41 (forty-one) is the
natural number
In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive in ...
following
40 and preceding
42.
In mathematics
41 is:
* the 13th smallest
prime number
A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime ...
. The next is
43, making both
twin prime
A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair or In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin prime' ...
s.
* the sum of the first six prime numbers (2 + 3 + 5 + 7 + 11 + 13).
* a
regular prime
In number theory, a regular prime is a special kind of prime number, defined by Ernst Kummer in 1850 to prove certain cases of Fermat's Last Theorem. Regular primes may be defined via the divisibility of either class numbers or of Bernoulli num ...
* a
Ramanujan prime
In mathematics, a Ramanujan prime is a prime number that satisfies a result proven by Srinivasa Ramanujan relating to the prime-counting function.
Origins and definition
In 1919, Ramanujan published a new proof of Bertrand's postulate which, as ...
* a
harmonic prime
A harmonic prime is a prime number that divides the numerators of exactly three harmonic numbers
In mathematics, the -th harmonic number is the sum of the Multiplicative inverse, reciprocals of the first natural numbers:
H_n= 1+\frac+\frac+ ...
* a
good prime A good prime is a prime number whose square is greater than the product of any two primes at the same number of positions before and after it in the sequence of primes.
That is, good prime satisfies the inequality
:p_n^2 > p_ \cdot p_
for all 1 ...
* the 12th
supersingular prime
* a
Newman–Shanks–Williams prime.
* the smallest
Sophie Germain prime
In number theory, a prime number ''p'' is a if 2''p'' + 1 is also prime. The number 2''p'' + 1 associated with a Sophie Germain prime is called a . For example, 11 is a Sophie Germain prime and 2 × 11 +&nbs ...
to start a
Cunningham chain
In mathematics, a Cunningham chain is a certain sequence of prime numbers. Cunningham chains are named after mathematician A. J. C. Cunningham. They are also called chains of nearly doubled primes.
Definition
A Cunningham chain of the first kin ...
of the first kind of three terms, .
* an
Eisenstein prime
In mathematics, the Eisenstein integers (named after Gotthold Eisenstein), occasionally also known as Eulerian integers (after Leonhard Euler), are the complex numbers of the form
: z = a + b\omega ,
where and are integers and
: \omega = \frac ...
, with no imaginary part and real part of the form 3''n'' − 1.
* a
Proth prime
A Proth number is a natural number ''N'' of the form N = k \times 2^n+1 where ''k'' and ''n'' are positive integers, ''k'' is odd and 2^n > k. A Proth prime is a Proth number that is prime. They are named after the French mathematician Françoi ...
as it is 5 × 2
3 + 1.
* the smallest
lucky number of Euler: the polynomial yields primes for all the integers ''k'' with .
* the sum of two
squares
In geometry, a square is a regular polygon, regular quadrilateral. It has four straight sides of equal length and four equal angles. Squares are special cases of rectangles, which have four equal angles, and of rhombuses, which have four equal si ...
(4
2 + 5
2), which makes it a
centered square number
In elementary number theory, a centered square number is a Centered polygonal number, centered figurate number that gives the number of dots in a Square (geometry), square with a dot in the center and all other dots surrounding the center dot i ...
.
* the sum of the first three
Mersenne prime
In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form for some integer . They are named after Marin Mersenne, a French Minim friar, who studied them in the early 1 ...
s, 3, 7, 31.
* the sum of the sum of the divisors of the first 7
positive integers
In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positiv ...
.
* the smallest integer whose reciprocal has a 5-digit
repetend
A repeating decimal or recurring decimal is a decimal representation of a number whose digits are eventually periodic (that is, after some place, the same sequence of digits is repeated forever); if this sequence consists only of zeros (that is ...
. That is a consequence of the fact that 41 is a factor of 99999.
* the smallest integer whose
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 ...
has a
simple continued fraction
A simple or regular continued fraction is a continued fraction with numerators all equal one, and denominators built from a sequence \ of integer numbers. The sequence can be finite or infinite, resulting in a finite (or terminated) continued fr ...
with
period
Period may refer to:
Common uses
* Period (punctuation)
* Era, a length or span of time
*Menstruation, commonly referred to as a "period"
Arts, entertainment, and media
* Period (music), a concept in musical composition
* Periodic sentence (o ...
3.
* a prime index prime, as 13 is prime.
In other fields
* In Mexico "cuarenta y uno" (41) is slang referring to a
homosexual
Homosexuality is romantic attraction, sexual attraction, or sexual behavior between people of the same sex or gender. As a sexual orientation, homosexuality is "an enduring pattern of emotional, romantic, and/or sexual attractions" exc ...
. This is due to the 1901 arrest of 41 homosexuals at a hotel in
Mexico City
Mexico City is the capital city, capital and List of cities in Mexico, largest city of Mexico, as well as the List of North American cities by population, most populous city in North America. It is one of the most important cultural and finan ...
during the government of Porfirio Díaz (1876–1911). See:
Dance of the Forty-One
* In
Switzerland
Switzerland, officially the Swiss Confederation, is a landlocked country located in west-central Europe. It is bordered by Italy to the south, France to the west, Germany to the north, and Austria and Liechtenstein to the east. Switzerland ...
, is the international calling code
References
{{DEFAULTSORT:41 (Number)
Integers