digit sum: 6
Digit product: 0
Digital root: 6
Palindrome: No
Bit width: 9 bits
Reversed: 24
Recamán's sequence: a(476) = 420
Square (n²): 176,400
Cube (n³): 74,088,000
Divisor count: 24
σ(n) — sum of divisors: 1,344
φ(n) — Euler's totient: 96
Sum of prime factors: 19

Primality

Prime factorization: 2 ² × 3 × 5 × 7

Nearest primes: 419 (−1) · 421 (+1)

Divisors & multiples

All divisors (24)

1 · 2 · 3 · 4 · 5 · 6 · 7 · 10 · 12 · 14 · 15 · 20 · 21 · 28 · 30 · 35 · 42 · 60 · 70 · 84 · 105 · 140 · 210 (half) · 420

Aliquot sum (sum of proper divisors): 924

Factor pairs (a × b = 420)

1 × 420

2 × 210

3 × 140

4 × 105

5 × 84

6 × 70

7 × 60

10 × 42

12 × 35

14 × 30

15 × 28

20 × 21

First multiples

420 · 840 (double) · 1,260 · 1,680 · 2,100 · 2,520 · 2,940 · 3,360 · 3,780 · 4,200

Sums & aliquot sequence

As consecutive integers: 139 + 140 + 141 82 + 83 + 84 + 85 + 86 57 + 58 + … + 63 49 + 50 + … + 56

Aliquot sequence: 420 → 924 → 1,764 → 3,423 → 1,825 → 469 → 75 → 49 → 8 → 7 → 1 → 0 — terminates at zero

Continued fraction of √n

√420 = [20; (2, 40)]

Period length 2 — the block in parentheses repeats forever.

Representations

In words: four hundred twenty
Ordinal: 420th
Roman numeral: CDXX
Binary: 110100100
Octal: 644
Hexadecimal: 0x1A4
Base64: AaQ=
One's complement: 65,115 (16-bit)
Scientific notation: 4.2 × 10²
As a duration: 420 s = 7 minutes

In other bases

ternary (3) 120120

quaternary (4) 12210

quinary (5) 3140

senary (6) 1540

septenary (7) 1140

nonary (9) 516

undecimal (11) 352

duodecimal (12) 2b0

tridecimal (13) 264

tetradecimal (14) 220

pentadecimal (15) 1d0

As an angle

420° = 1 × 360° + 60°

60° ≈ 1.047 rad

Compass bearing: ENE (east-northeast)

Why does a circle have 360 degrees? →

Historical numeral systems

Babylonian (base 60): 𒁹𒁹𒁹𒁹𒁹𒁹𒁹 ·
Egyptian hieroglyphic: 𓍢𓍢𓍢𓍢𓎆𓎆
Greek (Milesian): υκʹ
Mayan (base 20): 𝋡·𝋡·𝋠
Chinese: 四百二十
Chinese (financial): 肆佰貳拾

In other modern scripts

Eastern Arabic ٤٢٠ Devanagari ४२० Bengali ৪২০ Tamil ௪௨௦ Thai ๔๒๐ Tibetan ༤༢༠ Khmer ៤២០ Lao ໔໒໐ Burmese ၄၂၀

Digit at this position in famous constants

π — Pi (π): Digit 420 = 5
e — Euler's number (e): Digit 420 = 5
φ — Golden ratio (φ): Digit 420 = 6
√2 — Pythagoras's (√2): Digit 420 = 1
ln 2 — Natural log of 2: Digit 420 = 2
γ — Euler-Mascheroni (γ): Digit 420 = 5

Also seen as

Goldbach decomposition

Goldbach's conjecture says every even integer greater than 2 is the sum of two primes. For 420, here are decompositions:

11 + 409 = 420
19 + 401 = 420
23 + 397 = 420
31 + 389 = 420
37 + 383 = 420
41 + 379 = 420
47 + 373 = 420
53 + 367 = 420

Showing the first eight; more decompositions exist.

Unicode codepoint

Latin Capital Letter P With Hook

U+01A4

Uppercase letter (Lu)

UTF-8 encoding: C6 A4 (2 bytes).

Lookup U+01A4 on Compart ↗ Lookup on FileFormat.Info ↗

Hex color

#0001A4

RGB(0, 1, 164)

IPv4 address

As an unsigned 32-bit integer, this is the IPv4 address 0.0.1.164.

Address: 0.0.1.164
Class: reserved
IPv4-mapped IPv6: ::ffff:0.0.1.164

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

Musical pitch

Heard as a frequency, 420 Hz is closest to:

Concert pitch (A4 = 440 Hz): G♯4 (415.3 Hz, +19¢)
Scientific pitch (C4 = 256 Hz): A4 (430.5 Hz, -43¢)
Baroque pitch (A4 = 415 Hz): A4 (415 Hz, +21¢)

Food additive (E-number)

On an ingredients label, E420 is Sorbitol, a thickener, stabiliser or emulsifier — a sugar alcohol and sweetener.

E-number reference (Wikipedia) ↗