163
163 is the largest Heegner number, and makes e to the power of pi root 163 almost an integer.
- Odd
- Prime
Where 163 fits
Why 163 is special
That expression comes within a trillionth of a whole number, which looks like coincidence and is not — it follows from deep properties of the number 163. Ramanujan noticed such near-misses, and the phenomenon is sometimes called Ramanujan's constant.
163 is part of
Factors & digit properties
- Divisors (2)
- 1, 163
- Prime factorisation
- 163
- Digit sum
- 10
- Digital root
- 1
Representations
- Decimal
- 163
- Binary
- 10100011
- Octal
- 243
- Hexadecimal
- a3
- Roman numeral
- CLXIII
- Scientific notation
- 1.630 × 10^2
Other mathematical patterns
- Deficient number
- Lucky number (mathematical sieve)
Related numbers & connections
Two numbers associated with Ramanujan for near-coincidences that turn out to have structure — the taxicab number and the almost-integer from the largest Heegner number.
View 1729 →Other connections
- is associated with1729
why?
Strength 0.50, confidence "high".
Mathematics
e to the power of pi root 163 differs from a whole number by less than a trillionth. The near-miss follows from 163 being the largest Heegner number, a fact about class numbers proved in the 1950s — so the coincidence has an explanation rather than being one.
DocumentedMathematics
Common questions
Is 163 a prime number?
Yes, 163 is prime — it has exactly two positive divisors: 1 and itself.
What are the factors of 163?
The factors of 163 are 1, 163.
What is 163 in Roman numerals?
163 in Roman numerals is CLXIII.
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: 3 August 2026