# 137 (number)

 ← 136 137 138 →
Cardinalone hundred thirty-seven
Ordinal137th
(one hundred thirty-seventh)
Factorizationprime
Prime33rd
Divisors1, 137
Greek numeralΡΛΖ´
Roman numeralCXXXVII
Binary100010012
Ternary120023
Senary3456
Octal2118
DuodecimalB512

137 (one hundred [and] thirty-seven) is the natural number following 136 and preceding 138.

## In mathematics

137 is:

• the 33rd prime number; the next is 139, with which it comprises a twin prime, and thus 137 is a Chen prime.
• an Eisenstein prime with no imaginary part and a real part of the form ${\displaystyle 3n-1}$.
• the fourth Stern prime.[1]
• a Pythagorean prime: a prime number of the form ${\displaystyle 4n+1}$, where ${\displaystyle n=34}$ (${\displaystyle 137=4\times 34+1}$) or the sum of two squares ${\displaystyle 11^{2}+4^{2}=(121+16)}$.[2]
• a strong prime in the sense that it is more than the arithmetic mean of its two neighboring primes.
• a strictly non-palindromic number[3] and a primeval number.[4][citation needed]
• a factor of 10001 (the other being 73) and the repdigit 11111111 (= 10001 × 1111).
• using two radii to divide a circle according to the golden ratio yields sectors of approximately 137.51° (the golden angle) and 222° in degree system so 137 is the largest integer before it.
• In decimal notation, 1/137 = 0.007299270072992700..., so its period value happens to be palindromic and has a period length of only 8. However, this is only special to decimal, as in pentadecimal it (1/92) has a period length of thirty-four (24) and the period value is not at all palindromic.

## In physics

• Since the early 1900s, physicists have postulated that the number could lie at the heart of a grand unified theory, relating theories of electromagnetism, quantum mechanics and, especially, gravity.[5]
• 1/137 was once believed to be the exact value of the fine-structure constant. The fine-structure constant, a dimensionless physical constant, is approximately 1/137, and the astronomer Arthur Eddington conjectured in 1929 that its reciprocal was in fact precisely the integer 137, which he claimed could be "obtained by pure deduction".[6] This conjecture was not widely adopted, and by the 1940s, the experimental values for the constant were clearly inconsistent with the conjecture, being roughly 1/137.036.[7] Recent work at the Kastler Brossel Laboratory in Paris reported the most precise measurement yet taking the value of this constant to the 11th decimal place, nearly three times more precise than the 2018 results by a group led by Holger Müller at University of California, Berkeley, with a margin of error of just 81 parts per trillion.[8]
• Physicist Leon M. Lederman numbered his home near Fermilab 137 based on the significance of the number to those in his profession. Lederman expounded on the significance of the number in his book The God Particle: If the Universe Is the Answer, What Is the Question?, noting that not only was it the inverse of the fine-structure constant, but was also related to the probability that an electron will emit or absorb a photon—i.e., Feynman's conjecture.[n 1] He added that it also "contains the crux of electromagnetism (the electron), relativity (the velocity of light), and quantum theory (Planck's constant). It would be less unsettling if the relationship between all these important concepts turned out to be one or three or maybe a multiple of pi. But 137?" The number 137, according to Lederman, "shows up naked all over the place", meaning that scientists on any planet in the universe using whatever units they have for charge or speed, and whatever their version of Planck's constant may be, will all come up with 137, because it is a pure number. Lederman recalled that Richard Feynman had even suggested that all physicists put a sign in their offices with the number 137 to remind them of just how much they do not know.[9]

## In psychology and mysticism

• 137 has been the subject of psychological speculation by Swiss psychiatrist and psychoanalyst Carl Jung concerning his theory of synchronicity. Jung and physicist Wolfgang Pauli, according to the book Jung, Pauli, and the Pursuit of a Scientific Obsession by Emeritus Professor of History and Philosophy of Science at University College London, Arthur I. Miller, Jung and Pauli struggled in their search for a primal number that everything in the world hinges on, as well as a desire to quantify the unconscious.[10][11]

## In religion

• The Bible says that Ishmael,[12] Levi[13] and Amram[14] all lived to be 137 years old. The three appearances make it the most common lifespan of individuals in the Bible.
• According to the verse in Genesis (17:17) there was a ten-year age gap between Abraham and Sarah. Sarah died at the age of 127 (Genesis 23:1), thus Abraham was 137 years old at her death. According to Rashi's commentary on Genesis 23:2, Sarah died when she heard that Isaac had almost been sacrificed, thus Abraham was 137 years old at the Binding of Isaac.

## In other fields

• 137: Jung, Pauli, and the Pursuit of a Scientific Obsession by Arthur I. Miller, ISBN 978-0-393-33864-5, describes the friendship of Carl Jung and Wolfgang Pauli and their search for the meaning of 137 in science, medieval alchemy, dream interpretation, and the I Ching.
• The year AD 137 or 137 BC
• 137 AH is a year in the Islamic calendar that corresponds to 754755 CE
• 137 Meliboea is a large and dark main belt asteroid discovered in 1874
• The atomic number of an element not yet observed called untriseptium
• California Penal Code for "Offer bribe to influence testimony"
• The Samson 137 Indian reserve in Alberta, Canada
• Sonnet 137 by William Shakespeare
• Psalm 137
• The atomic number of the highest allowed element on the periodic table allowed for a point nucleus by the Bohr model and the Dirac equation.
• Caesium-137 is a radioactive isotope of caesium formed by nuclear fission
• The number of atoms in a chlorophyll molecule, for which the chemical formula is C55H72MgN4O5.
• Rick Sanchez, a fictional character from the Adult Swim animated television series Rick and Morty, is from a version of the universe numbered C-137, and is sometimes referred to as "C-137" in contexts where "Rick" would be ambiguous (e.g. there are multiple universes' versions of Rick present).

## Notes

1. ^ There is a most profound and beautiful question associated with the observed coupling constant, e, the amplitude for a real electron to emit or absorb a real photon. It is a simple number that has been experimentally determined to be close to −0.08542455. (My physicist friends won't recognize this number, because they like to remember it as the inverse of its square: about 137.03597 with about an uncertainty of about 2 in the last decimal place. It has been a mystery ever since it was discovered more than fifty years ago, and all good theoretical physicists put this number up on their wall and worry about it.) Immediately you would like to know where this number for a coupling comes from: is it related to p or perhaps to the base of natural logarithms? Nobody knows. It's one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man. You might say the "hand of God" wrote that number, and "we don't know how He pushed his pencil". We know what kind of a dance to do experimentally to measure this number very accurately, but we don't know what kind of dance to do on the computer to make this number come out, without putting it in secretly! — R. P. Feynman, QED: The Strange Theory of Light and Matter

## References

1. ^ "Sloane's A042978 : Stern primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-27.
2. ^ "Sloane's A002144 : Pythagorean primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-27.
3. ^ "Sloane's A016038 : Strictly non-palindromic numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-27.
4. ^ "Sloane's A072857 : Primeval numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-27.
5. ^ Rutland, G., Awesome Sovereign (Bloomington: AuthorHouse, 2016), p. 33.
6. ^ Eddington, A. S., The Constants of Nature in "The World of Mathematics", Vol. 2 (1956) Ed. Newman, J. R., Simon and Schuster, pp. 1074-1093.
7. ^ 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
8. ^ Morel, Leo; Yao, Zhibin (December 2020). "Determination of the fine-structure constant with an accuracy of 81 parts per trillion" (PDF). Nature. 588 (7836): 61–65. Bibcode:2020Natur.588...61M. doi:10.1038/s41586-020-2964-7. PMID 33268866. S2CID 227259475.
9. ^ Lederman, L. M., The God Particle: If the Universe is the Answer, What is the Question? (1993), Houghton Mifflin Harcourt, pp. 28–29.
10. ^ Miller, Arthur (2010). 137: Jung, Pauli, and the Pursuit of a Scientific Obsession. W. W. Norton & Company. p. 368. ISBN 978-0393065329.
11. ^ "One Over One Three Seven by Jack Dikian". Academia. February 2023. Retrieved 20 February 2023.
12. ^ Genesis 25:17
13. ^ Exodus 6:16
14. ^ Exodus 6:20