## Monday, July 19, 2010

### 137

137 is a prime number.

137 has a representation as a sum of two squares: 137 = 42 + 112.

137 and 139 form a twin prime pair.

137 is the hypotenuse of a primitive Pythagorean triple: 1372 = 882 + 1052.

137 is a divisor of 374 - 1.

137 = 128 + 8 + 1 = 27 + 23 + 20.

A molecule of chlorophyll a (C55H72O5N4Mg) consists of 137 atoms.

#### 1 comment:

Anonymous said...

Other properties of the number 137:
137 is sum of five consecutive primes 83+89+97 = 131+137
137 index of a Fibonacci primes,
A001605
137 is a cousin of Eisensteins to be of the form 3*46-1, A003627
137 is a cousin of Fermat because that 137 =4*34+1.It is also a Gaussian integer
137 is the 5th harmonic number, Hn = Sum[1/k,k,1,infinity]=1,3/2,11/6,25/12,137/60
137 is a primal number can be obtained by permutations of all or some of its digits, and http://primes.utm.edu/glossary
A072857
137 is the 4th number of Stern,
A042978
137 is the value of the number called the fine structure constant. This constant describes the probability of an electron will emit or absorb a photon.
Curiosity: 137^2=18769,133^2 = 17 689, 281^2 =78961 and 286^2=81796, four squares with the same digits in the solution.
Rafael Parra de Barcelona