While we’re listing numbers and their factors, can you post a list of only those board sizes containing a two-element prime factorization? I find these to be the most mathematically appealing boards to play on.
It’s interesting to note that 17x17 was popular in ancient times (The oldest surviving, complete go board was made this way and dated to ca. 206-25 BCE). I’m not sure when 19x19 became ubiquitous, but certainly by the Huangyou period of the Song dynasty (ca. 1049-1054 CE) 19x19 seemed to be the norm, as observed in Qijing Shisanpian (The Classic of Weiqi in Thirteen Chapters).
I think the interesting thing about the very small board sizes is that there is a small piece to learn from each:
0x0 - huh? let’s pass.
1x1 - you can not put a stone on, it’s self suizide. the only move both players can do is to pass.
2x1 - the player who puts a stone on the board first loses, because the other could capture in ko. recommended play: pass.
2x2 - the player who plays diagonal first wins.
Years ago in my go club in Cambridge, Massachusetts, 6x6 was always used to teach beginners. About a dozen people would sit around a large table made of a square of smaller tables, with a cardboard go board each, while the teacher would walk around the inside of the large table quickly playing moves. 6x6 games went by fast enough to avoid people getting bogged down over issues of ko, seki, or scoring, yet 6x6 games were complex enough to give newcomers a feel for the basics, such as territory, thickness, connection, and local tactics. If you never use 6x6 when playing those who are learning the rules, you might give it a try. There are some oddities in playing an even size, but beginners are not likely to notice them.
Here’s an abbreviated version with only the “proportionate” boards, which is to say those in which one side is no less than half the length of the other.
I also removed the redundant XxY, YxX mirroring.
moku
dim.
moku
dim.
moku
dim.
moku
dim.
moku
dim.
2
1x2, 2x1
54
6x9
120
8x15, 10x12
190
10x19
280
14x19
4
2x2
56
7x8
121
11x11
192
12x16
285
15x19
6
2x3
60
6x10
126
9x14
195
13x15
286
13x22
8
2x4
63
7x9
128
8x16
196
14x14
288
12x24, 16x18
9
3x3
64
8x8
130
10x13
198
11x18
289
17x17
12
3x4
70
7x10
132
11x12
200
10x20
294
14x21
15
3x5
72
6x12, 8x9
135
9x15
204
12x17
299
13x23
16
4x4
77
7x11
140
10x14
208
13x16
300
15x20
18
3x6
80
8x10
143
11x13
209
11x19
304
16x19
20
4x5
81
9x9
144
9x16, 12x12
210
14x15
306
17x18
24
4x6
84
7x12
150
10x15
221
13x17
308
14x22
25
5x5
88
8x11
154
11x14
231
11x21
312
13x24
28
4x7
90
9x10
154
12x13
247
13x19
315
15x21
30
5x6
91
7x12
160
10x16
252
12x21, 14x18
320
16x20
32
4x8
96
9x12
162
9x18
255
15x17
322
14x23
35
5x7
98
7x14
165
11x15
256
16x16
323
17x19
36
6x6
100
10x10
168
12x14
260
13x20
324
18x18
40
5x8
104
8x13
169
13x13
264
12x22
325
13x25
45
5x9
108
9x12
170
10x17
266
14x19
330
15x22
48
6x8
110
10x11
176
11x16
270
15x18
336
14x24, 16x21
49
7x7
112
8x14
180
10x18, 12x15
272
16x17
340
17x20
50
5x10
117
9x13
187
11x17
276
12x23
342
18x19
And that’s all that fits in this table.
In retrospect, I should have excluded side lengths above nineteen moku.