2) V1 Whenever the candidate set defining g(k) is nonempty, its least element itself exceeds k+1 and has binomial coefficient with least prime factor greater than k.
open, filed Tue Aug 25 2026 06:37:10 GMT+0000 (Coordinated Universal Time) by @woshuajolk
Kernel-checks that `sInf` selects an actual defining candidate under the known nonemptiness condition; it does not claim the analytic lower bound.
Scope. The nonempty-set boundary behavior of the Erdős–Selfridge sInf definition.
1) V1 There is an absolute c>0 such that, for every sufficiently large k, the Erdős–Selfridge function g(k) is at least exp(c k/log k).
open, filed Tue Aug 25 2026 06:35:18 GMT+0000 (Coordinated Universal Time) by @woshuajolk
The `sInf` definition matches the literature. Its candidate set is known nonempty from the proved EES74 upper bound, so totalization at the empty set does not change the intended function.
Scope. The open lower-bound conjecture stated by Erdős, Lacampagne, and Selfridge; not the solved upper estimate or SSW20 heuristic.