403
403 is the HTTP status code meaning Forbidden — the server understood the request and refuses to authorise it.
- Odd
- Composite
Where 403 fits
Why 403 is special
403 is the code people confuse with 404, and the difference matters: 404 says the server has nothing at that address, 403 says there is something there and you may not have it. It also differs from 401, which means the server wants credentials it has not been given — 403 means credentials will not help.
Not just a mathematical number
403is 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 (4)
- 1, 13, 31, 403
- Prime factorisation
- 13 × 31
- Digit sum
- 7
- Digital root
- 7
Representations
- Decimal
- 403
- Scientific notation
- 4.030 × 10^2
Roman numerals
C D I I I
CDIII uses the subtractive pair CD: a hundred before five hundred — five hundred minus a hundred.
Binary
1 1 0 0 1 0 0 1 1
1 × 256 + 1 × 128 + 0 × 64 + 0 × 32 + 1 × 16 + 0 × 8 + 0 × 4 + 1 × 2 + 1 × 1 = 403
Octal
6 2 3
6 × 64 + 2 × 8 + 3 × 1 = 403
Hexadecimal
1 9 3
1 × 256 + 9 × 16 + 3 × 1 = 403
Read as powers of two: 256 + 128 + 16 + 2 + 1 = 403.
In historical numeral systems
Egyptian
4 coils of rope, 3 strokes
4 × 100 + 3 × 1 = 403. 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 + 3 vertical wedges (units place)
6 × 60 + 43 = 403. Places are separated by a space on the tablet, with the higher place written first.
Greek (Ionic)
upsilon, then gamma, marked as a numeral
upsilon-gamma + keraia
upsilon + gamma 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 gimel
tav-gimel
tav (400) + gimel (3) = 403, 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
- Semiprime
Related numbers & connections
403 means the server understood the request and refuses to authorise it, as distinct from 404's nothing-is-here.
The pair whose names are the wrong way round. 401 means the server does not know who you are and will accept credentials; 403 means it knows and refuses regardless. Sending 401 where 403 belongs invites clients into a login loop that cannot succeed.
View 401 →Technology & computing
403 says the server understood the request, knows what you are asking for, and will not serve it. That is different from 404, which says there is nothing at that address, and from 401, which says the server wants credentials it has not received. Sites sometimes return 404 instead of 403 deliberately, to avoid confirming that a protected resource exists at all.
DocumentedTechnology & computing
Common questions
Is 403 a prime number?
No, 403 is not prime.
What are the factors of 403?
The factors of 403 are 1, 13, 31, 403.
What is 403 in Roman numerals?
403 in Roman numerals is CDIII. CD is subtractive: a hundred before five hundred — five hundred minus a hundred. Written additively it would be CCCCIII, 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