7825
7825 (seven thousand, eight hundred [and] twenty-five) is the natural number following 7824 and preceding 7826.
| ||||
|---|---|---|---|---|
| Cardinal | seven thousand, eight hundred [and] twenty-five | |||
| Ordinal | 7825th | |||
| Factorization | 52 × 313 | |||
| Greek numeral | ,ΖΩΚΕ´ | |||
| Roman numeral | VMMDCCCXXV, or VIIDCCCXXV | |||
| Binary | 11110100100012 | |||
| Ternary | 1012012113 | |||
| Senary | 1001216 | |||
| Octal | 172218 | |||
| Duodecimal | 464112 | |||
| Hexadecimal | 1E9116 | |||
In mathematics
- 7825 is the smallest number n when it is impossible to assign two colors to natural numbers 1 through n such that every Pythagorean triple is multicolored, i.e. where the Boolean Pythagorean triples problem becomes false. The 200-terabyte proof to verify this is the largest ever made.[1][2]
- 7825 is a magic constant of n × n normal magic square and n-Queens Problem for n = 25.
References
- Lamb, Evelyn (2016-06-02). "Two-hundred-terabyte maths proof is largest ever". Nature. 534 (7605): 17–18. Bibcode:2016Natur.534...17L. doi:10.1038/nature.2016.19990. PMID 27251254.
- Heule, Marijn J. H.; Kullmann, Oliver; Marek, Victor W. (2016-01-01). "Solving and Verifying the Boolean Pythagorean Triples Problem via Cube-and-Conquer". Theory and Applications of Satisfiability Testing – SAT 2016. Lecture Notes in Computer Science. Vol. 9710. pp. 228–245. arXiv:1605.00723. doi:10.1007/978-3-319-40970-2_15. ISBN 978-3-319-40969-6. S2CID 7912943.
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