131 (one hundred thirty 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
130 and preceding
132.
In mathematics
131 is a
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 ...
, an
irregular prime, the second 3-digit
palindromic prime, and also a
permutable prime
A permutable prime, also known as anagrammatic prime, is a prime number which, in a given radix, base, can have its digits' positions switched through any permutation and still be a prime number. H. E. Richert, who is supposedly the first to stu ...
with
113 113 may refer to:
*113 (number), a natural number
*AD 113, a year
*113 BC, a year
*113 (band), a French hip hop group
*113 (MBTA bus), Massachusetts Bay Transportation Authority bus route
*113 (New Jersey bus), Ironbound Garage in Newark and run to ...
and
311. It can be expressed as the sum of three consecutive primes, 131 = 41 + 43 + 47. 131 is an
Eisenstein prime with no imaginary part and real part of the form
. Because the next odd number, 133, is a
semiprime, 131 is a
Chen prime. 131 is an
Ulam number.
131 is a
full reptend prime
In number theory, a full reptend prime, full repetend prime, proper primeDickson, Leonard E., 1952, ''History of the Theory of Numbers, Volume 1'', Chelsea Public. Co. or long prime in base ''b'' is an odd prime number ''p'' such that the Fermat ...
in
base 10 (and also in
base 2). The decimal expansion of 1/131 repeats the digits 007633587786259541984732824427480916030534351145038167938931 297709923664122137404580152671755725190839694656488549618320 6106870229 indefinitely.
131 is the fifth discriminant of imaginary
quadratic field
In algebraic number theory, a quadratic field is an algebraic number field of Degree of a field extension, degree two over \mathbf, the rational numbers.
Every such quadratic field is some \mathbf(\sqrt) where d is a (uniquely defined) square-free ...
s with class number 5, where the 131st prime number 739 is the fifteenth such discriminant. Meanwhile, there are conjectured to be a total of 131 discriminants of class number 8 (only one more discriminant could exist).
References
{{DEFAULTSORT:131 (Number)
Integers