User:Eliora/Sandbox

On 29 January 2030, a series of major mathematical breakthroughs were announced within hours of one another, resolving several of the longest-standing open problems in mathematics. The events began at approximately 08:00–09:00 UTC, when a multinational research collaboration spanning twelve universities in seven countries announced the discovery and verification of the first known odd perfect number, designated [math]\displaystyle{ N }[/math], with an approximate value of [math]\displaystyle{ N=1.1274354961045…×10^{1,353,382} }[/math]. The discovery established for the first time that odd perfect numbers exist, resolving a problem whose origins date to antiquity.

At 12:24 UTC, an independent collaboration involving fourteen universities announced the discovery of the first 'elite number', the term used by the project for an even integer greater than 2 that cannot be expressed as the sum of two prime numbers and therefore constitutes a counterexample to the Goldbach conjecture. The number, designated [math]\displaystyle{ G }[/math], was approximately [math]\displaystyle{ G=2.368259249829…×10^{136,248,339,111} }[/math]. The discovery resulted from a reformulation of the collaboration's original research programme. Rather than attempting to establish the Goldbach conjecture universally, the project had increasingly treated its negation as a direct search problem, asking whether any elite numbers existed. The identification and subsequent verification of [math]\displaystyle{ G }[/math] disproved the conjecture.