Tuesday, December 13, 2011

197

197 is a prime number.


197 is the sum of the first 12 primes: 197 = 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37. It is also the smallest prime that is the sum of seven consecutive primes: 197 = 17 + 19 + 23 + 29 + 31 + 37 + 41.

197 is the sum of the digits of all two-digit primes.

197 is the sum of the squares of all composite digits: 197 = 42 + 62 + 82 + 92.

197 has a representation as a sum of two squares: 197 = 12 + 142.

197 and 199 form a twin prime pair.

197 is the hypotenuse of a primitive Pythagorean triple: 1972 = 282 + 1952.

The chemical element gold has one stable isotope, which has a total of 197 neutrons and protons in its nucleus.

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1 comment:

  1. AnonymousDecember 13, 2011 at 12:55 PM

    Algunas propiedades analíticas del número 197
    Ecuación Pell: 393^2-197*28^2=1
    http://hojamat.es/parra/cuadrbin.pdf
    Formas cuadráticas imaginarias:
    Si la norma es N(a+b(-D^(1/2)=x^2+D*y^2=197
    197=7^2+37*2^2 donde z^2-14z+197=0 con z =7+-2(37)^(1/2)i
    197=9^2+29*2^2 donde z^2-18z+197=0 con z=9+-2(29)^(1/2)i
    197=13^2+7*2^2 donde z^2-26z+197=0 con z=13+-2(7)^(1/2)i
    http://hojamat.es/parra/cuadrbin.pdf
    Grupos multiplicativos
    Como 15^2>197>14^2,210=14*15 donde mcd(14,15)=1=14(-1)+15(1)
    Si z=197+210t es un número algebraico,entonces
    x=197(mód.14)=1 e y=197(mód.15)=2, luego
    197=14(-1)*2(mód.210)+15(1)*1(mód.210)=182+15,por lo que
    f(197) = f(182)+f(15) es una función multiplicativa aditiva.
    http://hojamat.es/parra/funesp.pdf
    Rafael Parra Machío

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