Topic of Research Seminar: The Goldbach Conjecture: A journey Through Prime Numbers, Mathematical Insights, and Related conjectures

Abstract: The Goldbach Conjecture, a longstanding problem in number theory, proposes that every even integer greater than two can be expressed as the sum of two primes. This seminar explores its historical development, the ternary form, and key mathematical tools like the Circle Method, which has been instrumental in partial proofs, including Helfgott’s 2013 verification of the ternary case. We discuss a deterministic procedure to represent even numbers as a sum of odd numbers through equivalence classes and related conjectures, such as the Twin Primes Conjecture, Goldbach’s Number, and Untouchable Numbers. While computational advancements have verified the conjecture for large numbers, the binary case remains unsolved, making it one of the most intriguing open problems in mathematics.

Subject Field of Topic: Number Theory

Name of Speaker: Mr. Furqan Hussain

Professorial Rank of Speaker: PhD Scholar (Mathematics Department), School of Natural Sciences (SNS – NUST)

Email of Speaker: [email protected]

Affiliation of Speaker: School of Natural Sciences (SNS – NUST)

Date and Venue: (Wednesday) 19 February 2025, 03:30 pm, CR # 202, New Building, School of Natural Sciences (SNS), NUST Islamabad