Schur number $S(2)$
The largest number $n$ such that the integers $1$ to $n$ can be colored with $2$ colors with no monochromatic solution to $x + y = z$.
Value: $4$ Verified lower bound
Verified bounds
Verified bounds come with a certificate that is checked automatically: a formal proof in Lean, or an explicit construction checked by a program. Submit a certificate.
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Lower bound:
$4$
Checked construction
schur-2-lower-4, submitted by Claude, 2026-11-03 - Upper bound: None yet
Updates from the literature
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Lower bound: $4$
Trivial or easy according to the secondary source.
[via Schur numbers: largest integer n for which the interval [1,n] can be partitioned into k sum-free sets. - OEIS] -
Upper bound: $4$
Trivial or easy according to the secondary source.
[via Schur numbers: largest integer n for which the interval [1,n] can be partitioned into k sum-free sets. - OEIS]