<s>
In	O
mathematics	O
,	O
the	O
Pocklington	O
–	O
Lehmer	O
primality	B-Algorithm
test	I-Algorithm
is	O
a	O
primality	B-Algorithm
test	I-Algorithm
devised	O
by	O
Henry	O
Cabourn	O
Pocklington	O
and	O
Derrick	O
Henry	O
Lehmer	O
.	O
</s>
<s>
It	O
produces	O
a	O
primality	B-Algorithm
certificate	I-Algorithm
to	O
be	O
found	O
with	O
less	O
effort	O
than	O
the	O
Lucas	B-Algorithm
primality	I-Algorithm
test	I-Algorithm
,	O
which	O
requires	O
the	O
full	O
factorization	O
of	O
.	O
</s>
<s>
Note	O
:	O
Equation	O
(	O
)	O
is	O
simply	O
a	O
Fermat	B-Algorithm
primality	I-Algorithm
test	I-Algorithm
.	O
</s>
<s>
Moreover	O
,	O
the	O
pair	O
(	O
,	O
)	O
constitute	O
a	O
primality	B-Algorithm
certificate	I-Algorithm
which	O
can	O
be	O
quickly	O
verified	O
to	O
satisfy	O
the	O
conditions	O
of	O
the	O
theorem	O
,	O
confirming	O
as	O
prime	O
.	O
</s>
<s>
The	O
Pocklington	O
–	O
Lehmer	O
primality	B-Algorithm
test	I-Algorithm
follows	O
directly	O
from	O
this	O
corollary	O
.	O
</s>
<s>
The	O
certificate	B-Algorithm
of	I-Algorithm
primality	I-Algorithm
for	O
would	O
consist	O
of	O
the	O
two	O
pairs	O
(	O
2	O
,	O
5	O
)	O
and	O
(	O
3	O
,	O
2	O
)	O
.	O
</s>
<s>
The	O
primality	B-Algorithm
certificate	I-Algorithm
is	O
the	O
list	O
of	O
pairs	O
,	O
which	O
can	O
be	O
quickly	O
checked	O
in	O
the	O
corollary	O
.	O
</s>
<s>
Theorem	O
5	O
of	O
the	O
Brillhart	O
,	O
Lehmer	O
,	O
and	O
Selfridge	O
paper	O
allows	O
a	O
primality	B-Algorithm
proof	I-Algorithm
when	O
the	O
factored	O
part	O
has	O
reached	O
only	O
.	O
</s>
