<s>
If	O
n	O
is	O
an	O
odd	O
composite	O
integer	O
that	O
satisfies	O
the	O
above	O
congruence	O
,	O
then	O
n	O
is	O
called	O
an	O
Euler	B-Algorithm
–	I-Algorithm
Jacobi	I-Algorithm
pseudoprime	I-Algorithm
(	O
or	O
,	O
more	O
commonly	O
,	O
an	O
Euler	B-Algorithm
pseudoprime	I-Algorithm
)	O
to	O
base	O
a	O
.	O
</s>
<s>
The	O
equation	O
can	O
be	O
tested	O
rather	O
quickly	O
,	O
which	O
can	O
be	O
used	O
for	O
probabilistic	O
primality	B-Algorithm
testing	I-Algorithm
.	O
</s>
<s>
Every	O
Euler	B-Algorithm
–	I-Algorithm
Jacobi	I-Algorithm
pseudoprime	I-Algorithm
is	O
also	O
a	O
Fermat	B-Algorithm
pseudoprime	I-Algorithm
and	O
an	O
Euler	B-Algorithm
pseudoprime	I-Algorithm
.	O
</s>
<s>
There	O
are	O
no	O
numbers	O
which	O
are	O
Euler	B-Algorithm
–	I-Algorithm
Jacobi	I-Algorithm
pseudoprimes	I-Algorithm
to	O
all	O
bases	O
as	O
Carmichael	O
numbers	O
are	O
.	O
</s>
<s>
Solovay	O
and	O
Strassen	O
showed	O
that	O
for	O
every	O
composite	O
n	O
,	O
for	O
at	O
least	O
n/2	O
bases	O
less	O
than	O
n	O
,	O
n	O
is	O
not	O
an	O
Euler	B-Algorithm
–	I-Algorithm
Jacobi	I-Algorithm
pseudoprime	I-Algorithm
.	O
</s>
<s>
The	O
smallest	O
Euler	B-Algorithm
–	I-Algorithm
Jacobi	I-Algorithm
pseudoprime	I-Algorithm
base	O
2	O
is	O
561	O
.	O
</s>
<s>
There	O
are	O
11347	O
Euler	B-Algorithm
–	I-Algorithm
Jacobi	I-Algorithm
pseudoprimes	I-Algorithm
base	O
2	O
that	O
are	O
less	O
than	O
25·109	O
(	O
see	O
)	O
(	O
page	O
1005	O
of	O
)	O
.	O
</s>
<s>
In	O
the	O
literature	O
(	O
for	O
example	O
,	O
)	O
,	O
an	O
Euler	B-Algorithm
–	I-Algorithm
Jacobi	I-Algorithm
pseudoprime	I-Algorithm
as	O
defined	O
above	O
is	O
often	O
called	O
simply	O
an	O
Euler	B-Algorithm
pseudoprime	I-Algorithm
.	O
</s>
