Fun With Very Large Numbers
Robert Baillie

TL;DR
This paper presents formulas involving the sinc function that hold for extremely large values of N, up to about 10^102832732165, and discusses their failure beyond these bounds, including an example surpassing Skewes numbers.
Contribution
It introduces specific sinc-based formulas valid over enormous ranges of N and analyzes their limitations at astronomically large N values.
Findings
Formulas hold for N up to approximately 10^102832732165.
Another example remains valid until N exceeds a double exponential of e.
The second example surpasses the size of Skewes numbers.
Abstract
We give an example of a formula involving the sinc function that holds for every N = 0, 1, 2, ..., up to about 10^102832732165, then fails for all larger N. We give another example that begins to fail after about N ~ exp(exp(exp(exp(exp(exp(e)))))). This number is larger than the Skewes numbers.
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Taxonomy
TopicsAnalytic Number Theory Research · Advanced Mathematical Identities · Mathematics and Applications
