# 135 (number)

Short description: Natural number
 ← 134 135 136 →
Cardinalone hundred thirty-five
Ordinal135th
(one hundred thirty-fifth)
Factorization33 × 5
Divisors1, 3, 5, 9, 15, 27, 45, 135
Greek numeralΡΛΕ´
Roman numeralCXXXV
Binary100001112
Ternary120003
Quaternary20134
Quinary10205
Senary3436
Octal2078
DuodecimalB312
Vigesimal6F20
Base 363R36

135 (one hundred [and] thirty-five) is the natural number following 134 and preceding 136.

## In mathematics

This number in base 10 can be expressed in operations using its own digits in at least two different ways. One is as a sum-product number,

$\displaystyle{ 135 = (1 + 3 + 5)(1 \times 3 \times 5) }$

(1 and 144 share this property)[1] and the other is as the sum of consecutive powers of its digits:[2]

$\displaystyle{ 135 = 1^1 + 3^2 + 5^3 }$

(175, 518, and 598 also have this property).

There are a total of 135 primes between 1,000 and 2,000.

$\displaystyle{ 135 = 11 n^2 + 11 n + 3 }$ for $\displaystyle{ n = 3 }$. This polynomial plays an essential role in Apéry's proof that $\displaystyle{ \zeta(3) }$ is irrational.

## In transportation

• London Buses route 135 is a Transport for London contracted bus route in London
• 135th Street station on the IND Eighth Avenue Line of the New York City Subway on St. Nicholas Avenue in Manhattan
• 135th Street station on the IRT Lenox Avenue Line of the New York City Subway on Lenox Avenue in Manhattan

## In other fields

• The year AD 135 or 135 BC
• 135 AH is a year in the Islamic calendar that corresponds to 752–753 CE
• 135 Hertha is a large main belt asteroid which orbits among the Nysa asteroid family
• 135 film, the cartridge version of 35mm photographic film, used widely in still photography
• The Canon FD 135 mm lens
• In astrology, when two planets are 135 degrees apart, they are in an astrological aspect called a sesquiquadrate. The aspect was first used by Johannes Kepler
• Sonnet 135 by William Shakespeare
• Municipal District of Peace No. 135, a municipal district in northwest Alberta, Canada
• Enoch Cree Nation 135 Indian reserve in Alberta, Canada is home to the Enoch Cree Nation
• The EZ 135 Drive removable hard disk drive introduced by SyQuest Technology in 1995