In Mathematics
163 is a strong prime in the sense that it is greater than the arithmetic mean of its two neighboring primes. 163 is a lucky prime and a fortunate number.
163 is a strictly non-palindromic number. Given 163, the Mertens function returns 0.
163 figures in an approximation of π, in which .
163 figures in an approximation of e, in which .
163 is a Heegner number. That is, the ring of integers of the field has unique factorization for . The only other such integers are .
The square root of 163 occurs in several interesting pieces of mathematics.
The function gives prime values for all values of between 0 and 39, and for approximately half of all values are prime. 163 appears as a result of solving, which gives .
appears in the Ramanujan constant, in which almost equals the integer 262537412640768744 = 640320^3 + 744. Martin Gardner famously asserted that this identity was exact in a 1975 April Fools' hoax in Scientific American; in fact the value is 262537412640768743.99999999999925007259...
Read more about this topic: 163 (number)
Famous quotes containing the word mathematics:
“Mathematics alone make us feel the limits of our intelligence. For we can always suppose in the case of an experiment that it is inexplicable because we don’t happen to have all the data. In mathematics we have all the data ... and yet we don’t understand. We always come back to the contemplation of our human wretchedness. What force is in relation to our will, the impenetrable opacity of mathematics is in relation to our intelligence.”
—Simone Weil (1909–1943)
“It is a monstrous thing to force a child to learn Latin or Greek or mathematics on the ground that they are an indispensable gymnastic for the mental powers. It would be monstrous even if it were true.”
—George Bernard Shaw (1856–1950)