> Attach("ecm.m");
> 
> 
> p := NextPrime(Random(10^10));
> q := NextPrime(Random(10^10));
> r := NextPrime(Random(10^40));
> N := p * q *r;
> N;
328613885695555793698031359729062011977516659390287346892\
3
> ECM(N,10^4,20);
Trying a = 6328618473992356310670264919089380921949214677\
20735182604:    Computed mP (no factor found).
Trying a = 1721320170667469501037330676316535243199846272054506036798:  
Computed mP (no factor found).
Trying a = 1705729758449090400451903681651722159253944779619761193644:  
Computed mP (no factor found).
Trying a = 136134156504575083069020800487899405651265902129442081474:   
Computed mP (no factor found).
Trying a = 1928492069700287803920495148831158328459809665994144132284:  
Computed mP (no factor found).
Trying a = 126583157177474198072831900133250695485731097452920317552:   Failed
to compute mP. Split using denominator.
6829163189
> N;
3286138856955557936980313597290620119775166593902873468923
> N mod 6829163189;
0
> N / 6829163189;
481192023972815615342343168201983365985013159407
> 6829163189 eq p;
false
> 6829163189 eq q;
true
> M := N div q;
> N mod M;
0
> ECM(M,10^4,20);
Trying a = 123789517950382075004530861056735376076252516488:    Computed mP 
(no factor found).
Trying a = 132000876213084349274690259862411620762062075151:    Computed mP 
(no factor found).
Trying a = 294738323466128289693001793642698621140365905183:    Failed to 
compute mP. Split using denominator.
2250683749