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...
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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)
“The three main medieval points of view regarding universals are designated by historians as realism, conceptualism, and nominalism. Essentially these same three doctrines reappear in twentieth-century surveys of the philosophy of mathematics under the new names logicism, intuitionism, and formalism.”
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