Editing Pollard's rho algorithm (section)

== Example factorization ==
Let <math>n = 8051</math> and <math>g(x) = (x^2 + 1) \bmod 8051</math>.
[[File:Rho-example-animated.gif|thumb|348x348px|Pollard's rho algorithm example factorization for <math>n=253</math> and <math>g(x)=x^2 \bmod 253</math>, with starting value 2. The example is using [[Floyd's cycle-finding algorithm]].]]
{| class="wikitable" style="text-align:right"
! width=30 | {{mvar|i}} || width=60 | {{mvar|x}} || width=60 | {{mvar|y}} || {{math|gcd({{abs|''x'' − ''y''}}, 8051)}}
|-
| 1 || 5 || 26 || 1
|-
| 2 || 26 || 7474 || 1
|-
| 3 || 677 || 871 || 97
|-
| 4 || 7474 || 1481 || 1
|}

Now 97 is a non-trivial factor of 8051. Starting values other than {{math|1=''x'' = ''y'' = 2}} may give the cofactor (83) instead of 97. One extra iteration is shown above to make it clear that {{mvar|y}} moves twice as fast as {{mvar|x}}. Note that even after a repetition, the GCD can return to 1.