163 (number)

the number the internet services company NetEase 163 prime 38th 1, 163 163 (one hundred [and] sixty-three) is the natural number following 162 and preceding 164. In mathematics 163 is the 38th prime number and a strong prime in the sense that it is greater than the arithmetic mean of its two neighboring primes. 163 is a lucky primeA031157 Numbers that are both lucky and prime 2016-05-28 and a fortunate number.A005235 Fortunate numbers 2016-05-28 163 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.A100669 Zeros of the Mertens function that are also prime 2016-05-29 As approximations, , and 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 are 229 and 1021 in base 10, both of which are prime. The function gives prime values for all values of between 0 and 39, while for approximately half of all values are prime. 163 appears as a result of solving , which gives . 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 . A003173 163 is the number of linearly Z-independent McKay-Thompson series for the monster group, which also represent their collective maximum dimensional representation. This fact about 163 might be a clue for understanding monstrous moonshine.He, Yang-Hui McKay, John Sporadic and exceptional 1505.06742 2015 1–49 math.AG (See p. 13) appears in the Ramanujan constant, since −163 is a quadratic nonresidue to modulo all the primes 3, 5, 7, ..., 37. (By quadratic reciprocity, this is equivalent to saying that all the primes 2, 3, 5, 7, ..., 37 are quadratic nonresidues modulo 163). 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... It also satisfies .AlmostInteger Almost integer August 5, 2024 In other fields 163 is also: 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 References 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 http://www.numberphile.com/videos/163.html Numberphile Brady Haran 2013-04-02 https://web.archive.org/web/20130516045906/http://www.numberphile.com/videos/163.html 2013-05-16 dead The Number 163 The Positive Integer 163 Prime curiosities: 163 163.com website from NetEase The coolest number is 163April 2026 InternetArchiveBot 163, the Monster and Number Theory VirtueScience: 163 https://web.archive.org/web/20201127162707/https://www.virtuescience.com/163.html 2020-11-27 International Brotherhood of Electrical Workers Local Union 163 US Highway 163 Other interesting consequences of d=163?, from Mathematics Stack Exchange 1 Category:Integers Category: Prime numbers