<s>
It	O
was	O
factorised	O
between	O
September	O
1993	O
and	O
April	O
1994	O
,	O
using	O
MPQS	B-Algorithm
,	O
with	O
relations	O
contributed	O
by	O
about	O
600	O
people	O
through	O
the	O
internet	O
,	O
and	O
the	O
final	O
stages	O
of	O
the	O
calculation	O
performed	O
on	O
a	O
MasPar	B-Device
supercomputer	O
at	O
Bell	O
Labs	O
.	O
</s>
<s>
Between	O
January	O
and	O
August	O
1999	O
,	O
RSA-155	O
,	O
a	O
155-digit	O
challenge	O
number	O
prepared	O
by	O
the	O
RSA	O
company	O
,	O
was	O
factorised	O
using	O
GNFS	B-Algorithm
with	O
relations	O
again	O
contributed	O
by	O
a	O
large	O
group	O
,	O
and	O
the	O
final	O
stages	O
of	O
the	O
calculation	O
performed	O
in	O
just	O
over	O
nine	O
days	O
on	O
the	O
Cray	O
C916	B-Device
supercomputer	O
at	O
the	O
SARA	O
Amsterdam	O
Academic	O
Computer	O
Center	O
.	O
</s>
<s>
In	O
April	O
2003	O
,	O
the	O
same	O
team	O
factored	O
the	O
160-digit	O
RSA-160	O
using	O
about	O
a	O
hundred	O
CPUs	O
at	O
BSI	O
,	O
with	O
the	O
final	O
stages	O
of	O
the	O
calculation	O
done	O
using	O
25	O
processors	O
of	O
an	O
SGI	O
Origin	B-Application
supercomputer	O
.	O
</s>
<s>
between	O
December	O
2003	O
and	O
May	O
2005	O
,	O
using	O
a	O
cluster	O
of	O
80	O
Opteron	B-General_Concept
processors	O
at	O
BSI	O
in	O
Germany	O
;	O
the	O
announcement	O
was	O
made	O
on	O
9	O
May	O
2005	O
.	O
</s>
<s>
years	O
of	O
computing	O
on	O
a	O
single	O
core	O
2.2GHz	O
AMD	B-General_Concept
Opteron	I-General_Concept
.	O
</s>
<s>
63531	O
,	O
of	O
911	O
bits	O
(	O
275	O
digits	O
)	O
,	O
was	O
factored	O
by	O
Aoki	O
,	O
Kida	O
,	O
Shimoyama	O
and	O
Ueda	O
between	O
September	O
2005	O
and	O
January	O
2006	O
using	O
SNFS	B-Algorithm
.	O
</s>
<s>
210611	O
,	O
of	O
1061	O
bits	O
(	O
320	O
digits	O
)	O
was	O
factored	O
between	O
early	O
2011	O
and	O
4	O
August	O
2012	O
by	O
a	O
group	O
headed	O
by	O
Greg	O
Childers	O
at	O
CSU	O
Fullerton	O
,	O
using	O
the	O
nfs	O
@home	O
BOINC	B-Operating_System
project	O
for	O
about	O
300	O
CPU-years	O
of	O
sieving	O
;	O
the	O
linear	O
algebra	O
was	O
run	O
at	O
the	O
Trestles	O
cluster	O
at	O
SDSC	O
and	O
the	O
Lonestar	O
cluster	O
at	O
TACC	O
and	O
needed	O
additional	O
35	O
CPU-years	O
.	O
</s>
<s>
The	O
total	O
effort	O
for	O
the	O
project	O
is	O
of	O
the	O
order	O
of	O
7500	O
CPU-years	O
on	O
2.2GHz	O
Opterons	B-General_Concept
,	O
with	O
roughly	O
5700	O
years	O
spent	O
sieving	O
and	O
1800	O
years	O
on	O
linear	O
algebra	O
.	O
</s>
<s>
In	O
2009	O
,	O
Benjamin	O
Moody	O
factored	O
a	O
512-bit	O
(	O
155-digit	O
)	O
RSA	O
key	O
used	O
to	O
sign	O
the	O
TI-83	B-Device
graphing	O
calculator	O
using	O
software	O
found	O
on	O
the	O
internet	O
;	O
this	O
eventually	O
led	O
to	O
the	O
Texas	B-Architecture
Instruments	I-Architecture
signing	I-Architecture
key	I-Architecture
controversy	I-Architecture
.	O
</s>
<s>
The	O
largest	O
number	O
reliably	O
factored	O
by	O
Shor	B-Algorithm
's	I-Algorithm
algorithm	I-Algorithm
is	O
21	O
which	O
was	O
factored	O
in	O
2012	O
.	O
</s>
<s>
In	O
April	O
2016	O
the	O
18-bit	O
number	O
200,099	O
was	O
factored	O
using	O
quantum	B-Algorithm
annealing	I-Algorithm
on	O
a	O
D-Wave	O
2X	O
quantum	O
processor	O
.	O
</s>
<s>
Furthermore	O
,	O
the	O
three	O
numbers	O
factored	O
in	O
this	O
paper	O
(	O
200	O
,	O
099	O
,	O
291	O
,	O
311	O
,	O
and	O
1,099,551,473,989	O
)	O
can	O
easily	O
be	O
factored	O
using	O
Fermat	B-Algorithm
's	I-Algorithm
factorization	I-Algorithm
method	I-Algorithm
,	O
requiring	O
only	O
3	O
,	O
1	O
,	O
and	O
1	O
iterations	O
of	O
the	O
loop	O
respectively	O
.	O
</s>
