What question did this study set out to answer?

The aim is to reduce Gilbreath's Conjecture to a specific local condition for simplified analysis.

March 23, 20260 citationsOpen Access

Reducing Gilbreath's Conjecture to a Local Condition: How much of the triangle do we really need to watch?

Key Points

The aim is to reduce Gilbreath's Conjecture to a specific local condition for simplified analysis.
Established a local bound condition |Gᵣ[2] − Gᵣ[1]| ≤ 2 for r ≥ 1.
Outlined four supporting lemmas to assist in the reduction.
Described a minimal preimage structure related to a configuration that violates the conjecture.
Conducted computational verification using 100,000 rows.
Confirmed the local bound holds under the specified condition.
Isolated the key features of the conjecture that require further exploration.

Abstract

We present a reduction of Gilbreath’s Conjecture to an explicit local bound. Specifically, we show that the conjecture follows from the condition |Gᵣ2 − Gᵣ1| ≤ 2 for all r ≥ 1. We state four supporting lemmas used by the reduction, describe a minimal preimage structure associated with a model minimal violating configuration, and report computational verification of the local bound through 100,000 rows. The full conjecture remains open, but the remaining target is now clearly isolated. For correspondence and updates: BMorgan007(at)protonmail.com

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