137
137 is the approximate inverse of the fine-structure constant, the dimensionless number that sets the strength of the electromagnetic force.
- Odd
- Prime
Where 137 fits
Why 137 is special
137 is the closest physics comes to a number with a cult following. The fine-structure constant is dimensionless — the same in any unit system, so it cannot be an artefact of how we measure — and its inverse is close to 137. Physicists including Pauli and Feynman wrote about wanting to explain it; Feynman called it 'one of the greatest damn mysteries of physics'. The measured value is 137.035999…, not the integer, and no derivation of it is accepted.
Same number, different meanings
How 137 is understood across different contexts — never implying one meaning because of another.
- Mathematics
137 is the closest physics comes to a number with a cult following. The fine-structure constant is dimensionless — the same in any unit system, so it cannot be an artefact of how we measure — and its inverse is close to 137. Physicists including Pauli and Feynman wrote about wanting to explain it; Feynman called it 'one of the greatest damn mysteries of physics'. The measured value is 137.035999…, not the integer, and no derivation of it is accepted.
- Science
Caesium-137 has a half-life of about thirty years and behaves chemically like potassium, so it enters the food chain. It is the isotope that determines long-term exclusion zones after reactor accidents.
- Culture
137 has attracted more numerological attention than any other figure in physics, partly because Wolfgang Pauli — who wrote about it seriously — died in hospital room 137, a coincidence retold constantly. Physicists generally treat the mystique as a joke about the real open question, not as evidence of anything.
137 is part of
Factors & digit properties
- Divisors (2)
- 1, 137
- Prime factorisation
- 137
- Digit sum
- 11
- Digital root
- 2
Representations
- Decimal
- 137
- Scientific notation
- 1.370 × 10^2
Roman numerals
C X X X V I I
Binary
1 0 0 0 1 0 0 1
1 × 128 + 0 × 64 + 0 × 32 + 0 × 16 + 1 × 8 + 0 × 4 + 0 × 2 + 1 × 1 = 137
Octal
2 1 1
2 × 64 + 1 × 8 + 1 × 1 = 137
Hexadecimal
8 9
8 × 16 + 9 × 1 = 137
Read as powers of two: 128 + 8 + 1 = 137.
In historical numeral systems
Egyptian
1 coil of rope, 3 hobbles, 7 strokes
1 × 100 + 3 × 10 + 7 × 1 = 137. The signs are simply repeated and added; where they sit on the line is a matter of layout, not value.
Babylonian
2 vertical wedges (sixties place), 1 corner wedge + 7 vertical wedges (units place)
2 × 60 + 17 = 137. Places are separated by a space on the tablet, with the higher place written first.
Greek (Ionic)
rho, then lambda, then zeta, marked as a numeral
rho-lambda-zeta + keraia
rho + lambda + zeta written in descending order and added — the letters carry their values wherever they stand, so this is addition, not place value.
Hebrew numerals
qof, then lamed, then zayin
qof-lamed-zayin
qof (100) + lamed (30) + zayin (7) = 137, written in descending order.
Maya
1 bar + 1 dot (upper, twenties place) over 3 bars + 2 dots (lower, units place)
6 × 20 + 17 = 137. Places stack vertically with the smallest at the bottom, so the upper group is worth twenty times the lower.
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
- Twin prime
Related numbers & connections
Both are released in reactor accidents, one determining the immediate response and one the length of the exclusion.
View 131 →Both are synthetic or fission-derived isotopes encountered outside a laboratory, one in homes and one in contaminated land.
View 241 →Science
Caesium-137 has a half-life of about thirty years and behaves chemically like potassium, so it enters the food chain. It is the isotope that determines long-term exclusion zones after reactor accidents.
DocumentedScienceGeography: GlobalPeriod: 1930s–Most physical constants carry units, so their numeric value depends on the system you measure in. The fine-structure constant does not: it is a pure ratio, roughly 1/137, and any civilisation anywhere would measure the same figure. That is why its value is treated as a genuine fact about the universe rather than about our metres and seconds, and why the absence of any explanation for it is uncomfortable.
DocumentedScience
Culture
137 has attracted more numerological attention than any other figure in physics, partly because Wolfgang Pauli — who wrote about it seriously — died in hospital room 137, a coincidence retold constantly. Physicists generally treat the mystique as a joke about the real open question, not as evidence of anything.
DocumentedCultureCulture: physics community
Common questions
Is 137 a prime number?
Yes, 137 is prime — it has exactly two positive divisors: 1 and itself.
What are the factors of 137?
The factors of 137 are 1, 137.
What is 137 in Roman numerals?
137 in Roman numerals is CXXXVII.
About this page's data
Mathematical facts:computed directly from the number's value — nothing to source or verify externally.
Contextual records: 3 reviewer-confirmed records, sourced and reviewed before publication.
Last reviewed: 15 July 2026