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pseudoprimeira

Pseudoprimeira is a term used in some informal or speculative discussions to denote a composite number that passes a specified primality test for a prescribed set of bases. The word blends pseudoprime with a feminine suffix and is not a standard term in mainstream number theory. In this sense, the concept serves as a generalized or contextual version of pseudoprimes.

Definition and scope: Let T be a primality test defined by congruences or related conditions, and let

Relation to established concepts: Pseudoprimeiras generalize the idea of Fermat pseudoprimes and Carmichael numbers by varying

Properties and prevalence: The existence and abundance of pseudoprimeiras depend on the chosen test and base

See also: pseudoprime, Carmichael number, Fermat pseudoprime, Miller-Rabin primality test, strong pseudoprime.

B
be
a
set
of
integers
with
gcd(a,n)=1.
A
composite
number
n
is
a
pseudoprimeira
to
T
with
respect
to
B
if
for
every
a
in
B,
the
test
T
produces
a
result
that
would
be
correct
for
a
prime.
If
B
equals
the
full
set
of
units
modulo
n
and
T
is
the
Fermat
test,
such
numbers
align
with
the
classical
Carmichael
numbers.
If
T
is
a
strong
primality
test
(as
in
Miller-Rabin),
the
corresponding
objects
are
sometimes
discussed
as
strong
pseudoprimes
to
a
base
set.
the
test
and
the
base
set.
They
are
not
standardized
in
the
literature,
and
precise
definitions
can
vary
between
sources.
In
formal
contexts,
a
Carmichael
number
or
a
strong
pseudoprime
to
a
given
base
set
serves
a
comparable
role
to
what
some
discussions
label
a
pseudoprimeira.
set;
broader
base
sets
yield
fewer
composite
numbers
that
pass
the
test.
They
are
primarily
of
theoretical
interest
in
illustrating
exceptions
to
primality
tests.