163 (number)

← 162 163 164 →
← 160 161 162 163 164 165 166 167 168 169 → List of numbers — Integers ← 0 100 200 300 400 500 600 700 800 900 →
Cardinal	one hundred sixty-three
Ordinal	163rd (one hundred and sixty-third)
Factorization	prime
Prime	38th
Divisors	1, 163
Roman numeral	CLXIII
Binary	101000112
Ternary	200013
Quaternary	22034
Quinary	11235
Senary	4316
Octal	2438
Duodecimal	11712
Hexadecimal	A316
Vigesimal	8320
Base 36	4J36

163 (one hundred [and] sixty-three) is the natural number following 162 and preceding 164.

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^[1] and a fortunate number.^[2]

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.^[3]

163 figures in an approximation of π, in which $\pi \approx {2^{9} \over 163}\approx 3.1411$.

163 figures in an approximation of e, in which $e\approx {163 \over 3\cdot 4\cdot 5}\approx 2.7166\dots$.

163 is a Heegner number, the largest of the nine such numbers. That is, the ring of integers of the field ${\mathbb {Q}}({\sqrt {-a}})$ has unique factorization for $a=163$. The only other such integers are $a=1,2,3,7,11,19,43,67$. (sequence A003173 in the OEIS)

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 $f(n)=n^{2}+n+41$ gives prime values for all values of $n$ between 0 and 39, and for $n<10^{7}$ approximately half of all values are prime. 163 appears as a result of solving $f(n)=0$, which gives $n=(-1+{\sqrt {-163}})/2$.

${\sqrt {163}}$ appears in the Ramanujan constant, since -163 in a quadratic nonresidue to modulo all the primes 3, 5, 7, ..., 37. In which $e^{{\pi {\sqrt {163}}}}$ 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 astronomy

• 163 Erigone is a dark Main belt asteroid, the namesake of the Erigone family of asteroids

In the US military

• USNS Parkersburg (T-AO-163) was a United States Navy tanker ship during World War II
• USS Barracuda (SS-163) was a diesel-electric submarine during World War II
• USS Blount (AK-163) was a United States Navy Alamosa class cargo ship during World War II
• USS Cinnabar (IX-163) was a United States Navy Trefoil class concrete barge during World War II
• USS Concise (AM-163) was a United States Navy Admirable-class minesweeper during World War II
• USS Eastland (APA-163) was a United States Navy Haskell-class attack transport during World War II
• USS Livingston (AP-163) was a United States Navy Crater-class cargo ship during World War II
• USS McConnell (DE-163) was a United States Navy Cannon-class destroyer escort during World War II
• USS Utina (ATF-163) was a United States Navy Abnaki class fleet ocean tug following World War II
• USS Vedette (SP-163) was a commercial yacht during World War I
• USS Walker (DD-163) was a United States Navy Wickes class destroyer during World War I
• 163rd Fighter Squadron, a unit of the Indiana Air National Guard, flies the F-16C/D Fighting Falcon

In American sports

• Russ Howell at the Long Beach, California World Championship in 1977 performed a world record 163 full rotations in freestyle skateboarding tricks^[4]
• In darts, 163 is the least number that cannot be shot with three darts on a standard dart board

In transportation

• 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, USA, 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:

• 163 AH is a year in the Islamic calendar that corresponds to 779 – 780 CE
• The atomic number of an element temporarily called Unhextrium
• CD163 (Cluster of Differentiation 163) is a human protein encoded by the CD163 gene
• The Glossen Opus 163 waltz by Johann Strauss II (1855)
• The number of days following the first day of Passover (Pesach), used to calculate the date of Rosh Hashanah, the Jewish New Year.

See also

• 163 (disambiguation)
• United Nations Security Council Resolution 163
• United States Supreme Court cases, Volume 163

References

1. "Sloane's A031157 : Numbers that are both lucky and prime". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-28.
2. "Sloane's A005235 : Fortunate numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-28.
3. "Sloane's A100669 : Zeros of the Mertens function that are also prime". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
4. Boise Weekly (July 2, 2008), "Generations of skateboarders keep rolling" by Katy Dang

• Wells, D. (1987). The Penguin Dictionary of Curious and Interesting Numbers (pp. 141–142). London: Penguin Group.

External links

• Clark, Alex. "163 and Ramanujan Constant". Numberphile. Brady Haran.
• The Number 163
• The Positive Integer 163
• Prime curiosities: 163
• 163.com website from NetEase
• The coolest number is 163
• 163, the Monster and Number Theory
• VirtueScience: 163
• International Brotherhood of Electrical Workers Local Union 163
• US Highway 163
• Planetmath.Org 163
• Other interesting consequences of d=163?, from Mathematics Stack Exchange