**137**is a prime number.

**137**has a representation as a sum of two squares:

**137**= 4

^{2}+ 11

^{2}.

**137**and 139 form a twin prime pair.

**137**is the hypotenuse of a primitive Pythagorean triple:

**137**

^{2}= 88

^{2}+ 105

^{2}.

**137**is a divisor of 37

^{4}- 1.

**137**= 128 + 8 + 1 = 2

^{7}+ 2

^{3}+ 2

^{0}.

_{55}H

_{72}O

_{5}N

_{4}Mg) consists of

**137**atoms.

Source: Prime Curios!

## 1 comment:

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

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