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|---|---|---|---|---|
| Cardinal | one hundred sixty-three | |||
| Ordinal | 163rd (one hundred sixty-third) | |||
| Factorization | prime | |||
| Prime | 38th | |||
| Divisors | 1, 163 | |||
| Greek numeral | ΡΞΓ´ | |||
| Roman numeral | CLXIII,clxiii | |||
| Binary | 101000112 | |||
| Ternary | 200013 | |||
| Senary | 4316 | |||
| Octal | 2438 | |||
| Duodecimal | 11712 | |||
| Hexadecimal | A316 | |||
163 (one hundred [and] sixty-three) is thenatural number following162 and preceding164.
163 is the 38th prime number and astrong prime in the sense that it is greater than the arithmetic mean of its two neighboring primes.
163 is alucky prime[1] and afortunate number.[2]
163 is a strictly non-palindromic number, since it is not palindromic in anybase betweenbase 2 and base 161.
Given 163, theMertens function returns 0, it is the fourth prime with this property, the first three such primes are2,101 and149.[3]
As approximations,, and
163 is apermutable prime inbase 12, which it is written as 117, thepermutations of itsdigits are 171 and 711, the two numbers in base 12 are229 and1021 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 aHeegner number, the largest of the nine such numbers. That is, thering of integers of thefield hasunique factorization for. The only other such integers are. (sequenceA003173 in theOEIS)
163 is the number of linearlyZ-independent McKay-Thompson series for themonster group, which also represent their collective maximumdimensional representation. This fact about 163 might be a clue for understandingmonstrous moonshine.[4]
appears in theRamanujan constant, since -163 is aquadratic 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 inScientific American; in fact the value is 262537412640768743.99999999999925007259...
It also satisfies.[5]
163 is also:
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