71 (seventy-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
70 and preceding
72.
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In mathematics
71 is the 20th prime number. Because both rearrangements of its digits (17 and 71) are
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 ...
s, 71 is an
emirp and more generally a
permutable prime.
71 is a
centered heptagonal number.
It is a
regular prime, a
Ramanujan prime, a
Higgs prime, and a
good prime.
It is a
Pillai prime, since
is divisible by 71, but 71 is not one more than a multiple of 9.
It is part of the last known pair (71, 7) of
Brown numbers, since
.
71 is the smallest of thirty-one discriminants 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 of 7, negated (see also,
Heegner number
In number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from int ...
s).
71 is the largest number which occurs as a prime factor of an order of a
sporadic simple group, the largest (15th)
supersingular prime.
See also
*
71 (disambiguation)
References
{{Integers, zero
Integers