Ramsey numbers
R(5,15) ≥ 279
R(5,15) is at least 279: Quantavane found a red-blue colouring of the lines between 278 points with no 5 points joined all in red and no 15 points joined all in blue. The best lower bound known before was 275.
Sent to Stanisław Radziszowski, who maintains the survey, on 25 October 2026.
The record
| Ours | R(5,15) ≥ 279 |
|---|---|
| Previous best | R(5,15) ≥ 275 |
| Previous source | revision 18 (24 April 2026) of Small Ramsey Numbers, Stanisław Radziszowski's dynamic survey |
| Found | 24 October 2026 |
| Status | Sent to Stanisław Radziszowski, who maintains the survey, on 25 October 2026. |
| Check | Three separate programs found no red group of 5 and no blue group of 15. |
So among any 278 points the colouring can avoid both, and at least 279 points are needed to force a red group of 5 or a blue group of 15. The exact value of R(5,15) is unknown.
Stanisław Radziszowski, who maintains the survey, replied that it will go into the next revision.
How it was found and checked
A circulant colouring: whether two points are joined in red depends only on how far apart they sit on a circle of 278 points. Three separate programs found no red group of 5 and no blue group of 15.
git clone https://github.com/arhancanli/quantavane-ramsey-records
cd quantavane-ramsey-records
cc -O2 -o check check.c
./check colourings/R5_15_K278.txtColour every line between n points red or blue. The Ramsey number R(s,t) is the smallest n for which every colouring has s points joined all in red or t points joined all in blue. Most values are unknown. A colouring of n points with neither shows R(s,t) is at least n + 1.
Questions
What is the best known lower bound for R(5,15)?
279, from our colouring of 278 points; before it, 275 (revision 18 (24 April 2026) of Small Ramsey Numbers, Stanisław Radziszowski's dynamic survey).
Is the exact value of R(5,15) known?
No. Only lower and upper bounds are known.
Where is the colouring?
In the public repository, https://github.com/arhancanli/quantavane-ramsey-records/blob/main/colourings/R5_15_K278.txt.