421
HTTP 421 Misdirected Request means the request reached a server that cannot produce a response for that authority.
- Odd
- Prime
Where 421 fits
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.
- Mathematics
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.
- 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.
- 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.
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).
421 is part of
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
- Deficient number
- Lucky number (mathematical sieve)
- Twin prime
Related numbers & connections
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".
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