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# 137

The only known primeval number whose sum of digits equals the number of primes "contained."

The largest prime number of characters allowed per "tweet" on the social networking site Twitter.

137 is the largest prime factor of 123456787654321.

The reciprocal of the fine-structure constant of electromagnetism is close to 137. Throughout his life, physicist Wolfgang Pauli had been preoccupied with the question of why the fine-structure constant has this value. He died in Room 137 of the Rotkreuz hospital in Zürich, Switzerland.

The start of twelve consecutive primes with symmetrical gaps about the center.

William Shanks (1812-1882), a British amateur mathematician, manually calculated the logarithms of 2, 3, 5, and 10 to 137 decimal places in 1853.

2^{137} - 1 is a semiprime (containing exactly two prime factors). [Brillhart]

137 divides 11111111.

The most frequent digits to occur among primes less than 10^{10} start out 1, 3, and 7, in that order. [McCranie]

"And these are the years of the life of Ishmael, an **hundred and thirty and seven** years: and he gave up the ghost and died; and was gathered unto his people." (*Genesis* 25:17, KJV)

The sum of the squares of the digits of 137 is another prime and all five odd digits are used. [Trotter]

The number seven occurs 137 times in the Book of Revelation (KJV). [Blanton]

137 is the first integer parameter n_{1} in Gilson's formula α(n_{1}, n_{2}) = n_{2}cos(π/n_{1})tan(π/(n_{1}n_{2}))/π for the value of the *fine structure constant* α = α(137, 29) = 0.0072973525318....

The sum of Rosie's measurements (42-39-56) equals 137 in the song "Whole Lotta Rosie" by the Australian hard rock band AC/DC.

The greatest prime factor of any 8-digit repdigit is 137. [La Haye]

The Hawaiian Island chain is made up of 137 islands, islets, and shoals.

137^{2} = 1 (mod 391).
[Croll]

A molecule of chlorophyll *a*, C_{55}H_{72}MgN_{4}O_{5}, consists of 137 atoms. [Blanton]

The sum of the squares of the first seven digits of π is the smallest such prime: 3^2 + 1^2 + 4^2 + 1^2 + 5^2 + 9^2 + 2^2 = 137. [Post]

137 * 2^(3 * 137^2) + 1 is prime. Note that 137 appears twice. [Buddenhagen and McCranie]

137 * 2^523283 + 1 is prime. [McCranie]

The James A. FitzPatrick nuclear power plant on the shore of Lake Ontario has 137 control rods. [Gonyeau]

137 is the Chilean National Sea Rescue emergency number. [Vogel]

(137!-1)/139 is prime. Note that 137 and 139 are twin primes. [Gallardo]

Mabkhout (1993) showed that every number x^4 + 1, for x > 3, has a prime factor greater than or equal to 137. He used a classical result of Størmer. [Post]

The numerical value of the Hebrew word Kabbalah is 137 (using the "common" Hebrew gematria method), which is equal to the combined value of the words chochmah (73), "wisdom," and nevuah (64), "prophecy." [Scholem]

One of the math papers of Ted Kaczynski (also known as the Unabomber) is *Boundary Functions for Bounded Harmonic Functions*, Transactions of the American Mathematical Society 137.

Baseball player Barry Bonds batted in 137 runs in 2001, his highest yearly total to date. [McCranie]

2^{137} reversed is prime. [Nash]

Garry Kasparov and Anatoly Karpov played 137 draws in chess. [McCranie]

On the day before his presidential inauguration, Barack H. Obama made a 137-mile train trip from Philadelphia to Washington, DC. [McCranie]

The smallest prime with 3 distinct digits that remains prime if any one of its digits is removed. [Post]

The comic book series *Superman's Girl Friend, Lois Lane* ran for 137 issues (March 1958 to October 1974).

137^(odd power) = 137 mod (17 * 23); 137^(even power) = 1 mod (17 * 23). [Sirag]

The full chemical name for caffeine is 1,3,7-trimethylxanthine.

The first three solutions to the Tower of Hanoi & End of the World game/puzzle using 1, 2 & 3 discs is the sequence 1,3,7. [Phillips]

Legend has it that the Great Chicago Fire started at 137 DeKoven Street in Mrs. O'Leary's barn.

A triangle with base 137 and height π has the hypotenuse 137.0360157, which is very close to the measured inverse of the fine structure constant. [Sirag]

The only 3-digit prime whose reciprocal number is an infinite periodic palindrome: 1/137 = 0.007299270072992700729927... . [Machusky]

The smallest prime that can be represented as sum of products of n pairs of first consecutive odd numbers, (n=3), i.e., 1*3 + 5*7 + 9*11. Can you find the 2nd such prime? [Loungrides]

For each integer n greater than 137, there are at least [2*sqrt(n)] primes between n^2 and (n+1)^2. Here [x] denotes the integer part of x.

Richard Feynman determined that element 137 (Feynmanium) is the last stably neutrally-charged element, as larger elements would need electrons travelling faster than light to become neutral.

The 13th term of the puzzle sequence that begins 2, 23, 235, 2357, 12357, 3, 37, 37, 3, 3, 3, 37, ... . Can you guess the rule for generating this sequence? [Honaker, 2018]

137 is the only 3-digit prime that divides all of the numbers of form aaaaabbaabbaaaaa. [Loungrides]

1^1 + 3^3 + 7^7 + 137^2 +/- 1 and 1^1 + 3^3 + 7^7 - 137^2 + 1 are all prime. [Homewood]

British researchers calculate the average person weighs around 137 lb. [McGrath]