401
401 is the HTTP status code Unauthorized — the server wants credentials it has not been given.
- Odd
- Prime
Where 401 fits
Why 401 is special
401 is misnamed and everyone knows it: it means unauthenticated, not unauthorised. The server is saying it does not know who you are and will accept a credential; 403 is the one that says it knows and still refuses. The name has survived since the earliest HTTP drafts because changing it would break more than it would fix.
Not just a mathematical number
401is 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).
401 is part of
Factors & digit properties
- Divisors (2)
- 1, 401
- Prime factorisation
- 401
- Digit sum
- 5
- Digital root
- 5
Representations
- Decimal
- 401
- Scientific notation
- 4.010 × 10^2
Roman numerals
C D I
CDI uses the subtractive pair CD: a hundred before five hundred — five hundred minus a hundred.
Binary
1 1 0 0 1 0 0 0 1
1 × 256 + 1 × 128 + 0 × 64 + 0 × 32 + 1 × 16 + 0 × 8 + 0 × 4 + 0 × 2 + 1 × 1 = 401
Octal
6 2 1
6 × 64 + 2 × 8 + 1 × 1 = 401
Hexadecimal
1 9 1
1 × 256 + 9 × 16 + 1 × 1 = 401
Read as powers of two: 256 + 128 + 16 + 1 = 401.
In historical numeral systems
Egyptian
4 coils of rope, 1 stroke
4 × 100 + 1 × 1 = 401. The signs are simply repeated and added; where they sit on the line is a matter of layout, not value.
Babylonian
6 vertical wedges (sixties place), 4 corner wedges + 1 vertical wedge (units place)
6 × 60 + 41 = 401. Places are separated by a space on the tablet, with the higher place written first.
Greek (Ionic)
upsilon, then alpha, marked as a numeral
upsilon-alpha + keraia
upsilon + 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 alef
tav-alef
tav (400) + alef (1) = 401, 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
Related numbers & connections
401 means unauthenticated — the server wants credentials it has not received.
Both are shipyard hull numbers that became better known than the yards; one for a disaster and one for a depression.
View 534 →Technology & computing
401 means the server does not yet know who you are and is inviting credentials — it must send a WWW-Authenticate header saying how. 403 means it knows and refuses anyway. The names are the wrong way round, a quirk preserved since the earliest drafts because too much software depends on the numbers.
DocumentedTechnology & computing
Common questions
Is 401 a prime number?
Yes, 401 is prime — it has exactly two positive divisors: 1 and itself.
What are the factors of 401?
The factors of 401 are 1, 401.
What is 401 in Roman numerals?
401 in Roman numerals is CDI. CD is subtractive: a hundred before five hundred — five hundred minus a hundred. Written additively it would be CCCCI, 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: 1 reviewer-confirmed record, sourced and reviewed before publication.
Last reviewed: 15 July 2026