The
number
A number is a mathematical object used to count, measure, and label. The most basic examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More universally, individual numbers can ...
4,294,967,295 is a
whole number
An integer is the number zero ( 0), a positive natural number (1, 2, 3, ...), or the negation of a positive natural number ( −1, −2, −3, ...). The negations or additive inverses of the positive natural numbers are referred to as negative ...
equal to 2 − 1. It is a
perfect totient number, meaning it is equal to the sum of its iterated
totient
In number theory, Euler's totient function counts the positive integers up to a given integer that are relatively prime to . It is written using the Greek letter phi as \varphi(n) or \phi(n), and may also be called Euler's phi function. In othe ...
s. It follows 4,294,967,294 and precedes 4,294,967,296. It has a factorization of
.
In computing, 4,294,967,295 is the highest
unsigned (that is, not negative)
32-bit
In computer architecture, 32-bit computing refers to computer systems with a processor, memory, and other major system components that operate on data in a maximum of 32- bit units. Compared to smaller bit widths, 32-bit computers can perform la ...
integer, which makes it the highest possible number a 32-bit system can store in memory.
In geometry
Since the prime factors of 2 − 1 are exactly the five known
Fermat prime
In mathematics, a Fermat number, named after Pierre de Fermat (1601–1665), the first known to have studied them, is a positive integer of the form:F_ = 2^ + 1, where ''n'' is a non-negative integer. The first few Fermat numbers are: 3, 5, ...
s, this number is the largest known odd value ''n'' for which a
regular ''n''-sided polygon is
constructible using compass and straightedge.
Equivalently, it is the largest known odd number ''n'' for which the angle
can be constructed, or for which
can be expressed in terms of
square root
In mathematics, a square root of a number is a number such that y^2 = x; in other words, a number whose ''square'' (the result of multiplying the number by itself, or y \cdot y) is . For example, 4 and −4 are square roots of 16 because 4 ...
s.
Not only is 4,294,967,295 the largest known odd number of sides of a constructible polygon, but since constructibility is related to factorization, the list of odd numbers ''n'' for which an ''n''-sided polygon is constructible begins with the list of factors of 4,294,967,295. If there are no more Fermat primes, then the two lists are identical. Namely (assuming 65537 is the largest Fermat prime), an odd-sided polygon is constructible if and only if it has 3, 5, 15, 17, 51, 85, 255, 257, 771, 1285, 3855, 4369, 13107, 21845, 65535, 65537, 196611, 327685, 983055, 1114129, 3342387, 5570645, 16711935, 16843009, 50529027, 84215045, 252645135, 286331153, 858993459, 1431655765, or 4294967295 sides.
If there are more numbers in this list, they must be at least 2+1 (approximately 10), because every intervening Fermat number is known to be composite.
In computing
The number 4,294,967,295, equivalent to the
hexadecimal
Hexadecimal (also known as base-16 or simply hex) is a Numeral system#Positional systems in detail, positional numeral system that represents numbers using a radix (base) of sixteen. Unlike the decimal system representing numbers using ten symbo ...
value , is the maximum value for a
32-bit
In computer architecture, 32-bit computing refers to computer systems with a processor, memory, and other major system components that operate on data in a maximum of 32- bit units. Compared to smaller bit widths, 32-bit computers can perform la ...
unsigned integer
In computer science, an integer is a datum of integral data type, a data type that represents some range of mathematical integers. Integral data types may be of different sizes and may or may not be allowed to contain negative values. Integers are ...
in
computing
Computing is any goal-oriented activity requiring, benefiting from, or creating computer, computing machinery. It includes the study and experimentation of algorithmic processes, and the development of both computer hardware, hardware and softw ...
. It is therefore the maximum value for a
variable declared as an unsigned integer (usually indicated by the codeword) in many programming languages running on modern computers. The presence of the value may reflect an error, overflow condition, or missing value.
This value is also the largest
memory
Memory is the faculty of the mind by which data or information is encoded, stored, and retrieved when needed. It is the retention of information over time for the purpose of influencing future action. If past events could not be remembe ...
address for CPUs using a 32-bit address bus. Being an odd value, its appearance may reflect an erroneous (misaligned) memory
address
An address is a collection of information, presented in a mostly fixed format, used to give the location of a building, apartment, or other structure or a plot of land, generally using border, political boundaries and street names as references, ...
. Such a value may also be used as a
sentinel value
In computer programming, a sentinel value (also referred to as a flag value, trip value, rogue value, signal value, or dummy data) is a special value in the context of an algorithm which uses its presence as a condition of termination, typically ...
to initialize newly allocated memory for debugging purposes.
Internet Protocol version 4 (
IPv4
Internet Protocol version 4 (IPv4) is the first version of the Internet Protocol (IP) as a standalone specification. It is one of the core protocols of standards-based internetworking methods in the Internet and other packet-switched networks. ...
) uses a 32-
bit addresses which limits the
address space
In computing, an address space defines a range of discrete addresses, each of which may correspond to a network host, peripheral device, disk sector, a memory cell or other logical or physical entity.
For software programs to save and retrieve ...
to (2
32) unique addresses.
In 2004, 800 aircraft over Los Angeles were put in danger when the LA Air Route Traffic Control Center lost radio contact with all of the aircraft for about three hours, delaying 400 flights and cancelling 600, due to a computer design that kept time by starting at 4,294,967.295 seconds and counting down to zero, or 49 days, 17 hours, 2 minutes and 47.295 seconds. Some people were aware that the system needed to be restarted at least every 30 days, but the root problem was the choice of such a small number.
On May 4, 2021,
Nasdaq
The Nasdaq Stock Market (; National Association of Securities Dealers Automated Quotations) is an American stock exchange based in New York City. It is the most active stock trading venue in the U.S. by volume, and ranked second on the list ...
temporarily suspended price feeds for
Berkshire Hathaway
Berkshire Hathaway Inc. () is an American multinational conglomerate holding company headquartered in Omaha, Nebraska. Originally a textile manufacturer, the company transitioned into a conglomerate starting in 1965 under the management of c ...
Class A shares (), which reached $421,000. Nasdaq stores stock prices as 32-bit unsigned integers in increments of ten-thousandths of a
dollar
Dollar is the name of more than 25 currencies. The United States dollar, named after the international currency known as the Spanish dollar, was established in 1792 and is the first so named that still survives. Others include the Australian d ...
, so the maximum price that could be represented was $429,496.7295.
See also
*
2,147,483,647
The number 2147483647 is the eighth Mersenne prime, equal to 231 − 1. It is one of only four known double Mersenne primes.
The primality of this number was proven by Leonhard Euler, who reported the proof in a letter to Daniel Be ...
(2-1)
*
Power of two
A power of two is a number of the form where is an integer, that is, the result of exponentiation with number 2, two as the Base (exponentiation), base and integer as the exponent. In the fast-growing hierarchy, is exactly equal to f_1^ ...
*
Equilateral triangle
An equilateral triangle is a triangle in which all three sides have the same length, and all three angles are equal. Because of these properties, the equilateral triangle is a regular polygon, occasionally known as the regular triangle. It is the ...
*
Pentagon
In geometry, a pentagon () is any five-sided polygon or 5-gon. The sum of the internal angles in a simple polygon, simple pentagon is 540°.
A pentagon may be simple or list of self-intersecting polygons, self-intersecting. A self-intersecting ...
*
Heptadecagon (17-sides)
*
257-gon
In geometry, a 257-gon is a polygon with 257 sides. The sum of the interior angles of any non- self-intersecting 257-gon is 45,900°.
Regular 257-gon
The area of a regular 257-gon is (with )
:A = \frac t^2 \cot \frac\approx 5255.751t^2.
A wh ...
*
65537-gon
References
{{DEFAULTSORT:4294967295
Integers
Constructible polygons