The Erdős-Straus conjecture New modular equations and checking up to $N=10^{17}$
Abstract
In 1999 Allan Swett checked (in 150 hours) the Erdős-Straus conjecture up to $N=10^{14}$ with a sieve based on a single modular equation. After having proved the existence of a "complete" set of seven modular equations (including three new ones), this paper offers an optimized sieve based on these equations. A program written in C++ (and given elsewhere) allows then to make a checking whose running time, on a typical computer, range from few minutes for $N=10^{14}$ to about 16 hours for $N=10^{17}$.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2014
- DOI:
- 10.48550/arXiv.1406.6307
- arXiv:
- arXiv:1406.6307
- Bibcode:
- 2014arXiv1406.6307S
- Keywords:
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- Mathematics - Number Theory;
- 11D68 (Primary) 11N35 (Secondary)
- E-Print:
- 13 pages, 1 version fran\c{c}aise, 1 C++ program