Numberwise

421

HTTP 421 Misdirected Request means the request reached a server that cannot produce a response for that authority.

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Where 421 fits

Where 421 fits: Mathematics, Technology, Related numbersMathematics: Prime, Lucky number (mathematical sieve), Twin prime. Technology: HTTP status codes. Related numbers: 441.MathematicsPrimeLucky number (mathematical …Twin primeTechnologyHTTP status codesRelated numbers441421
421 connects to 3 worlds: mathematics, technology, related numbers.

Why 421 is special

421 is a consequence of connection reuse. HTTP/2 lets a browser send requests for several hostnames down one connection when their certificates match, and 421 is how a server says this particular hostname is not one it serves — a signal to open a new connection rather than an error the user caused.

421 connects to:

  • 441 appears alongside
  • http status codes appears in

Same number, different meanings

How 421 is understood across different contexts — never implying one meaning because of another.

Not just a mathematical number

421is also used in ways where ordinary arithmetic doesn't apply — each listed below with what genuinely does and doesn't follow from it.

  • Mathematical number

    A genuine quantity — its mathematical properties (prime, square, factors, and so on) are real facts about it.

    A genuine quantity that ordinary arithmetic applies to — it can be prime, even, a perfect square, added to another number meaningfully, and so on.

  • Code

    Also used as a code — HTTP status codes.

    An assigned identifier from a fixed registry or standard — its digits don't represent an amount, and arithmetic on it is meaningless (HTTP status 404 + 1 is not a 'better' status; it's a different, unrelated code).

Factors & digit properties

Divisors (2)
1, 421
Prime factorisation
421
Digit sum
7
Digital root
7

Representations

Decimal
421
Scientific notation
4.210 × 10^2

Roman numerals

C D X X I

CDXXI uses the subtractive pair CD: a hundred before five hundred — five hundred minus a hundred.

Binary

1 1 0 1 0 0 1 0 1

1 × 256 + 1 × 128 + 0 × 64 + 1 × 32 + 0 × 16 + 0 × 8 + 1 × 4 + 0 × 2 + 1 × 1 = 421

Octal

6 4 5

6 × 64 + 4 × 8 + 5 × 1 = 421

Hexadecimal

1 a 5

1 × 256 + a × 16 + 5 × 1 = 421

Read as powers of two: 256 + 128 + 32 + 4 + 1 = 421.

In historical numeral systems

Egyptian

4 coils of rope, 2 hobbles, 1 stroke

4 × 100 + 2 × 10 + 1 × 1 = 421. The signs are simply repeated and added; where they sit on the line is a matter of layout, not value.

Babylonian

7 vertical wedges (sixties place), 1 vertical wedge (units place)

7 × 60 + 1 = 421. Places are separated by a space on the tablet, with the higher place written first.

Greek (Ionic)

upsilon, then kappa, then alpha, marked as a numeral

upsilon-kappa-alpha + keraia

upsilon + kappa + alpha written in descending order and added — the letters carry their values wherever they stand, so this is addition, not place value.

Hebrew numerals

tav, then kaf, then alef

tav-kaf-alef

tav (400) + kaf (20) + alef (1) = 421, written in descending order.

Systems that simply cannot reach this value are left out. Where a script needs a font most readers do not have, the reading is given instead of the glyphs — see number systems for each system in full.

Other mathematical patterns

Related numbers & connections

Documented appearance
Both are Sennheiser dynamic microphones with switchable bass roll-off, one supercardioid and one cardioid.

Both are Sennheiser dynamic microphones with switchable bass roll-off, one supercardioid and one cardioid.

View 441

Numbers Around Us

  • appears alongside441
    why?

    Strength 0.50, confidence "high".

  • appears inHTTP status codes
    why?

    Strength 0.50, confidence "high".

How is 421 connected to another number? →

Technology & computing

  • HTTP/2 lets a browser reuse one connection for several hostnames whose certificates match. 421 is the server saying this hostname is not one it can answer for, and the correct client response is to open a fresh connection rather than to show the user an error.

    DocumentedTechnology & computing

Media & popular culture

  • The Sennheiser MD 421 is a large-diaphragm dynamic microphone with a five-position bass roll-off, standard on tom-toms, guitar cabinets and broadcast speech since 1960.

    DocumentedMedia & popular cultureGeography: GermanyPeriod: 1960–

Common questions

Is 421 a prime number?

Yes, 421 is prime — it has exactly two positive divisors: 1 and itself.

What are the factors of 421?

The factors of 421 are 1, 421.

What is 421 in Roman numerals?

421 in Roman numerals is CDXXI. CD is subtractive: a hundred before five hundred — five hundred minus a hundred. Written additively it would be CCCCXXI, which Roman inscriptions used freely — the strict subtractive form is a later convention.

About this page's data

Mathematical facts:computed directly from the number's value — nothing to source or verify externally.

Contextual records: 2 reviewer-confirmed records, sourced and reviewed before publication.

Last reviewed: 15 July 2026