Strategy for selecting the number of primes in the p-curvature filter

Determine an effective and principled strategy for choosing the number (and, if relevant, the specific choices) of primes to use in the p-curvature approach of Cluzeau–van Hoeij (2006) when pruning candidate ratios λ = c·A/B in the search for hypergeometric solutions of first-order linear difference systems τ(Y) = M Y over C(x), balancing pruning effectiveness against computational cost.

Background

The authors implement algorithms to compute hypergeometric solutions of linear difference systems and explore using the p-curvature approach of Cluzeau and van Hoeij (2006) to reduce the number of candidate ratios λ = c·A/B that must be tested.

In practice, they settled on using a single prime (p = 2) in one implementation and none in another, but they state that a general strategy for how many primes to use remains unresolved, indicating a need for a principled selection method that trades off computational overhead with the strength of candidate pruning.