When randomCurveP1P2 generates a random curve in ℙ3 using the SpaceCurves package, it is possible the resulting curve will intersect the base loci of the projections used to construct the curve in ℙ1×ℙ2. If the curve does intersect the base locusi it will generate a new random curve in ℙ3. The option Attempts limits the number of attempts to find a curve disjoint from the base loci before quitting. By default, Attempt is set to 1000.