|Cardinal||one hundred sixty-three|
(one hundred sixty-third)
In mathematics edit
163 is a strong prime in the sense that it is greater than the arithmetic mean of its two neighboring primes.
As approximations, , and
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 . (sequence A003173 in the OEIS)
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.
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 other fields edit
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.
- The Burj Khalifa in Dubai, United Arab Emirates, which is the tallest building in the world, has 163 floors.
- In darts, 163 is the lowest number that cannot be shot with three darts on a standard dart board.
See also edit
- Sloane, N. J. A. (ed.). "Sequence A031157 (Numbers that are both lucky and prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-28.
- Sloane, N. J. A. (ed.). "Sequence A005235 (Fortunate numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-28.
- Sloane, N. J. A. (ed.). "Sequence A100669 (Zeros of the Mertens function that are also prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
- He, Yang-Hui; McKay, John (2015). "Sporadic and exceptional". pp. 1–49. arXiv:1505.06742 [math.AG]. (See p. 13)
- Wells, D. (1987). The Penguin Dictionary of Curious and Interesting Numbers (pp. 141–142). London: Penguin Group.
- Clark, Alex. "163 and Ramanujan Constant". Numberphile. Brady Haran. Archived from the original on 2013-05-16. Retrieved 2013-04-02.
- 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 Archived 2020-11-27 at the Wayback Machine
- International Brotherhood of Electrical Workers Local Union 163
- US Highway 1633?], from Mathematics Stack Exchange