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AUTHOR(S): Amara Chandoul
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TITLE A Breakthrough in Andrica’s Conjecture: An Hybrid Diophantine-Irrationality Approach |
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ABSTRACT Andrica’s conjecture, formulated in 1985, states that the inequality √pn+1 −√pn < 1 holds for all consecutive primes pn and pn+1. Despite its simple statement, the conjecture has remained unresolved in number theory. This paper presents a direct proof by combining Diophantine analysis for the integer case with realvalued constraints for the non-integer case, deriving a contradiction from the converse assumption. The key to our approach lies in the irrationality of √pnpn+1 and a systematic unification of discrete and continuous analysis. We thereby establish the conjecture unconditionally for all consecutive primes. This result yields new insights into the distribution of consecutive primes. |
KEYWORDS Diophantine-analytic hybrid method, Prime Gap Characterization, Andrica’s Conjecture Resolution, Unconditional Proof Framework |
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Cite this paper Amara Chandoul. (2025) A Breakthrough in Andrica’s Conjecture: An Hybrid Diophantine-Irrationality Approach. International Journal of Mathematical and Computational Methods, 10, 206-211 |
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