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.