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)
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“I must study politics and war that my sons may have liberty to study mathematics and philosophy.”
—John Adams (1735–1826)
“In mathematics he was greater
Than Tycho Brahe, or Erra Pater:
For he, by geometric scale,
Could take the size of pots of ale;
Resolve, by sines and tangents straight,
If bread and butter wanted weight;
And wisely tell what hour o’ th’ day
The clock doth strike, by algebra.”
—Samuel Butler (1612–1680)