1931
1931 is the year the Empire State Building was completed.
- Odd
- Prime
Where 1931 fits
Why 1931 is special
It went up in 410 days during the Depression and stood as the world's tallest building for nearly forty years. It was largely empty for its first decade, earning the nickname the Empty State Building.
Same number, different meanings
How 1931 is understood across different contexts — never implying one meaning because of another.
- Mathematics
It went up in 410 days during the Depression and stood as the world's tallest building for nearly forty years. It was largely empty for its first decade, earning the nickname the Empty State Building.
- History
In 1931, Kurt Gödel proved that any consistent formal system rich enough for arithmetic contains true statements it cannot prove (Austria).
- Finance & economics
The Empire State Building was finished in 410 days and then struggled to find tenants through the 1930s. Being the tallest structure in the world and being a viable investment turned out to be unrelated properties.
1931 is part of
Factors & digit properties
- Divisors (2)
- 1, 1931
- Prime factorisation
- 1931
- Digit sum
- 14
- Digital root
- 5
Representations
- Decimal
- 1931
- Scientific notation
- 1.931 × 10^3
Roman numerals
M C M X X X I
MCMXXXI uses the subtractive pair CM: a hundred before a thousand — a thousand minus a hundred.
Binary
1 1 1 1 0 0 0 1 0 1 1
1 × 1,024 + 1 × 512 + 1 × 256 + 1 × 128 + 0 × 64 + 0 × 32 + 0 × 16 + 1 × 8 + 0 × 4 + 1 × 2 + 1 × 1 = 1,931
Octal
3 6 1 3
3 × 512 + 6 × 64 + 1 × 8 + 3 × 1 = 1,931
Hexadecimal
7 8 b
7 × 256 + 8 × 16 + b × 1 = 1,931
Read as powers of two: 1,024 + 512 + 256 + 128 + 8 + 2 + 1 = 1,931.
In historical numeral systems
Egyptian
1 lotus, 9 coils of rope, 3 hobbles, 1 stroke
1 × 1,000 + 9 × 100 + 3 × 10 + 1 × 1 = 1,931. The signs are simply repeated and added; where they sit on the line is a matter of layout, not value.
Babylonian
3 corner wedges + 2 vertical wedges (sixties place), 1 corner wedge + 1 vertical wedge (units place)
32 × 60 + 11 = 1931. Places are separated by a space on the tablet, with the higher place written first.
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
- Sophie Germain prime
- Twin prime
Related numbers & connections
1931 is a year in the 20th century, in the 1930s.
Cheap steel from 1856 made tall buildings structurally possible, and the Empire State Building of 1931 is among the results — finished in 410 days and largely empty for a decade.
View 1856 →Numbers Around Us
- appears inHistorical years
why?
Strength 0.50, confidence "high".
Other connections
- developed from1856
why?
Strength 0.50, confidence "high".
History
In 1931, Kurt Gödel proved that any consistent formal system rich enough for arithmetic contains true statements it cannot prove (Austria).
DocumentedHistoryGeography: AustriaPeriod: 1931
Finance & economics
The Empire State Building was finished in 410 days and then struggled to find tenants through the 1930s. Being the tallest structure in the world and being a viable investment turned out to be unrelated properties.
DocumentedFinance & economicsGeography: New York, United StatesPeriod: 1931
Common questions
Is 1931 a prime number?
Yes, 1931 is prime — it has exactly two positive divisors: 1 and itself.
What are the factors of 1931?
The factors of 1931 are 1, 1931.
What is 1931 in Roman numerals?
1931 in Roman numerals is MCMXXXI. CM is subtractive: a hundred before a thousand — a thousand minus a hundred. Written additively it would be MDCCCCXXXI, 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