<s>
In	O
number	O
theory	O
,	O
Proth	B-Algorithm
's	I-Algorithm
theorem	I-Algorithm
is	O
a	O
primality	B-Algorithm
test	I-Algorithm
for	O
Proth	O
numbers	O
.	O
</s>
<s>
Thus	O
,	O
in	O
contrast	O
to	O
many	O
Monte	O
Carlo	O
primality	B-Algorithm
tests	I-Algorithm
(	O
randomized	O
algorithms	O
that	O
can	O
return	O
a	O
false	O
positive	O
)	O
,	O
the	O
primality	B-Algorithm
testing	I-Algorithm
algorithm	O
based	O
on	O
Proth	B-Algorithm
's	I-Algorithm
theorem	I-Algorithm
is	O
a	O
Las	O
Vegas	O
algorithm	O
,	O
always	O
returning	O
the	O
correct	O
answer	O
but	O
with	O
a	O
running	O
time	O
that	O
varies	O
randomly	O
.	O
</s>
<s>
It	O
was	O
found	O
by	O
Peter	O
Szabolcs	O
in	O
the	O
PrimeGrid	B-Operating_System
volunteer	B-Operating_System
computing	I-Operating_System
project	O
which	O
announced	O
it	O
on	O
6	O
November	O
2016	O
.	O
</s>
<s>
The	O
second	O
largest	O
known	O
Proth	O
prime	O
is	O
,	O
found	O
by	O
PrimeGrid	B-Operating_System
.	O
</s>
<s>
The	O
proof	O
for	O
this	O
theorem	O
uses	O
the	O
Pocklington-Lehmer	B-Algorithm
primality	I-Algorithm
test	I-Algorithm
,	O
and	O
closely	O
resembles	O
the	O
proof	O
of	O
Pépin	B-Algorithm
's	I-Algorithm
test	I-Algorithm
.	O
</s>
