
TL;DR
This paper demonstrates that the Ramanujan tau function does not take prime values for any prime less than or equal to 8.0×10^{25}, revealing a significant gap in its prime outputs.
Contribution
It establishes a new large bound showing the tau function's prime values do not occur below this threshold, advancing understanding of its prime value distribution.
Findings
Tau function misses all primes ≤ 8.0×10^{25}
No prime values of tau function below this bound
Provides a new large-scale computational result
Abstract
This note shows that the prime values of the Ramanujan tau function misses every prime .
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Taxonomy
TopicsAnalytic Number Theory Research · Advanced Mathematical Identities · Advanced Algebra and Geometry
