What question did this study set out to answer?

This research aims to extend Gilbreath's conjecture by introducing a new operator on prime numbers.

June 11, 2026Open Access

A Relation between Prime Numbers : Extension of Gilbreath's Conjecture

Key Points

This research aims to extend Gilbreath's conjecture by introducing a new operator on prime numbers.
Introduced a shifted difference operator on sequences of prime numbers based on a parameter m ≥ 1.
Established basic structural properties of the operator and generated iterated difference sequences.
Discussed computational aspects and directions for finite primes and various shifts.
Conjectured that the first element of the generated sequences will eventually reach the value 1.

Abstract

We introduce a shifted difference operator on the sequence of prime numbers, extending the classical framework associated with Gilbreath’s conjecture. This operator depends on a fixed integer parameter m ≥ 1 and generates iterated difference sequences. We conjecture that the first element of these sequences eventually attains the value 1. Basic structural properties are established, and computational directions are discussed. But a thing to note is that this is a completely experimental paper. We have computed for finite primes and different shift.

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