Is anyone interested in knowing the details of this algorithm?

I generate a twelve digit positive integer that is the product of two 6

digit primes.

>>> p12[0]

776206165373L

The parameters of FactorIterate are (z,trace,scale).

If trace is > 0, intermediate results are printed out.

Scale controls the size of the iteration step.

If scale is smaller, each iteration step skips over

a larger number of possible factors.

If scale is larger, each iteration step skips over a

smaller number of possible factors.

>>> FactorIterate(p12[0],0,3500)

Factor Iteration did not converge within 10000 steps.

If convergence does not occur reasonably soon,

then I should try again with a smaller scale parameter.

Or I can try again with the same scale parameter,

because the algorithm relies heavily on random integers,

and it behaves differently each time it is called.

>>> FactorIterate(p12[0],0,3500)

Factor Iteration did not converge within 10000 steps.

Trying again with a smaller scale.

>>> FactorIterate(p12[0],0,3000)

Factor Iteration did not converge within 10000 steps.

Trying again with a smaller scale.

>>> FactorIterate(p12[0],0,2000)

Factor Iteration did not converge within 10000 steps.

Trying again with a smaller scale.

>>> FactorIterate(p12[0],0,1000)

Factor Iteration did not converge within 10000 steps.

Trying again with a smaller scale.

>>> FactorIterate(p12[0],0,500)

Factor Iteration did not converge within 10000 steps.

Trying again with a smaller scale.

>>> FactorIterate(p12[0],0,200)

Found factor at iteration step 1291

by s2 has factor in common with z.

[976177L, 795149L]

>>> p12[1]

134117759761L

>>> FactorIterate(p12[1],0,200)

Factor iteration converged in 3690 steps,

but did not discover the factors of z.

[1, 134117759761L]

Trying again with a larger scale.

>>> FactorIterate(p12[1],0,300)

Factor iteration converged in 4896 steps,

but did not discover the factors of z.

[1, 134117759761L]

Trying again with a smaller scale.

>>> FactorIterate(p12[1],0,250)

Factor iteration converged in 5432 steps,

but did not discover the factors of z.

[1, 134117759761L]

Trying again with a larger scale.

>>> FactorIterate(p12[1],0,275)

Factor iteration converged in 5990 steps,

but did not discover the factors of z.

[1, 134117759761L]

Trying again with a larger scale.

>>> FactorIterate(p12[1],0,280)

Factor iteration converged in 4952 steps,

but did not discover the factors of z.

[1, 134117759761L]

Trying again with a larger scale.

>>> FactorIterate(p12[1],0,290)

Factor iteration converged in 7996 steps,

but did not discover the factors of z.

[1, 134117759761L]

Trying again with a larger scale

>>> FactorIterate(p12[1],0,295)

Found factor at iteration step 2481

by s4 has factor in common with z.

[213461L, 628301L]>>>