137 (number)

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137 is the natural number following 136 and preceding 138.

List of numbers — Integers << 100 110 120 130 140 150 160 170 180 190 >>
Cardinal	One hundred [and] thirty seven
Ordinal	137th
Factorization	prime
Roman numeral	CXXXVII
Binary	10001001
Octal	211
Hexadecimal	89

1 In mathematics
2 In physics
3 In other fields
4 External links

[edit] In mathematics

One hundred [and] thirty-seven is the 33rd prime number; the next is 139, with which it comprises a twin prime, and thus 137 is a Chen prime. 137 is an Eisenstein prime with no imaginary part and a real part of the form $3 n - 1$ . It is also the fourth Stern prime. 137 is a strong prime in the sense that it is more than the arithmetic mean of its two neighboring primes.

Using two radii to divide a circle according to the golden ratio yields sectors of approximately 137° (the golden angle) and 222°.

137 is a strictly non-palindromic number and a primeval number.

[edit] In physics

The numerical value of the fine structure constant is almost precisely 1/137. This quantity is given by combining several fundamental constants of nature:

$\alpha = \frac{e^2}{\hbar c \ 4 \pi \epsilon_0} = \frac{1}{137.035 999 11(46)}$ ,

where $e$ is the elementary charge, $c$ is the speed of light, $\hbar$ is the reduced Planck's constant and $ε 0$ represents the vacuum permittivity. The fine structure constant is a dimensionless quantity, i.e. its value is the same regardless of what system of measurement we use.

The importance of the constant is that it measures the strength of the electromagnetic interaction. It is precisely because the constant is so small (i.e. 1/137 as opposed to 1/3 or 5 or 100...) that quantum electrodynamics (QED) works so amazingly well as a quantum theory of electromagnetism. It means that when we go to calculate simple processes, such as two electrons scattering off one another through the exchange of photons, we only need to consider the simple case of one photon exchange -- every additional photon you consider is less important by a factor of 1/137. This is why theorists have been so successful at making incredibly accurate predictions using QED. By contrast, the equivalent 'fine-structure' constant for the theory of strong interactions (quantum chromodynamics or QCD) is just about 1 at laboratory energy scales. This makes calculating things in QCD much, much more involved.

[edit] In other fields

137 is also:

The year AD 137 or 137 BC.
The Gematria (i.e. Hebrew numerology) value of the word "Kabbalah", which is of special significance to Jewish mystics.
California penal code for "Offer bribe to influence testimony".