历年googology记号强度榜

本条目列举自1980年至2025年，每一年中，googology社区记号的强度榜。值得注意的是，这里的排行按照当时社区的估计来排。

1980年

	名称	作者
1	Graham's Function G(n)	Ronald Graham
2	Graham's Function g(n)	Ronald Graham
3	Hyperlicious Function	-
4	Ackermann's Function	Wilhelm Ackermann
5	Kunth's Up-Arraw	Donald Ervin Kunth
6	Hyper Operation	-
7	Down-Arraw	Donald Ervin Kunth
8	Sudan function	Sudan
9	Godel numbers	Godel
10	Grzegorczyk's hierarchy	Grzegorczyk
11	G_n+2(n) function	Milton Green
12	B_n(n) function	Milton Green
13	M_n+2(n) function	Milton Green
14	Peter's function	Rosza Peter
15	Robinsion's function	Raphael M. Robinson
16	Buck's function	Buck
17	Robert's function	Robert Ritchie
18	Meyer-Ritchie function	Meyer & Robert Ritchie
19	Mixed Factorial	-
20	Moser's Polygon Notation	Leo Moser
21	Pentiration	-
22	Old Polygon Notation	Leo Moser
23	Left tower	-
24	Tetration	Hans Maurer
25	Iterative Factorial	-
26	Power Towers	-
27	'yillion' System	Donald Ervin Kunth
28	'illion' System	-
29	HuaYan Sutra	-
30	Hyper Factorial	-

1981年

	名称	作者
1	Graham's Function G(n)	Ronald Graham
2	Graham's Function g(n)	Ronald Graham
3	Hyperlicious Function	-
4	Ackermann's Function	Wilhelm Ackermann
5	Kunth's Up-Arraw	Donald Ervin Kunth
6	Hyper Operation	-
7	Down-Arraw	Donald Ervin Kunth
8	Sudan function	Sudan
9	Godel numbers	Godel
10	Grzegorczyk's hierarchy	Grzegorczyk
11	G_n+2(n) function	Milton Green
12	B_n(n) function	Milton Green
13	M_n+2(n) function	Milton Green
14	Peter's function	Rosza Peter
15	Robinsion's function	Raphael M. Robinson
16	Buck's function	Buck
17	Robert's function	Robert Ritchie
18	Meyer-Ritchie function	Meyer & Robert Ritchie
19	Mixed Factorial	-
20	Moser's Polygon Notation	Leo Moser
21	Pentiration	-
22	Old Polygon Notation	Leo Moser
23	Left tower	-
24	Tetration	Hans Maurer
25	Iterative Factorial	-
26	Power Towers	-
27	'yillion' System	Donald Ervin Kunth
28	'illion' System	-
29	HuaYan Sutra	-
30	Hyper Factorial	-

1982年

	名称	作者
1	Goodstein Sequence	Goodstein
2	Graham's Function G(n)	Ronald Graham
3	Graham's Function g(n)	Ronald Graham
4	Hyperlicious Function	-
5	Ackermann's Function	Wilhelm Ackermann
6	Kunth's Up-Arraw	Donald Ervin Kunth
7	Hyper Operation	-
8	Down-Arraw	Donald Ervin Kunth
9	Sudan function	Sudan
10	Godel numbers	Godel
11	Grzegorczyk's hierarchy	Grzegorczyk
12	G_n+2(n) function	Milton Green
13	B_n(n) function	Milton Green
14	M_n+2(n) function	Milton Green
15	Peter's function	Rosza Peter
16	Robinsion's function	Raphael M. Robinson
17	Buck's function	Buck
18	Robert's function	Robert Ritchie
19	Meyer-Ritchie function	Meyer & Robert Ritchie
20	Mixed Factorial	-
21	Moser's Polygon Notation	Leo Moser
22	Pentiration	-
23	Old Polygon Notation	Leo Moser
24	Left tower	-
25	Tetration	Hans Maurer
26	Iterative Factorial	-
27	Power Towers	-
28	'yillion' System	Donald Ervin Kunth
29	'illion' System	-
30	HuaYan Sutra	-

1983年

	名称	作者
1	Goodstein Sequence	Goodstein
2	Graham's Function G(n)	Ronald Graham
3	Graham's Function g(n)	Ronald Graham
4	Hyperlicious Function	-
5	Ackermann's Function	Wilhelm Ackermann
6	Kunth's Up-Arraw	Donald Ervin Kunth
7	Hyper Operation	-
8	Down-Arraw	Donald Ervin Kunth
9	Sudan function	Sudan
10	Godel numbers	Godel
11	Grzegorczyk's hierarchy	Grzegorczyk
12	G_n+2(n) function	Milton Green
13	B_n(n) function	Milton Green
14	M_n+2(n) function	Milton Green
15	Peter's function	Rosza Peter
16	Robinsion's function	Raphael M. Robinson
17	Buck's function	Buck
18	Robert's function	Robert Ritchie
19	Meyer-Ritchie function	Meyer & Robert Ritchie
20	Mixed Factorial	-
21	Moser's Polygon Notation	Leo Moser
22	Pentiration	-
23	Old Polygon Notation	Leo Moser
24	Left tower	-
25	Tetration	Hans Maurer
26	Iterative Factorial	-
27	Power Towers	-
28	'yillion' System	Donald Ervin Kunth
29	'illion' System	-
30	HuaYan Sutra	-

1984年

	名称	作者
1	Goodstein Sequence	Goodstein
2	Kirby-Paris Hydra	Laurie Kirby & Jeff Paris
3	Graham's Function G(n)	Ronald Graham
4	Graham's Function g(n)	Ronald Graham
5	Hyperlicious Function	-
6	Ackermann's Function	Wilhelm Ackermann
7	Kunth's Up-Arraw	Donald Ervin Kunth
8	Hyper Operation	-
9	Down-Arraw	Donald Ervin Kunth
10	Sudan function	Sudan
11	Godel numbers	Godel
12	Grzegorczyk's hierarchy	Grzegorczyk
13	G_n+2(n) function	Milton Green
14	B_n(n) function	Milton Green
15	M_n+2(n) function	Milton Green
16	Peter's function	Rosza Peter
17	Robinsion's function	Raphael M. Robinson
18	Buck's function	Buck
19	Robert's function	Robert Ritchie
20	Meyer-Ritchie function	Meyer & Robert Ritchie
21	Mixed Factorial	-
22	Moser's Polygon Notation	Leo Moser
23	Pentiration	-
24	Old Polygon Notation	Leo Moser
25	Left tower	-
26	Tetration	Hans Maurer
27	Iterative Factorial	-
28	Power Towers	-
29	'yillion' System	Donald Ervin Kunth
30	'illion' System	-

1985年

	名称	作者
1	Goodstein Sequence	Goodstein
2	Kirby-Paris Hydra	Laurie Kirby & Jeff Paris
3	Graham's Function G(n)	Ronald Graham
4	Graham's Function g(n)	Ronald Graham
5	Hyperlicious Function	-
6	Ackermann's Function	Wilhelm Ackermann
7	Kunth's Up-Arraw	Donald Ervin Kunth
8	Hyper Operation	-
9	Down-Arraw	Donald Ervin Kunth
10	Sudan function	Sudan
11	Godel numbers	Godel
12	Grzegorczyk's hierarchy	Grzegorczyk
13	G_n+2(n) function	Milton Green
14	B_n(n) function	Milton Green
15	M_n+2(n) function	Milton Green
16	Peter's function	Rosza Peter
17	Robinsion's function	Raphael M. Robinson
18	Buck's function	Buck
19	Robert's function	Robert Ritchie
20	Meyer-Ritchie function	Meyer & Robert Ritchie
21	Mixed Factorial	-
22	Moser's Polygon Notation	Leo Moser
23	Pentiration	-
24	Old Polygon Notation	Leo Moser
25	Left tower	-
26	Tetration	Hans Maurer
27	Iterative Factorial	-
28	Power Towers	-
29	'yillion' System	Donald Ervin Kunth
30	'illion' System	-

1986年

	名称	作者
1	Goodstein Sequence	Goodstein
2	Kirby-Paris Hydra	Laurie Kirby & Jeff Paris
3	Graham's Function G(n)	Ronald Graham
4	Graham's Function g(n)	Ronald Graham
5	Hyperlicious Function	-
6	Ackermann's Function	Wilhelm Ackermann
7	Kunth's Up-Arraw	Donald Ervin Kunth
8	Hyper Operation	-
9	Down-Arraw	Donald Ervin Kunth
10	Sudan function	Sudan
11	Godel numbers	Godel
12	Grzegorczyk's hierarchy	Grzegorczyk
13	G_n+2(n) function	Milton Green
14	B_n(n) function	Milton Green
15	M_n+2(n) function	Milton Green
16	Peter's function	Rosza Peter
17	Robinsion's function	Raphael M. Robinson
18	Buck's function	Buck
19	Robert's function	Robert Ritchie
20	Meyer-Ritchie function	Meyer & Robert Ritchie
21	Mixed Factorial	-
22	Moser's Polygon Notation	Leo Moser
23	Pentiration	-
24	Old Polygon Notation	Leo Moser
25	Left tower	-
26	Tetration	Hans Maurer
27	Iterative Factorial	-
28	Power Towers	-
29	'yillion' System	Donald Ervin Kunth
30	'illion' System	-

1987年

	名称	作者
1	Goodstein Sequence	Goodstein
2	Kirby-Paris Hydra	Laurie Kirby & Jeff Paris
3	Graham's Function G(n)	Ronald Graham
4	Graham's Function g(n)	Ronald Graham
5	Hyperlicious Function	-
6	Ackermann's Function	Wilhelm Ackermann
7	Kunth's Up-Arraw	Donald Ervin Kunth
8	Hyper Operation	-
9	Down-Arraw	Donald Ervin Kunth
10	Sudan function	Sudan
11	Godel numbers	Godel
12	Grzegorczyk's hierarchy	Grzegorczyk
13	G_n+2(n) function	Milton Green
14	B_n(n) function	Milton Green
15	M_n+2(n) function	Milton Green
16	Peter's function	Rosza Peter
17	Robinsion's function	Raphael M. Robinson
18	Buck's function	Buck
19	Robert's function	Robert Ritchie
20	Meyer-Ritchie function	Meyer & Robert Ritchie
21	Edelsbrunner-Herbert's function	Edelsbrunner & Herbert
22	Mixed Factorial	-
23	Moser's Polygon Notation	Leo Moser
24	Pentiration	-
25	Old Polygon Notation	Leo Moser
26	Left tower	-
27	Tetration	Hans Maurer
28	Iterative Factorial	-
29	Power Towers	-
30	'yillion' System	Donald Ervin Kunth

1988年

	名称	作者
1	Goodstein Sequence	Goodstein
2	Kirby-Paris Hydra	Laurie Kirby & Jeff Paris
3	Graham's Function G(n)	Ronald Graham
4	Graham's Function g(n)	Ronald Graham
5	Hyperlicious Function	-
6	Ackermann's Function	Wilhelm Ackermann
7	Kunth's Up-Arraw	Donald Ervin Kunth
8	Hyper Operation	-
9	Down-Arraw	Donald Ervin Kunth
10	Sudan function	Sudan
11	Godel numbers	Godel
12	Grzegorczyk's hierarchy	Grzegorczyk
13	G_n+2(n) function	Milton Green
14	B_n(n) function	Milton Green
15	M_n+2(n) function	Milton Green
16	Peter's function	Rosza Peter
17	Robinsion's function	Raphael M. Robinson
18	Buck's function	Buck
19	Robert's function	Robert Ritchie
20	Meyer-Ritchie function	Meyer & Robert Ritchie
21	Edelsbrunner-Herbert's function	Edelsbrunner & Herbert
22	Alteration of M/R's Ackf	-
23	Mixed Factorial	-
24	Moser's Polygon Notation	Leo Moser
25	Pentiration	-
26	Old Polygon Notation	Leo Moser
27	Left tower	-
28	Tetration	Hans Maurer
29	Iterative Factorial	-
30	Power Towers	-

1989年

	名称	作者
1	Goodstein Sequence	Goodstein
2	Kirby-Paris Hydra	Laurie Kirby & Jeff Paris
3	Graham's Function G(n)	Ronald Graham
4	Graham's Function g(n)	Ronald Graham
5	Hyperlicious Function	-
6	Ackermann's Function	Wilhelm Ackermann
7	Kunth's Up-Arraw	Donald Ervin Kunth
8	Hyper Operation	-
9	Down-Arraw	Donald Ervin Kunth
10	Sudan function	Sudan
11	Godel numbers	Godel
12	Grzegorczyk's hierarchy	Grzegorczyk
13	G_n+2(n) function	Milton Green
14	B_n(n) function	Milton Green
15	M_n+2(n) function	Milton Green
16	Peter's function	Rosza Peter
17	Robinsion's function	Raphael M. Robinson
18	Buck's function	Buck
19	Robert's function	Robert Ritchie
20	Meyer-Ritchie function	Meyer & Robert Ritchie
21	Edelsbrunner-Herbert's function	Edelsbrunner & Herbert
22	Alteration of M/R's Ackf	-
23	Mixed Factorial	-
24	Moser's Polygon Notation	Leo Moser
25	Pentiration	-
26	Old Polygon Notation	Leo Moser
27	Left tower	-
28	Tetration	Hans Maurer
29	Iterative Factorial	-
30	Power Towers	-

1990年

	名称	作者
1	Goodstein Sequence	Goodstein
2	Kirby-Paris Hydra	Laurie Kirby & Jeff Paris
3	Graham's Function G(n)	Ronald Graham
4	Graham's Function g(n)	Ronald Graham
5	Hyperlicious Function	-
6	Ackermann's Function	Wilhelm Ackermann
7	Kunth's Up-Arraw	Donald Ervin Kunth
8	Hyper Operation	-
9	Down-Arraw	Donald Ervin Kunth
10	Sudan function	Sudan
11	Godel numbers	Godel
12	Grzegorczyk's hierarchy	Grzegorczyk
13	G_n+2(n) function	Milton Green
14	B_n(n) function	Milton Green
15	M_n+2(n) function	Milton Green
16	Peter's function	Rosza Peter
17	Robinsion's function	Raphael M. Robinson
18	Buck's function	Buck
19	Robert's function	Robert Ritchie
20	Meyer-Ritchie function	Meyer & Robert Ritchie
21	Edelsbrunner-Herbert's function	Edelsbrunner & Herbert
22	Alteration of M/R's Ackf	-
23	Mixed Factorial	-
24	Moser's Polygon Notation	Leo Moser
25	Pentiration	-
26	Old Polygon Notation	Leo Moser
27	Left tower	-
28	Tetration	Hans Maurer
29	Iterative Factorial	-
30	Power Towers	-

1991年

	名称	作者
1	Goodstein Sequence	Goodstein
2	Kirby-Paris Hydra	Laurie Kirby & Jeff Paris
3	Graham's Function G(n)	Ronald Graham
4	Graham's Function g(n)	Ronald Graham
5	Hyperlicious Function	-
6	Ackermann's Function	Wilhelm Ackermann
7	Kunth's Up-Arraw	Donald Ervin Kunth
8	Hyper Operation	-
9	Down-Arraw	Donald Ervin Kunth
10	Sudan function	Sudan
11	Godel numbers	Godel
12	Grzegorczyk's hierarchy	Grzegorczyk
13	G_n+2(n) function	Milton Green
14	B_n(n) function	Milton Green
15	M_n+2(n) function	Milton Green
16	Peter's function	Rosza Peter
17	Robinsion's function	Raphael M. Robinson
18	Buck's function	Buck
19	Robert's function	Robert Ritchie
20	Meyer-Ritchie function	Meyer & Robert Ritchie
21	Edelsbrunner-Herbert's function	Edelsbrunner & Herbert
22	Alteration of M/R's Ackf	-
23	Mixed Factorial	-
24	Moser's Polygon Notation	Leo Moser
25	Pentiration	-
26	Old Polygon Notation	Leo Moser
27	Left tower	-
28	Tetration	Hans Maurer
29	Iterative Factorial	-
30	Power Towers	-

1992年

	名称	作者
1	Goodstein Sequence	Goodstein
2	Kirby-Paris Hydra	Laurie Kirby & Jeff Paris
3	Graham's Function G(n)	Ronald Graham
4	Graham's Function g(n)	Ronald Graham
5	Hyperlicious Function	-
6	Ackermann's Function	Wilhelm Ackermann
7	Kunth's Up-Arraw	Donald Ervin Kunth
8	Hyper Operation	-
9	Down-Arraw	Donald Ervin Kunth
10	Sudan function	Sudan
11	Godel numbers	Godel
12	Grzegorczyk's hierarchy	Grzegorczyk
13	G_n+2(n) function	Milton Green
14	B_n(n) function	Milton Green
15	M_n+2(n) function	Milton Green
16	Peter's function	Rosza Peter
17	Robinsion's function	Raphael M. Robinson
18	Buck's function	Buck
19	Robert's function	Robert Ritchie
20	Meyer-Ritchie function	Meyer & Robert Ritchie
21	Edelsbrunner-Herbert's function	Edelsbrunner & Herbert
22	Alteration of M/R's Ackf	-
23	Mixed Factorial	-
24	Moser's Polygon Notation	Leo Moser
25	Pentiration	-
26	Old Polygon Notation	Leo Moser
27	Left tower	-
28	Tetration	Hans Maurer
29	Iterative Factorial	-
30	Power Towers	-

1993年

	名称	作者
1	Goodstein Sequence	Goodstein
2	Kirby-Paris Hydra	Laurie Kirby & Jeff Paris
3	Graham's Function G(n)	Ronald Graham
4	Graham's Function g(n)	Ronald Graham
5	Hyperlicious Function	-
6	Ackermann's Function	Wilhelm Ackermann
7	Kunth's Up-Arraw	Donald Ervin Kunth
8	Hyper Operation	-
9	Down-Arraw	Donald Ervin Kunth
10	Sudan function	Sudan
11	Godel numbers	Godel
12	Grzegorczyk's hierarchy	Grzegorczyk
13	G_n+2(n) function	Milton Green
14	B_n(n) function	Milton Green
15	M_n+2(n) function	Milton Green
16	Peter's function	Rosza Peter
17	Robinsion's function	Raphael M. Robinson
18	Buck's function	Buck
19	Robert's function	Robert Ritchie
20	Meyer-Ritchie function	Meyer & Robert Ritchie
21	Edelsbrunner-Herbert's function	Edelsbrunner & Herbert
22	Alteration of M/R's Ackf	-
23	Mixed Factorial	-
24	Moser's Polygon Notation	Leo Moser
25	Pentiration	-
26	Old Polygon Notation	Leo Moser
27	Left tower	-
28	Tetration	Hans Maurer
29	Iterative Factorial	-
30	Power Towers	-

1994年

	名称	作者
1	Goodstein Sequence	Goodstein
2	Kirby-Paris Hydra	Laurie Kirby & Jeff Paris
3	Graham's Function G(n)	Ronald Graham
4	Graham's Function g(n)	Ronald Graham
5	Hyperlicious Function	-
6	Ackermann's Function	Wilhelm Ackermann
7	Kunth's Up-Arraw	Donald Ervin Kunth
8	Hyper Operation	-
9	Down-Arraw	Donald Ervin Kunth
10	Sudan function	Sudan
11	Godel numbers	Godel
12	Grzegorczyk's hierarchy	Grzegorczyk
13	G_n+2(n) function	Milton Green
14	B_n(n) function	Milton Green
15	M_n+2(n) function	Milton Green
16	Peter's function	Rosza Peter
17	Robinsion's function	Raphael M. Robinson
18	Buck's function	Buck
19	Robert's function	Robert Ritchie
20	Meyer-Ritchie function	Meyer & Robert Ritchie
21	Edelsbrunner-Herbert's function	Edelsbrunner & Herbert
22	Alteration of M/R's Ackf	-
23	Baxter's Derivation	Lew Baxter
24	Mixed Factorial	-
25	Moser's Polygon Notation	Leo Moser
26	Pentiration	-
27	Old Polygon Notation	Leo Moser
28	Left tower	-
29	Tetration	Hans Maurer
30	Iterative Factorial	-

1995年

	名称	作者
1	Goodstein Sequence	Goodstein
2	Kirby-Paris Hydra	Laurie Kirby & Jeff Paris
3	CG Function	John Horton Conway & Richard Kenneth Guy
4	Chained Arrow	John Horton Conway & Richard Kenneth Guy
5	Graham's Function G(n)	Ronald Graham
6	Graham's Function g(n)	Ronald Graham
7	Hyperlicious Function	-
8	Ackermann's Function	Wilhelm Ackermann
9	Kunth's Up-Arraw	Donald Ervin Kunth
10	Hyper Operation	-
11	Down-Arraw	Donald Ervin Kunth
12	Sudan function	Sudan
13	Godel numbers	Godel
14	Grzegorczyk's hierarchy	Grzegorczyk
15	G_n+2(n) function	Milton Green
16	B_n(n) function	Milton Green
17	M_n+2(n) function	Milton Green
18	Peter's function	Rosza Peter
19	Robinsion's function	Raphael M. Robinson
20	Buck's function	Buck
21	Robert's function	Robert Ritchie
22	Meyer-Ritchie function	Meyer & Robert Ritchie
23	Edelsbrunner-Herbert's function	Edelsbrunner & Herbert
24	Alteration of M/R's Ackf	-
25	Baxter's Derivation	Lew Baxter
26	Mixed Factorial	-
27	Moser's Polygon Notation	Leo Moser
28	Pentiration	-
29	Old Polygon Notation	Leo Moser
30	Left tower	-

1996年

	名称	作者
1	Goodstein Sequence	Goodstein
2	Kirby-Paris Hydra	Laurie Kirby & Jeff Paris
3	CG Function	John Horton Conway & Richard Kenneth Guy
4	Chained Arrow	John Horton Conway & Richard Kenneth Guy
5	Graham's Function G(n)	Ronald Graham
6	Graham's Function g(n)	Ronald Graham
7	Hyperlicious Function	-
8	Ackermann's Function	Wilhelm Ackermann
9	Kunth's Up-Arraw	Donald Ervin Kunth
10	Hyper Operation	-
11	Down-Arraw	Donald Ervin Kunth
12	Munafo's Hyper Operation	Munafo
13	Sudan function	Sudan
14	Godel numbers	Godel
15	Grzegorczyk's hierarchy	Grzegorczyk
16	G_n+2(n) function	Milton Green
17	B_n(n) function	Milton Green
18	M_n+2(n) function	Milton Green
19	Peter's function	Rosza Peter
20	Robinsion's function	Raphael M. Robinson
21	Buck's function	Buck
22	Robert's function	Robert Ritchie
23	Meyer-Ritchie function	Meyer & Robert Ritchie
24	Edelsbrunner-Herbert's function	Edelsbrunner & Herbert
25	Alteration of M/R's Ackf	-
26	Baxter's Derivation	Lew Baxter
27	E# (Old)	-
28	Mixed Factorial	-
29	Moser's Polygon Notation	Leo Moser
30	Pentiration	-

1997年

	名称	作者
1	Goodstein Sequence	Goodstein
2	Kirby-Paris Hydra	Laurie Kirby & Jeff Paris
3	CG Function	John Horton Conway & Richard Kenneth Guy
4	Chained Arrow	John Horton Conway & Richard Kenneth Guy
5	Graham's Function G(n)	Ronald Graham
6	Graham's Function g(n)	Ronald Graham
7	Hyperlicious Function	-
8	Ackermann's Function	Wilhelm Ackermann
9	Kunth's Up-Arraw	Donald Ervin Kunth
10	Hyper Operation	-
11	Down-Arraw	Donald Ervin Kunth
12	Munafo's Hyper Operation	Munafo
13	Mythical tree problem	Harvey Friedman
14	Sudan function	Sudan
15	Godel numbers	Godel
16	Grzegorczyk's hierarchy	Grzegorczyk
17	G_n+2(n) function	Milton Green
18	B_n(n) function	Milton Green
19	M_n+2(n) function	Milton Green
20	Peter's function	Rosza Peter
21	Robinsion's function	Raphael M. Robinson
22	Buck's function	Buck
23	Robert's function	Robert Ritchie
24	Meyer-Ritchie function	Meyer & Robert Ritchie
25	Edelsbrunner-Herbert's function	Edelsbrunner & Herbert
26	Alteration of M/R's Ackf	-
27	Baxter's Derivation	Lew Baxter
28	E# (Old)	-
29	Mixed Factorial	-
30	Moser's Polygon Notation	Leo Moser

1998年

	名称	作者
1	Frideman's Sequence	Harvey Friedman
2	Goodstein Sequence	Goodstein
3	Kirby-Paris Hydra	Laurie Kirby & Jeff Paris
4	CG Function	John Horton Conway & Richard Kenneth Guy
5	Chained Arrow	John Horton Conway & Richard Kenneth Guy
6	Clarkkkkson	-
7	Graham's Function G(n)	Ronald Graham
8	Graham's Function g(n)	Ronald Graham
9	Hyperlicious Function	-
10	Ackermann's Function	Wilhelm Ackermann
11	Kunth's Up-Arraw	Donald Ervin Kunth
12	Hyper Operation	-
13	Down-Arraw	Donald Ervin Kunth
14	Munafo's Hyper Operation	Munafo
15	Mythical tree problem	Harvey Friedman
16	Munafo's function	Munafo
17	Sudan function	Sudan
18	Godel numbers	Godel
19	Grzegorczyk's hierarchy	Grzegorczyk
20	G_n+2(n) function	Milton Green
21	B_n(n) function	Milton Green
22	M_n+2(n) function	Milton Green
23	Peter's function	Rosza Peter
24	Robinsion's function	Raphael M. Robinson
25	Buck's function	Buck
26	Robert's function	Robert Ritchie
27	Meyer-Ritchie function	Meyer & Robert Ritchie
28	Edelsbrunner-Herbert's function	Edelsbrunner & Herbert
29	Alteration of M/R's Ackf	-
30	Baxter's Derivation	Lew Baxter

1999年

	名称	作者
1	Frideman's Sequence	Harvey Friedman
2	Goodstein Sequence	Goodstein
3	Kirby-Paris Hydra	Laurie Kirby & Jeff Paris
4	CG Function	John Horton Conway & Richard Kenneth Guy
5	Chained Arrow	John Horton Conway & Richard Kenneth Guy
6	Clarkkkkson	-
7	Graham's Function G(n)	Ronald Graham
8	Graham's Function g(n)	Ronald Graham
9	Hyperlicious Function	-
10	Ackermann's Function	Wilhelm Ackermann
11	Kunth's Up-Arraw	Donald Ervin Kunth
12	Hyper Operation	-
13	Bowers' Operators	Jonathan Bowers
14	Nambir's Hyper Operation	Nambir
15	R-R Hyper Operation	Ruzorbov & Romolio
16	Down-Arraw	Donald Ervin Kunth
17	Munafo's Hyper Operation	Munafo
18	Mythical tree problem	Harvey Friedman
19	Sudan function	Sudan
20	Godel numbers	Godel
21	Grzegorczyk's hierarchy	Grzegorczyk
22	G_n+2(n) function	Milton Green
23	B_n(n) function	Milton Green
24	M_n+2(n) function	Milton Green
25	Peter's function	Rosza Peter
26	Robinsion's function	Raphael M. Robinson
27	Buck's function	Buck
28	Robert's function	Robert Ritchie
29	Meyer-Ritchie function	Meyer & Robert Ritchie
30	Edelsbrunner-Herbert's function	Edelsbrunner & Herbert

2000年

	名称	作者
1	Frideman's Sequence	Harvey Friedman
2	Goodstein Sequence	Goodstein
3	Kirby-Paris Hydra	Laurie Kirby & Jeff Paris
4	CG Function	John Horton Conway & Richard Kenneth Guy
5	Bowers' {}	Jonathan Bowers
6	Chained Arrow	John Horton Conway & Richard Kenneth Guy
7	Clarkkkkson	-
8	Graham's Function G(n)	Ronald Graham
9	Graham's Function g(n)	Ronald Graham
10	Hyperlicious Function	-
11	Ackermann's Function	Wilhelm Ackermann
12	Kunth's Up-Arraw	Donald Ervin Kunth
13	Hyper Operation	-
14	Bowers' Operators	Jonathan Bowers
15	Nambir's Hyper Operation	Nambir
16	R-R Hyper Operation	Ruzorbov & Romolio
17	Down-Arraw	Donald Ervin Kunth
18	Munafo's Hyper Operation	Munafo
19	Mythical tree problem	Harvey Friedman
20	Sudan function	Sudan
21	Godel numbers	Godel
22	Grzegorczyk's hierarchy	Grzegorczyk
23	G_n+2(n) function	Milton Green
24	B_n(n) function	Milton Green
25	M_n+2(n) function	Milton Green
26	Peter's function	Rosza Peter
27	Robinsion's function	Raphael M. Robinson
28	Buck's function	Buck
29	Robert's function	Robert Ritchie
30	Meyer-Ritchie function	Meyer & Robert Ritchie

2001年

	名称	作者
1	Marxen C.function	Heiner Marxen
2	Frideman's Sequence	Harvey Friedman
3	Goodstein Sequence	Goodstein
4	Kirby-Paris Hydra	Laurie Kirby & Jeff Paris
5	Extended Bowers'Array Notation	Jonathan Bowers
6	Bowers'Array Notation	Jonathan Bowers
7	Pete.C function series	Pete
8	CG Function	John Horton Conway & Richard Kenneth Guy
9	Bowers' {}	Jonathan Bowers
10	Chained Arrow	John Horton Conway & Richard Kenneth Guy
11	Clarkkkkson	-
12	Graham's Function G(n)	Ronald Graham
13	Graham's Function g(n)	Ronald Graham
14	Hyperlicious Function	-
15	Ackermann's Function	Wilhelm Ackermann
16	Kunth's Up-Arraw	Donald Ervin Kunth
17	Hyper Operation	-
18	Bowers' Operators	Jonathan Bowers
19	Nambir's Hyper Operation	Nambir
20	R-R Hyper Operation	Ruzorbov & Romolio
21	Down-Arraw	Donald Ervin Kunth
22	Munafo's Hyper Operation	Munafo
23	Mythical tree problem	Harvey Friedman
24	Sudan function	Sudan
25	Godel numbers	Godel
26	Grzegorczyk's hierarchy	Grzegorczyk
27	G_n+2(n) function	Milton Green
28	B_n(n) function	Milton Green
29	M_n+2(n) function	Milton Green
30	Peter's function	Rosza Peter

2002年

	名称	作者
1	Marxen C.function	Heiner Marxen
2	Multi Dimensional Arrays	Jonathan Bowers
3	Frideman's Sequence	Harvey Friedman
4	Worm function	-
5	Goodstein Sequence	Goodstein
6	Kirby-Paris Hydra	Laurie Kirby & Jeff Paris
7	Dimensional Arrays	Jonathan Bowers
8	Linar Arrays	Jonathan Bowers
9	Extended Bowers'Array Notation	Jonathan Bowers
10	Bowers'Array Notation	Jonathan Bowers
11	Pete.C function series	Pete
12	CG Function	John Horton Conway & Richard Kenneth Guy
13	Bowers' {}	Jonathan Bowers
14	Chained Arrow	John Horton Conway & Richard Kenneth Guy
15	Clarkkkkson	-
16	Graham's Function G(n)	Ronald Graham
17	Graham's Function g(n)	Ronald Graham
18	Hyperlicious Function	-
19	Ackermann's Function	Wilhelm Ackermann
20	Kunth's Up-Arraw	Donald Ervin Kunth
21	Hyper Operation	-
22	Bowers' Operators	Jonathan Bowers
23	Nambir's Hyper Operation	Nambir
24	R-R Hyper Operation	Ruzorbov & Romolio
25	Down-Arraw	Donald Ervin Kunth
26	Munafo's Hyper Operation	Munafo
27	Mythical tree problem	Harvey Friedman
28	Sudan function	Sudan
29	Godel numbers	Godel
30	Grzegorczyk's hierarchy	Grzegorczyk

2003年

	名称	作者
1	Bower's Dimensional Arrays with []	-
2	Marxen C.function	Heiner Marxen
3	Multi Dimensional Arrays	Jonathan Bowers
4	Frideman's Sequence	Harvey Friedman
5	Worm function	-
6	Goodstein Sequence	Goodstein
7	Kirby-Paris Hydra	Laurie Kirby & Jeff Paris
8	Dimensional Arrays	Jonathan Bowers
9	Linar Arrays	Jonathan Bowers
10	Extended Bowers'Array Notation	Jonathan Bowers
11	Bowers'Array Notation	Jonathan Bowers
12	Pete.C function series	Pete
13	CG Function	John Horton Conway & Richard Kenneth Guy
14	Bowers' {}	Jonathan Bowers
15	Chained Arrow	John Horton Conway & Richard Kenneth Guy
16	Clarkkkkson	-
17	Graham's Function G(n)	Ronald Graham
18	Graham's Function g(n)	Ronald Graham
19	Hyperlicious Function	-
20	Ackermann's Function	Wilhelm Ackermann
21	Kunth's Up-Arraw	Donald Ervin Kunth
22	Hyper Operation	-
23	Bowers' Operators	Jonathan Bowers
24	Nambir's Hyper Operation	Nambir
25	R-R Hyper Operation	Ruzorbov & Romolio
26	Down-Arraw	Donald Ervin Kunth
27	Munafo's Hyper Operation	Munafo
28	Mythical tree problem	Harvey Friedman
29	Sudan function	Sudan
30	Godel numbers	Godel

2004年

	名称	作者
1	E# with '#' Hyper Operation	Sbiis Saibian
2	Bower's Dimensional Arrays with []	-
3	Marxen C.function	Heiner Marxen
4	Multi Dimensional Arrays	Jonathan Bowers
5	E# with '#' Operation	Sbiis Saibian
6	Frideman's Sequence	Harvey Friedman
7	Worm function	-
8	Goodstein Sequence	Goodstein
9	Kirby-Paris Hydra	Laurie Kirby & Jeff Paris
10	Dimensional Arrays	Jonathan Bowers
11	Linar Arrays	Jonathan Bowers
12	E# with multiple #	Sbiis Saibian
13	Extended Bowers'Array Notation	Jonathan Bowers
14	Bowers'Array Notation	Jonathan Bowers
15	Pete.C function series	Pete
16	CG Function	John Horton Conway & Richard Kenneth Guy
17	Bowers' {}	Jonathan Bowers
18	Chained Arrow	John Horton Conway & Richard Kenneth Guy
19	Clarkkkkson	-
20	Graham's Function G(n)	Ronald Graham
21	Graham's Function g(n)	Ronald Graham
22	Hyperlicious Function	-
23	Ackermann's Function	Wilhelm Ackermann
24	Kunth's Up-Arraw	Donald Ervin Kunth
25	Hyper Operation	-
26	Bowers' Operators	Jonathan Bowers
27	Nambir's Hyper Operation	Nambir
28	R-R Hyper Operation	Ruzorbov & Romolio
29	Down-Arraw	Donald Ervin Kunth
30	Munafo's Hyper Operation	Munafo

2005年

	名称	作者
1	E# with '#' Hyper Operation	Sbiis Saibian
2	Bower's Dimensional Arrays with []	-
3	Marxen C.function	Heiner Marxen
4	Multi Dimensional Arrays	Jonathan Bowers
5	E# with '#' Operation	Sbiis Saibian
6	Frideman's Sequence	Harvey Friedman
7	Worm function	-
8	Goodstein Sequence	Goodstein
9	Kirby-Paris Hydra	Laurie Kirby & Jeff Paris
10	Dimensional Arrays	Jonathan Bowers
11	Linar Arrays	Jonathan Bowers
12	E# with multiple #	Sbiis Saibian
13	Extended Bowers'Array Notation	Jonathan Bowers
14	Bowers'Array Notation	Jonathan Bowers
15	Pete.C function series	Pete
16	CG Function	John Horton Conway & Richard Kenneth Guy
17	Bowers' {}	Jonathan Bowers
18	Chained Arrow	John Horton Conway & Richard Kenneth Guy
19	Clarkkkkson	-
20	Graham's Function G(n)	Ronald Graham
21	Graham's Function g(n)	Ronald Graham
22	Hyperlicious Function	-
23	Ackermann's Function	Wilhelm Ackermann
24	Kunth's Up-Arraw	Donald Ervin Kunth
25	Hyper Operation	-
26	Bowers' Operators	Jonathan Bowers
27	Nambir's Hyper Operation	Nambir
28	R-R Hyper Operation	Ruzorbov & Romolio
29	Down-Arraw	Donald Ervin Kunth
30	Munafo's Hyper Operation	Munafo

2006年

	名称	作者
1	Bird's Array (V1)	Chris Bird
2	E# with '#' Hyper Operation	Sbiis Saibian
3	Bower's Dimensional Arrays with []	-
4	Bird's multiple []	Chris Bird
5	Marxen C.function	Heiner Marxen
6	Multi Dimensional Arrays	Jonathan Bowers
7	E# with '#' Operation	Sbiis Saibian
8	Bird's []	Chris Bird
9	Frideman's Sequence	Harvey Friedman
10	Worm function	-
11	Goodstein Sequence	Goodstein
12	Kirby-Paris Hydra	Laurie Kirby & Jeff Paris
13	Dimensional Arrays	Jonathan Bowers
14	Linar Arrays	Jonathan Bowers
15	E# with multiple #	Sbiis Saibian
16	Bird's Linar Arrays	Chris Bird
17	Extended Bowers'Array Notation	Jonathan Bowers
18	Bowers'Array Notation	Jonathan Bowers
19	Pete.C function series	Pete
20	CG Function	John Horton Conway & Richard Kenneth Guy
21	Bowers' {}	Jonathan Bowers
22	Chained Arrow	John Horton Conway & Richard Kenneth Guy
23	Clarkkkkson	-
24	Graham's Function G(n)	Ronald Graham
25	Graham's Function g(n)	Ronald Graham
26	Hyperlicious Function	-
27	Ackermann's Function	Wilhelm Ackermann
28	Kunth's Up-Arraw	Donald Ervin Kunth
29	Hyper Operation	-
30	Bowers' Operators	Jonathan Bowers

2007年

	名称	作者
1	Bird's Array (V1)	Chris Bird
2	Bowers' &	Jonathan Bowers
3	E# with '#' Hyper Operation	Sbiis Saibian
4	Bower's Dimensional Arrays with []	-
5	Bird's multiple []	Chris Bird
6	Marxen C.function	Heiner Marxen
7	Multi Dimensional Arrays	Jonathan Bowers
8	E# with '#' Operation	Sbiis Saibian
9	Bird's []	Chris Bird
10	Frideman's Sequence	Harvey Friedman
11	Worm function	-
12	Goodstein Sequence	Goodstein
13	Kirby-Paris Hydra	Laurie Kirby & Jeff Paris
14	Dimensional Arrays	Jonathan Bowers
15	Linar Arrays	Jonathan Bowers
16	Taro's multivariable Ackermann function	Taro
17	E# with multiple #	Sbiis Saibian
18	Bird's Linar Arrays	Chris Bird
19	Extended Bowers'Array Notation	Jonathan Bowers
20	Bowers'Array Notation	Jonathan Bowers
21	Pete.C function series	Pete
22	CG Function	John Horton Conway & Richard Kenneth Guy
23	Bowers' {}	Jonathan Bowers
24	Chained Arrow	John Horton Conway & Richard Kenneth Guy
25	Clarkkkkson	-
26	Graham's Function G(n)	Ronald Graham
27	Graham's Function g(n)	Ronald Graham
28	Hyperlicious Function	-
29	Ackermann's Function	Wilhelm Ackermann
30	Kunth's Up-Arraw	Donald Ervin Kunth

2008年

	名称	作者
1	Bird's Array (V1)	Chris Bird
2	Bowers' Exploding Array Function	Jonathan Bowers
3	Bowers' &	Jonathan Bowers
4	Hyper-E Notation	Sbiis Saibian
5	E# with '#' Hyper Operation	Sbiis Saibian
6	Bower's Dimensional Arrays with []	-
7	Bird's multiple []	Chris Bird
8	Marxen C.function	Heiner Marxen
9	Multi Dimensional Arrays	Jonathan Bowers
10	E# with '#' Operation	Sbiis Saibian
11	Bird's []	Chris Bird
12	Frideman's Sequence	Harvey Friedman
13	Worm function	-
14	Goodstein Sequence	Goodstein
15	Kirby-Paris Hydra	Laurie Kirby & Jeff Paris
16	Dimensional Arrays	Jonathan Bowers
17	Linar Arrays	Jonathan Bowers
18	Taro's multivariable Ackermann function	Taro
19	E# with multiple #	Sbiis Saibian
20	Bird's Linar Arrays	Chris Bird
21	Extended Bowers'Array Notation	Jonathan Bowers
22	Bowers'Array Notation	Jonathan Bowers
23	Pete.C function series	Pete
24	CG Function	John Horton Conway & Richard Kenneth Guy
25	Bowers' {}	Jonathan Bowers
26	Chained Arrow	John Horton Conway & Richard Kenneth Guy
27	Clarkkkkson	-
28	Graham's Function G(n)	Ronald Graham
29	Graham's Function g(n)	Ronald Graham
30	Hyperlicious Function	-

2009年

	名称	作者
1	Bird's Array (V1)	Chris Bird
2	Bowers' Exploding Array Function	Jonathan Bowers
3	Bowers' &	Jonathan Bowers
4	Hyper-E Notation	Sbiis Saibian
5	E# with '#' Hyper Operation	Sbiis Saibian
6	Bower's Dimensional Arrays with []	-
7	Bird's multiple []	Chris Bird
8	Marxen C.function	Heiner Marxen
9	Multi Dimensional Arrays	Jonathan Bowers
10	E# with '#' Operation	Sbiis Saibian
11	Bird's []	Chris Bird
12	Frideman's Sequence	Harvey Friedman
13	Worm function	-
14	Goodstein Sequence	Goodstein
15	Kirby-Paris Hydra	Laurie Kirby & Jeff Paris
16	Dimensional Arrays	Jonathan Bowers
17	Linar Arrays	Jonathan Bowers
18	Taro's multivariable Ackermann function	Taro
19	E# with multiple #	Sbiis Saibian
20	Bird's Linar Arrays	Chris Bird
21	Extended Bowers'Array Notation	Jonathan Bowers
22	Bowers'Array Notation	Jonathan Bowers
23	Pete.C function series	Pete
24	CG Function	John Horton Conway & Richard Kenneth Guy
25	Bowers' {}	Jonathan Bowers
26	Chained Arrow	John Horton Conway & Richard Kenneth Guy
27	Clarkkkkson	-
28	Graham's Function G(n)	Ronald Graham
29	Graham's Function g(n)	Ronald Graham
30	Hyperlicious Function	-

2010年

	名称	作者
1	Bird's Array (V2)	Chris Bird
2	Bird's ~	Chris Bird
3	Bird's Array (V1)	Chris Bird
4	Bowers' Exploding Array Function	Jonathan Bowers
5	Bowers' &	Jonathan Bowers
6	Hyper-E Notation	Sbiis Saibian
7	E# with '#' Hyper Operation	Sbiis Saibian
8	Bower's Dimensional Arrays with []	-
9	Bird's multiple []	Chris Bird
10	Marxen C.function	Heiner Marxen
11	Multi Dimensional Arrays	Jonathan Bowers
12	E# with '#' Operation	Sbiis Saibian
13	Bird's []	Chris Bird
14	Frideman's Sequence	Harvey Friedman
15	Worm function	-
16	Goodstein Sequence	Goodstein
17	Kirby-Paris Hydra	Laurie Kirby & Jeff Paris
18	Dimensional Arrays	Jonathan Bowers
19	Linar Arrays	Jonathan Bowers
20	Taro's multivariable Ackermann function	Taro
21	E# with multiple #	Sbiis Saibian
22	Bird's Linar Arrays	Chris Bird
23	Extended Bowers'Array Notation	Jonathan Bowers
24	Bowers'Array Notation	Jonathan Bowers
25	Pete.C function series	Pete
26	CG Function	John Horton Conway & Richard Kenneth Guy
27	Bowers' {}	Jonathan Bowers
28	Chained Arrow	John Horton Conway & Richard Kenneth Guy
29	Clarkkkkson	-
30	Graham's Function G(n)	Ronald Graham

2011年

	名称	作者
1	Bird's Array (V2)	Chris Bird
2	Bird's ~	Chris Bird
3	Bird's Array (V1)	Chris Bird
4	Bowers' Exploding Array Function	Jonathan Bowers
5	Bowers' &	Jonathan Bowers
6	Hyper-E Notation	Sbiis Saibian
7	E# with '#' Hyper Operation	Sbiis Saibian
8	Bower's Dimensional Arrays with []	-
9	Bird's multiple []	Chris Bird
10	Marxen C.function	Heiner Marxen
11	Multi Dimensional Arrays	Jonathan Bowers
12	E# with '#' Operation	Sbiis Saibian
13	Bird's []	Chris Bird
14	Frideman's Sequence	Harvey Friedman
15	Worm function	-
16	Goodstein Sequence	Goodstein
17	Kirby-Paris Hydra	Laurie Kirby & Jeff Paris
18	Dimensional Arrays	Jonathan Bowers
19	Linar Arrays	Jonathan Bowers
20	Taro's multivariable Ackermann function	Taro
21	E# with multiple #	Sbiis Saibian
22	Bird's Linar Arrays	Chris Bird
23	C Function	Peter Hurford
24	Extended Bowers'Array Notation	Jonathan Bowers
25	Extended Chained Arrow	Peter Hurford
26	Bowers'Array Notation	Jonathan Bowers
27	Pete.C function series	Pete
28	CG Function	John Horton Conway & Richard Kenneth Guy
29	Bowers' {}	Jonathan Bowers
30	Chained Arrow	John Horton Conway & Richard Kenneth Guy

2012年

	名称	作者
1	Bird's Array (V2)	Chris Bird
2	Bird's ~	Chris Bird
3	Bird's Array (V1)	Chris Bird
4	Bowers' Exploding Array Function	Jonathan Bowers
5	Bowers' &	Jonathan Bowers
6	Hyper-E Notation	Sbiis Saibian
7	E# with '#' Hyper Operation	Sbiis Saibian
8	Bower's Dimensional Arrays with []	-
9	Bird's multiple []	Chris Bird
10	Marxen C.function	Heiner Marxen
11	Burning number	-
12	Multi Dimensional Arrays	Jonathan Bowers
13	E# with '#' Operation	Sbiis Saibian
14	Bird's []	Chris Bird
15	Frideman's Sequence	Harvey Friedman
16	Worm function	-
17	Goodstein Sequence	Goodstein
18	Kirby-Paris Hydra	Laurie Kirby & Jeff Paris
19	Dimensional Arrays	Jonathan Bowers
20	Linar Arrays	Jonathan Bowers
21	Taro's multivariable Ackermann function	Taro
22	E# with multiple #	Sbiis Saibian
23	Bird's Linar Arrays	Chris Bird
24	Linar R Function (Old)	Hyp_Cos
25	C Function	Peter Hurford
26	Extended Bowers'Array Notation	Jonathan Bowers
27	Extended Chained Arrow	Peter Hurford
28	Bowers'Array Notation	Jonathan Bowers
29	Pete.C function series	Pete
30	CG Function	John Horton Conway & Richard Kenneth Guy

2013年

	名称	作者
1	Dollar Function	Wythagoras
2	Linar R Function	Hyp_Cos
3	Hyper-factoral Array Notation	Lawerence Hollom
4	Bowers' Exploding Array Function	Jonathan Bowers
5	Bird's U(n) function	Chris Bird
6	Bowers' &	Jonathan Bowers
7	Bird's Array (V2)	Chris Bird
8	Bird's ~	Chris Bird
9	Bird's S(n) function	Chris Bird
10	Bird's Array (V1)	Chris Bird
11	Bird's H(n) function	Chris Bird
12	Extended Hyper-E	-
13	Hyper-E Notation	Sbiis Saibian
14	E# with '#' Hyper Operation	Sbiis Saibian
15	Bower's Dimensional Arrays with []	-
16	Bird's multiple []	Chris Bird
17	Marxen C.function	Heiner Marxen
18	Burning number	-
19	Multi Dimensional Arrays	Jonathan Bowers
20	E# with '#' Operation	Sbiis Saibian
21	Bird's []	Chris Bird
22	Frideman's Sequence	Harvey Friedman
23	Worm function	-
24	Goodstein Sequence	Goodstein
25	Kirby-Paris Hydra	Laurie Kirby & Jeff Paris
26	Cascading-E Notation	Sbiis Saibian
27	Dimensional Arrays	Jonathan Bowers
28	Linar Arrays	Jonathan Bowers
29	Taro's multivariable Ackermann function	Taro
30	E# with multiple #	Sbiis Saibian

2014年

自这一年起，序数记号被认为和大数记号同等重要。于是序数记号加入榜单。

	名称	作者
1	[]-Stb	Hyp_Cos
2	Rathjen's Ordinal Collapsing Function	Rathjen
3	Catching Function	Hyp_Cos
4	R Function	Hyp_Cos
5	Bowers' Exploding Array Function	Jonathan Bowers
6	Stegart's Large OCF	Jan-Carl Stegart
7	Stegart's Small OCF	Jan-Carl Stegart
8	Duchhart's OCF	Duchhart
9	Dollar Function	Wythagoras
10	Rathjen's Ξ	Rathjen
11	K OCF	-
12	Rathjen's χ	Rathjen
13	Mahlo OCF	-
14	Linar R Function	Hyp_Cos
15	Hyper-factoral Array Notation	Lawerence Hollom
16	I OCF	Gerhard Jäger & Wilfried Buchholz
17	Buchhoz's Φ	Wilfried Buchholz
18	Bird's Array	Chris Bird
19	Ordinal diagrams	Gaisi Takeuti
20	Feferman's θ	Fefermann
21	Buchholz's Hydra	Wilfried Buchholz
22	Buchholz's ψ Function	Wilfried Buchholz
23	SCG Function	-
24	SSCG Function	-
25	Bowers' &	Jonathan Bowers
26	Taranovsky's Ordinal Notation (Old)	Taranovsky
27	Patterns of Resemblance	Carlson
28	Wilken's θ	Gunnar Wilken
29	Extended Hyper-E	-
30	1st Catching Point of G/F	Girard
31	Bird's U(n) function	Chris Bird
32	Bird's Array (V2)	Chris Bird
33	Bird's ~	Chris Bird
34	Madore's ψ Function	Madore
35	Bachmann's ψ	Bachmann
36	Bird's S(n) function	Chris Bird
37	Bird's Array (V1)	Chris Bird
38	Bird's H(n) function	Chris Bird
39	Veblen Function	Oswald Veblen
40	TREE function	Harvey Friedman

2015年

	名称	作者
1	Taranovsky's Ordinal Notation	Taranovsky
2	Trio Sequence System	Bashicu
3	[]-Stb	Hyp_Cos
4	Catching Function	Hyp_Cos
5	Strong Array Notation	Hyp_Cos
6	Rathjen's Ordinal Collapsing Function	Rathjen
7	R Function	Hyp_Cos
8	Bowers' Exploding Array Function	Jonathan Bowers
9	Secondry Dropping Array Notation	Hyp_Cos
10	Degrees of Reflection	Taranovsky
11	Stegart's Large OCF	Jan-Carl Stegart
12	Pirmary Dropping Array Notation	Hyp_Cos
13	Stegart's Small OCF	Jan-Carl Stegart
14	Duchhart's OCF	Duchhart
15	Dollar Function	Wythagoras
16	Rathjen's Ξ	Rathjen
17	K OCF	-
18	Rathjen's χ	Rathjen
19	Mahlo OCF	-
20	Linar R Function	Hyp_Cos
21	Hyper-factoral Array Notation	Lawerence Hollom
22	I OCF	Gerhard Jäger & Wilfried Buchholz
23	Buchhoz's Φ	Wilfried Buchholz
24	Bird's H(n) function	Chris Bird
25	Bird's Array	Chris Bird
26	Ordinal diagrams	Gaisi Takeuti
27	Feferman's θ	Fefermann
28	Buchholz's Hydra	Wilfried Buchholz
29	Buchholz's ψ Function	Wilfried Buchholz
30	SCG Function	-
31	SSCG Function	-
32	Bowers' &	Jonathan Bowers
33	Taranovsky's Ordinal Notation (Old)	Taranovsky
34	Patterns of Resemblance	Carlson
35	Wilken's θ	Gunnar Wilken
36	Pair Sequence System	Bashicu
37	Extended Hyper-E	-
38	Mulptily Expanding Array Notation	Hyp_Cos
39	1st Catching Point of G/F	Girard
40	Bird's U(n) function	Chris Bird

2016年

	名称	作者
1	Taranovsky's Ordinal Notation	Taranovsky
2	Trio Sequence System	Bashicu
3	[]-Stb	Hyp_Cos
4	Rathjen's Ordinal Collapsing Function	Rathjen
5	Iteration of n-built from below	Taranovsky
6	Built-from-below	Taranovsky
7	Degrees of Reflection	Taranovsky
8	Reflection configuration	Taranovsky
9	Catching Function	Hyp_Cos
10	Strong Array Notation	Hyp_Cos
11	Dropping hydra	Hyp_Cos
12	R Function	Hyp_Cos
13	3-Dropping hydra	Hyp_Cos
14	Bowers' Exploding Array Function	Jonathan Bowers
15	Secondry Dropping Array Notation	Hyp_Cos
16	Stegart's Large OCF	Hyp_Cos
17	Pirmary Dropping Array Notation	Jan-Carl Stegart
18	Stegart's Small OCF	Hyp_Cos
19	2-Dropping hydra	Jan-Carl Stegart
20	Duchhart's OCF	Wythagoras
21	Dollar Function	Duchhart
22	Rathjen's Ξ	Rathjen
23	K OCF	-
24	Rathjen's χ	Rathjen
25	Mahlo OCF	-
26	Linar R Function	Hyp_Cos
27	Hyper-factoral Array Notation	Lawerence Hollom
28	I OCF	Gerhard Jäger & Wilfried Buchholz
29	Buchhoz's Φ	Wilfried Buchholz
30	Extended Buchholz's ψ Function	Denis Maksudov
31	Bird's H(n) function	Chris Bird
32	Bird's Array	Chris Bird
33	Ordinal diagrams	Gaisi Takeuti
34	Feferman's θ	Fefermann
35	Buchholz's Hydra	Wilfried Buchholz
36	Buchholz's ψ Function	Wilfried Buchholz
37	SCG Function	-
38	SSCG Function	-
39	Bowers' &	Jonathan Bowers
40	Taranovsky's Ordinal Notation (Old)	Taranovsky

2017年

	名称	作者
1	Taranovsky's Ordinal Notation	Taranovsky
2	idealized Bashicu Martix System	Bashicu
3	Trio Sequence System	Bashicu
4	primary Dropper Dropping Notation	Hyp_Cos
5	[]-Stb	Hyp_Cos
6	Rathjen's Ordinal Collapsing Function	Rathjen
7	WDmEN	Hyp_Cos
8	Iteration of n-built from below	Taranovsky
9	Built-from-below	Taranovsky
10	Degrees of Reflection	Taranovsky
11	Reflection configuration	Taranovsky
12	Catching Function	Hyp_Cos
13	Multiple Weak Declinator Expanding	Hyp_Cos
14	Weak Declinator Expanding	Hyp_Cos
15	Nested Dropping Array Notation	Hyp_Cos
16	Strong Array Notation	Hyp_Cos
17	Dropping hydra	Hyp_Cos
18	R Function	Hyp_Cos
19	3-Dropping hydra	Hyp_Cos
20	Bowers' Exploding Array Function	Jonathan Bowers
21	Secondry Dropping Array Notation	Hyp_Cos
22	Stegart's Large OCF	Jan-Carl Stegart
23	Pirmary Dropping Array Notation	Hyp_Cos
24	Stegart's Small OCF	Jan-Carl Stegart
25	2-Dropping hydra	Hyp_Cos
26	Duchhart's OCF	Duchhart
27	Dollar Function	Wythagoras
28	Rathjen's Ξ	Rathjen
29	K OCF	-
30	Rathjen's χ	Rathjen
31	Mahlo OCF	-
32	Linar R Function	Hyp_Cos
33	Hyper-factoral Array Notation	Lawerence Hollom
34	I OCF	Gerhard Jäger & Wilfried Buchholz
35	Buchhoz's Φ	Wilfried Buchholz
36	Sudden Sequence System	Bashicu
37	Extended Buchholz's ψ Function	Denis Maksudov
38	Bird's H(n) function	Chris Bird
39	Bird's Array	Chris Bird
40	Ordinal diagrams	Gaisi Takeuti

2018年

	名称	作者
1	Bashicu Matrix System	Bashicu
2	BMOCF	P進大好きbot
3	idealized Bashicu Martix System	Bashicu
4	Quadro Sequence System	Bashicu
5	Trio Sequence System	Bashicu
6	primary Dropper Dropping Notation	Hyp_Cos
7	[]-Stb	Hyp_Cos
8	Rathjen's Ordinal Collapsing Function	Rathjen
9	Sudden Hydra	Bashicu
10	WDmEN	Hyp_Cos
11	Iteration of n-built from below	Taranovsky
12	Built-from-below	Taranovsky
13	Degrees of Reflection	Taranovsky
14	Reflection configuration	Taranovsky
15	Catching Function	Hyp_Cos
16	Multiple Weak Declinator Expanding	Hyp_Cos
17	Weak Declinator Expanding	Hyp_Cos
18	Nested Dropping Array Notation	Hyp_Cos
19	Username5243's OCF	Username5243
20	Taranovsky's Ordinal Notation	Taranovsky
21	Strong Array Notation	Hyp_Cos
22	Dropping hydra	Hyp_Cos
23	R Function	Hyp_Cos
24	NICE Function	Naroyuko
25	3-Dropping hydra	Hyp_Cos
26	Bowers' Exploding Array Function	Jonathan Bowers
27	Secondry Dropping Array Notation	Hyp_Cos
28	Stegart's Large OCF	Jan-Carl Stegart
29	Pirmary Dropping Array Notation	Hyp_Cos
30	Stegart's Small OCF	Jan-Carl Stegart
31	2-Dropping hydra	Hyp_Cos
32	π Notation	Username5243
33	Duchhart's OCF	Duchhart
34	Dollar Function	Wythagoras
35	Weak Username5243's OCF	Username5243
36	Rathjen's Ξ	Rathjen
37	K OCF	-
38	Rathjen's χ	Rathjen
39	Mahlo OCF	-
40	Linar R Function	Hyp_Cos

2019年

	名称	作者
1	Bubby3 TBMS Extended	Bubby3
2	Bubby3 TBMS Normal	Bubby3
3	Bashicu Sudden Matrix	Bashicu
4	Bashicu Hyper Matrix	Bashicu
5	Bashicu Matrix System	Bashicu
6	Bashicu Matrix V4.1	Bashicu
7	BMOCF	P進大好きbot
8	idealized Bashicu Martix System	Bashicu
9	Quadro Sequence System	Bashicu
10	Trio Sequence System	Bashicu
11	primary Dropper Dropping Notation	Hyp_Cos
12	[]-Stb	Hyp_Cos
13	Rathjen's Ordinal Collapsing Function	Rathjen
14	Sudden Hydra	Bashicu
15	WDmEN	Hyp_Cos
16	Iteration of n-built from below	Taranovsky
17	Built-from-below	Taranovsky
18	Degrees of Reflection	Taranovsky
19	Reflection configuration	Taranovsky
20	Multiple Weak Declinator Expanding	Hyp_Cos
21	Weak Declinator Expanding	Hyp_Cos
22	Nested Dropping Array Notation	Hyp_Cos
23	Username5243's OCF	Username5243
24	Taranovsky's Ordinal Notation	Taranovsky
25	Strong Array Notation	Hyp_Cos
26	Dropping hydra	Hyp_Cos
27	R Function	Hyp_Cos
28	NICE Function	Naroyuko
29	3-Dropping hydra	Hyp_Cos
30	Secondry Dropping Array Notation	Hyp_Cos
31	Catching Function	Hyp_Cos
32	Stegart's Large OCF	Jan-Carl Stegart
33	Pirmary Dropping Array Notation	Hyp_Cos
34	Stegart's Small OCF	Jan-Carl Stegart
35	2-Dropping hydra	Hyp_Cos
36	Order Level Array Notation V3	ych
37	π Notation	Username5243
38	Duchhart's OCF	Duchhart
39	Dollar Function	Wythagoras
40	Weak Username5243's OCF	Username5243

2020年

	名称	作者
1	Y Sequence	Yukito
2	Bubby3 TBMS Extended	Bubby3
3	Bubby3 TBMS Normal	Bubby3
4	Hassium's TBMS	Hassium
5	Weak Splatium TBMS	Bubby3
6	Bashicu Sudden Matrix	Bashicu
7	Bashicu Hyper Matrix	Bashicu
8	Bashicu Matrix System	Bashicu
9	Bashicu Matrix V4.1	Bashicu
10	0-Y Sequence	Yukito
11	BMOCF	P進大好きbot
12	idealized Bashicu Martix System	Bashicu
13	Quadro Sequence System	Bashicu
14	Small Hyper Projection Notation	test_alpha0
15	Trio Sequence System	Bashicu
16	Simple Projection	test_alpha0
17	ex-UNOCF	P進大好きbot
18	3-Projection	test_alpha0
19	primary Dropper Dropping Notation	Hyp_Cos
20	[]-Stb	Hyp_Cos
21	Rathjen's Ordinal Collapsing Function	Rathjen
22	Sudden Hydra	Bashicu
23	WDmEN	Hyp_Cos
24	Iteration of n-built from below	Taranovsky
25	Built-from-below	Taranovsky
26	Degrees of Reflection	Taranovsky
27	Reflection configuration	Taranovsky
28	2-Projection	test_alpha0
29	Multiple Weak Declinator Expanding	Hyp_Cos
30	Weak Declinator Expanding	Hyp_Cos
31	Nested Dropping Array Notation	Hyp_Cos
32	Username5243's OCF	Username5243
33	Taranovsky's Ordinal Notation	Taranovsky
34	Strong Array Notation	Hyp_Cos
35	Dropping hydra	Hyp_Cos
36	R Function	Hyp_Cos
37	Order Level Array Notation V4	ych
38	NICE Function	Naroyuko
39	3-Dropping hydra	Hyp_Cos
40	Secondry Dropping Array Notation	Hyp_Cos

2021年

	名称	作者
1	Crater BMS	Bubby3 & Aarex
2	ω-Y Sequence	Yukito & naruyoko
3	2-Y Sequence	Yukito & naruyoko
4	Y Sequence	Yukito
5	Dimensional Bashicu Martix System	-
6	ω+1 row Y	-
7	Bubby3 TBMS Extended	Bubby3
8	Bubby3 TBMS Normal	Bubby3
9	Aarex's strong ex-UNOCF with $	Aarex
10	Hassium's TBMS	Hassium
11	Weak Splatium TBMS	Bubby3
12	Uncountable TBMS	-
13	Apotheosis Ordinal Notation	-
14	Bashicu Sudden Matrix	Bashicu
15	Bashicu Hyper Matrix	Bashicu
16	Bashicu Matrix System	Bashicu
17	Bashicu Matrix V4.1	Bashicu
18	0-Y Sequence	Yukito
19	BMOCF	P進大好きbot
20	idealized Bashicu Martix System	Bashicu
21	Σ₂ Stb System	Yukito
22	Quadro Sequence System	Bashicu
23	Small Hyper Projection Notation	test_alpha0
24	Non-recursive TON	Taranovsky
25	Weak MCS projection	Test_alpha0
26	Trio Sequence System	Bashicu
27	HPrSSψ	-
28	Simple Projection	test_alpha0
29	ex-UNOCF	P進大好きbot
30	3-Projection	test_alpha0
31	primary Dropper Dropping Notation	Hyp_Cos
32	Lifting K-Notation	test_alpha0
33	[]-Stb	Hyp_Cos
34	Rathjen's Ordinal Collapsing Function	Rathjen
35	Sudden Hydra	Bashicu
36	WDmEN	Hyp_Cos
37	Lifting Omega Notation	test_alpha0
38	Iteration of n-built from below	Taranovsky
39	Built-from-below	Taranovsky
40	Degrees of Reflection	Taranovsky

2022年

	名称	作者
1	fake fake fake Z function	yahtzee
2	Strong Ω-Y	-
3	Crater BMS	Bubby3 & Aarex
4	Yto's Y-Y	-
5	CIF's Ω-Y Sequence	CIF & Hyp_cos
6	ω-Y Sequence	Yukito & naruyoko
7	2-Y Sequence	Yukito & naruyoko
8	Patterns of Resemblance	Carlson
9	Y Sequence	Yukito
10	VZ-Sequense	-
11	Dimensional Bashicu Martix System	-
12	ω+1 row Y	-
13	Bubby3 TBMS Extended	Bubby3
14	Bubby3 TBMS Normal	Bubby3
15	Aarex's TBMS	Aarex
16	Aarex's strong ex-UNOCF with $	Aarex
17	Aarex's Redirection	Aarex
18	Hassium's TBMS	Hassium
19	Weak Splatium TBMS	Bubby3
20	Uncountable TBMS	-
21	Crazy-Hydra Notation	Gomen
22	Apotheosis Ordinal Notation	-
23	Bashicu Sudden Matrix	Bashicu
24	Bashicu Hyper Matrix	Bashicu
25	Bashicu Matrix System	Bashicu
26	Bashicu Matrix V4.1	Bashicu
27	0-Y Sequence	Yukito
28	BMOCF	P進大好きbot
29	idealized Bashicu Martix System	Bashicu
30	Σ₂ Stb System	Yukito
31	Quadro Sequence System	Bashicu
32	strong DLON	Aarex
33	Small Hyper Projection Notation	Test_alpha0
34	Strong ex-UNOCF	-
35	Non-recursive TON	Taranovsky
36	Weak MCS projection	Test_alpha0
37	Trio Sequence System	Bashicu
38	HPrSSψ	-
39	Simple Projection	test_alpha0
40	ex-UNOCF	P進大好きbot

2023年

	名称	作者
1	Mutant Martix System	Aarex & Hyp_cos
2	Nested Crater Y	Bubby3
3	Crater Y	Bubby3 & Aarex
4	Strong Ω-Y	-
5	Crater BMS	Bubby3 & Aarex
6	Yto's Y-Y	-
7	CIF's Ω-Y Sequence	CIF & Hyp_cos
8	X-Y Sequence	Gomen
9	Transfinite DBMS	-
10	ω-Y Sequence	Yukito & naruyoko
11	Dementional n-Y	Gomen
12	2-Y Sequence	Yukito & naruyoko
13	Strong Y Sequence	-
14	Y Sequence	Yukito
15	Apotheosis Ordinal Notation	-
16	VZ-Sequense	-
17	Dimensional Bashicu Martix System	-
18	fake fake fake Z function	yahtzee
19	ω+1 row Y	-
20	Bubby3 TBMS Extended	Bubby3
21	Strong Splatium TBMS	-
22	Bubby3 TBMS Normal	Bubby3
23	Aarex's TBMS	Aarex
24	Aarex's strong ex-UNOCF with $	Aarex
25	Aarex's Redirection	Aarex
26	Hassium's TBMS	Hassium
27	Weak Splatium TBMS	Bubby3
28	α-Ordinaal Notation	Bugit
29	Strong ex-UNOCF Redirection+rows	-
30	Strong ex-UNOCF Defection+1-plus rows	-
31	Uncountable TBMS	-
32	KPrSS	摆烂的小猫
33	Crazy-Hydra Notation	Gomen
34	Arai's OCF	Toshiyasu Arai
35	Patterns of Resemblance	Carlson
36	Bashicu Sudden Matrix	Bashicu
37	Bashicu Hyper Matrix	Bashicu
38	Crane Matrix System	test_alpha0
39	Bashicu Matrix System	Bashicu
40	Bashicu Matrix V4.1	Bashicu

2024年

	名称	作者
1	FOS 911	318`4
2	Fake Fake Fake Z rules	Asheep233 & xyxk
3	Fake Fake Fake Z actions	Yathzee & Aarex
4	X-P	最菜萌新
5	a-Y Description	-
6	ω2 Mountain Notation	Hyp_cos
7	Mutant Martix System	Aarex & Hyp_cos
8	X-Y Sequence	Gomen
9	Nested Crater Y	Bubby3
10	High Elevate System	xyxk
11	Crater Y	Bubby3 & Aarex
12	Differential Matrix System	xyxk & Asheep233
13	SFSS	waffle3z
14	Strong Ω-Y	-
15	Experimental Remaning Matrix	Asheep233
16	Crater BMS	Bubby3 & Aarex
17	Yto's Y-Y	-
18	Transfinite ω Mountain Notation	Hyp_cos
19	CIF's Ω-Y Sequence	CIF & Hyp_cos
20	Transfinite DBMS	-
21	ω-Y Sequence	Yukito & naruyoko
22	ω Mountain Notation	Hyp_cos
23	ω〜Y Sequence (Dimensional)	Gomen
24	ω-Dimension Multi Layer BMS Relation	Asheep233
25	abc Notation	-
26	2-Y Sequence	Yukito & naruyoko
27	Strong Y Sequence	-
28	Remaining Y System	-
29	Y Sequence	Yukito
30	Apotheosis Ordinal Notation	-
31	VZ-Sequense	-
32	Proportional Difference Martix	318`4
33	ω+1 row Y	-
34	-	Test_alpha0
35	Bracket Sequence System	貓娘
36	Bubby3 TBMS Extended	Bubby3
37	Strong Splatium TBMS	-
38	Bubby3 TBMS Normal	Bubby3
39	Aarex's TBMS	Aarex
40	Aarex's strong ex-UNOCF with $	Aarex

2025年

	名称	作者
1	Fake Fake Fake Z rules	Asheep233 & xyxk
2	Fake Fake Fake Z actions	Yathzee & Aarex
3	Fundamental Ordinal Sequence (911)	318`4
4	α-Y Description	-
5	Ω row DBMS	qwerty
6	X Ω-Y Sequence	waking 😰
7	Mutant Martix System	Aarex & Hyp_cos
8	Transfinite ω^ω Mountain Notation	Hyp_cos
9	Defective ω^ω Mountain Notation	Hyp_cos
10	Defective ω^2 Mountain Notation	Hyp_cos
11	Defective ω2 Mountain Notation	Hyp_cos
12	Astral ω2 Mountain Notation	Hyp_cos
13	X-Y Sequence	Gomen
14	Nested Crater Y	Bubby3
15	High Elevate System	xyxk
16	Crater Y	Bubby3 & Aarex
17	Differential Matrix System	xyxk & Asheep233
18	Strong Ω-Y	-
19	Experimental Remaning Matrix	Asheep233
20	Crater BMS	Bubby3 & Aarex
21	Yto's Y-Y	Yto
22	Transfinite ω Mountain Notation	Hyp_cos
23	Transfinite DBMS	-
24	ω-Y Sequence	Yukito & naruyoko
25	ω Mountain Notation	Hyp_cos
26	ω〜Y Sequence (Dimensional)	Gomen
27	ω-Dimension Multi Layer BMS Relation	Asheep233
28	abc Notation	-
29	2-Y Sequence	Yukito & naruyoko
30	Remaining Y System	-
31	Strong Y Sequence	-
32	Y Sequence	Yukito
33	Idealized Y Sequence	-
34	Apotheosis Ordinal Notation	-
35	Vulcaniz Sequense	Vulcaniz
36	Proportional Difference Martix	318`4
37	ω+1 row Y	-
38	Defective Embeeding Notation	Hyp_cos
39	Basic Laver Pattern	Renrui Qi
40	Bracket Sequence System	waffle3z