163 (one hundred [and] sixty-three) is the natural number following 162 and preceding 164.
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, since it is not palindromic in any base between base 2 and base 161.
Given 163, the Mertens function returns 0, it is the fourth prime with this property, the first three such primes are 2, 101 and 149.
163 figures in an approximation of π, in which .
163 figures in an approximation of e, in which .
163 is a Heegner number, the largest of the nine such numbers. That is, the ring of integers of the field has unique factorization for . The only other such integers are
. (sequence A003173 in the OEIS)
163 is the number of Z-independent McKay-Thompson series for the monster group. This fact about 163 might be a clue for understanding monstrous moonshine.
163 is a permutable prime in base 12, which it is written as 117, the permutations of its digits are 171 and 711, the two numbers in base 12 is 229 and 1021 in base 10, both of them are primes.
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, since -163 is a quadratic nonresidue to modulo all the primes 3, 5, 7, ..., 37. In which almost equals the integer 262537412640768744 = 6403203 + 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...
In the US military
- Peugeot Type 163 automobile produced from 1919 to 1924
- Messerschmitt Me 163 Komet was a German rocket-powered fighter aircraft. during World War II
- Intervale Avenue –163rd Street subway station, Bronx, New York subway station on the IRT White Plains Road Line of the New York City Subway in the USA.
- 163rd Street–Amsterdam Avenue station on the IND Eighth Avenue Line of the New York City Subway in America.
- The Bunche Park Metrorail station in Bunche Park, Florida, United States, at Northwest 163rd Street and 27th Avenue, set to open in 2014
- Saudi Arabian Airlines Flight 163 caught fire at Riyadh's International Airport en route from Karachi, Pakistan on August 19, 1980
- Iraqi Airways Flight 163, en route from Baghdad's Baghdad International Airport to Amman, Jordan, was hijacked and crashed on December 25, 1986
- List of highways numbered 163
In other fields
163 is also: