137 (number)

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137 is the natural number following 136 and preceding 138.


Cardinal One hundred [and]
thirty seven
Ordinal 137th
Factorization prime
Roman numeral CXXXVII
Binary 10001001
Octal 211
Hexadecimal 89

Contents

[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 3n − 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.

The fifth harmonic number is \frac{137}{60}

[edit] In physics

The fine structure constant, a dimensionless physical constant, approximates 1/137, and the astronomer Arthur Eddington conjectured in 1929 that its inverse was in fact precisely the integer 137, which he claimed could be "obtained by pure deduction". This conjecture was not widely adopted, and by the 1940's, the experimental values for the constant were clearly inconsistent with it.[1]

[edit] In other fields

137 is also:

  • The year CE 137 or 137 BC.
  • The Gematria (i.e. Hebrew numerology) value of the word "Kabbalah", which is of special significance to Jewish mystics.
  • In the Bible, it is the lifespan of three notable men: Ishmael, Levi, and Amram. Each of them supposedly lived to the age of 137. Genesis 25:17, Exodus 6:16-20.
  • California penal code for "Offer bribe to influence testimony".
  • A molecule of chlorophyll a, C55H72O5N4Mg, consists of 137 atoms.
  • There are 137 islands in the Hawaiian island chain.

[edit] References

  1. ^ Helge Kragh, "Magic Number: A Partial History of the Fine-Structure Constant", Archive for History of Exact Sciences 57:5:395 (July, 2003) doi:10.1007/s00407-002-0065-7