7825 Explained

Number:	7825
Cardinal:	seven thousand, eight hundred [and] twenty-five
Roman:	MMDCCCXXV, or DCCCXXV
Ordinal:	7825th
Ordinal Text:	seven thousand, eight hundred [and] twenty-fifth

7825 (seven thousand, eight hundred [and] twenty-five) is the natural number following 7824 and preceding 7826.

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

1. Lamb. Evelyn. 2016-06-02. Two-hundred-terabyte maths proof is largest ever. Nature. en. 534. 7605. 17–18. 10.1038/nature.2016.19990. 2016Natur.534...17L. 27251254. free.
2. Book: Heule. Marijn J. H.. Marijn Heule. Kullmann. Oliver. Marek. Victor W.. 2016-01-01. 1605.00723 . 9710. 228–245. 10.1007/978-3-319-40970-2_15. 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. 978-3-319-40969-6. 7912943.