Graham's number - Revision history

Jacobzheng at 08:35, 9 October 2026

2026-10-09T08:35:57Z

← Older revision		Revision as of 08:35, 9 October 2026
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	The current known bounds for <math>N_G</math> are:		The current known bounds for <math>N_G</math> are:
	<math display="block">		<math display="block">
	6 \le N_G \le 13		6 \le N_G \le 10
	</math>		</math>

2026-10-09T08:35:40Z

← Older revision		Revision as of 08:35, 9 October 2026
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	</math>		</math>

	The lower bound comes from the proof that [[BB(5)]] = 47,176,870 and the upper bound from a specific 13-state TM found by ~~50_ft_lock~~ in ~~March~~ 2026 which runs for <math> > f_{\omega + 1}(2\~~,046~~) > g_{64} </math> steps.		The lower bound comes from the proof that [[BB(5)]] = 47,176,870 and the upper bound from a specific 10-state TM found by Jeff Ketchersid in October 2026 which runs for <math>> f_{\omega+1}(2 \uparrow^{36} 3) > g_{64}</math> steps.

	=== History of Graham-beating TMs ===		=== History of Graham-beating TMs ===

2026-10-09T06:50:29Z

History of Graham-beating TMs

← Older revision		Revision as of 06:50, 9 October 2026
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	\|"50_ft_lock"		\|"50_ft_lock"
	\|[https://discord.com/channels/960643023006490684/1331570843829932063/1481871400640839691 Discord Message]		\|[https://discord.com/channels/960643023006490684/1331570843829932063/1481871400640839691 Discord Message]
			\|
			\|-
			\|10
			\|9 October 2026
			\|Jeff Ketchersid
			\|[https://discord.com/channels/960643023006490684/1331570843829932063/1557806386073702622 Discord Message]
			\|
	\|}		\|}

2026-05-22T19:50:15Z

History of Graham-beating TMs: consistent quotation marks, removed link to nonexistent user page (racheline)

← Older revision		Revision as of 19:50, 22 May 2026
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	\|14		\|14
	\|17 Aug 2024		\|17 Aug 2024
	\|~~[[User:~~Racheline~~\|Racheline]]~~		\|"Racheline"
	\|[https://discord.com/channels/960643023006490684/960643023530762341/1274366178529120287 Discord Message]		\|[https://discord.com/channels/960643023006490684/960643023530762341/1274366178529120287 Discord Message]
	\|		\|
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	\|13		\|13
	\|13 March 2026		\|13 March 2026
	\|50_ft_lock		\|"50_ft_lock"
	\|[https://discord.com/channels/960643023006490684/1331570843829932063/1481871400640839691 Discord Message]		\|[https://discord.com/channels/960643023006490684/1331570843829932063/1481871400640839691 Discord Message]
	\|}		\|}

2026-05-22T05:49:28Z

Looks like Wythagoras originally had a 19-state machine, then <4 hours later improved it to 18 states History of Graham-beating TMs

← Older revision		Revision as of 05:49, 22 May 2026
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	\|"Wythagoras"		\|"Wythagoras"
	\|[https://googology.fandom.com/wiki/User_blog:Wythagoras/NEWS!_I_found_a_22-state_machine_that_beats_G! Googology Post]		\|[https://googology.fandom.com/wiki/User_blog:Wythagoras/NEWS!_I_found_a_22-state_machine_that_beats_G! Googology Post]
			\|
			\|-
			\|19
			\|24 Jul 2016
			\|"Wythagoras"
			\|[https://googology.fandom.com/wiki/User_blog:Wythagoras/The_nineteenth_Busy_Beaver_number_is_greater_than_Graham's_Number!?useskin=oasis Googology Post]
	\|		\|
	\|-		\|-

2026-04-06T06:05:44Z

fix run time

← Older revision		Revision as of 06:05, 6 April 2026
Line 22:		Line 22:
	</math>		</math>

	The lower bound comes from the proof that [[BB(5)]] = 47,176,870 and the upper bound from a specific 13-state TM found by 50_ft_lock in March 2026 which runs for <math> > f_{\omega + 1}(2\,~~047~~) > g_{64} </math> steps.		The lower bound comes from the proof that [[BB(5)]] = 47,176,870 and the upper bound from a specific 13-state TM found by 50_ft_lock in March 2026 which runs for <math> > f_{\omega + 1}(2\,046) > g_{64} </math> steps.

	=== History of Graham-beating TMs ===		=== History of Graham-beating TMs ===

2026-03-14T18:36:55Z

Correction

← Older revision		Revision as of 18:36, 14 March 2026
Line 22:		Line 22:
	</math>		</math>

	The lower bound comes from the proof that [[BB(5)]] = 47,176,870 and the upper bound from a specific 13-state TM found by 50_ft_lock in ~~August 2024~~ which runs for <math> > f_{\omega + 1}(2\,047) > g_{64} </math> steps.		The lower bound comes from the proof that [[BB(5)]] = 47,176,870 and the upper bound from a specific 13-state TM found by 50_ft_lock in March 2026 which runs for <math> > f_{\omega + 1}(2\,047) > g_{64} </math> steps.

	=== History of Graham-beating TMs ===		=== History of Graham-beating TMs ===

2026-03-14T18:36:41Z

Update Bounds

← Older revision		Revision as of 18:36, 14 March 2026
Line 19:		Line 19:
	The current known bounds for <math>N_G</math> are:		The current known bounds for <math>N_G</math> are:
	<math display="block">		<math display="block">
	6 \le N_G \le 14		6 \le N_G \le 13
	</math>		</math>

	The lower bound comes from the proof that [[BB(5)]] = 47,176,870 and the upper bound from a specific 14-state TM found ~~Racheline~~ in August 2024 which runs for <math> > f_{\omega + 1}(65\,~~536~~) > g_{64} </math> steps.		The lower bound comes from the proof that [[BB(5)]] = 47,176,870 and the upper bound from a specific 13-state TM found by 50_ft_lock in August 2024 which runs for <math> > f_{\omega + 1}(2\,047) > g_{64} </math> steps.

	=== History of Graham-beating TMs ===		=== History of Graham-beating TMs ===

2026-03-14T18:36:08Z

History of Graham-beating TMs

← Older revision		Revision as of 18:36, 14 March 2026
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	\|[https://discord.com/channels/960643023006490684/960643023530762341/1274366178529120287 Discord Message]		\|[https://discord.com/channels/960643023006490684/960643023530762341/1274366178529120287 Discord Message]
	\|		\|
			\|-
			\|13
			\|13 March 2026
			\|50_ft_lock
			\|[https://discord.com/channels/960643023006490684/1331570843829932063/1481871400640839691 Discord Message]
	\|}		\|}

2026-03-14T08:15:06Z

History of Graham-beating TMs

← Older revision		Revision as of 08:15, 14 March 2026
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	\|"Wythagoras"		\|"Wythagoras"
	\|[https://googology.fandom.com/wiki/User_blog:Deedlit11/Okay,_more_Turing_machines?commentId=4400000000000011880&replyId=4400000000000036301 Googology Comment]		\|[https://googology.fandom.com/wiki/User_blog:Deedlit11/Okay,_more_Turing_machines?commentId=4400000000000011880&replyId=4400000000000036301 Googology Comment]
			\|
			\|-
			\|22
			\|5 August 2014
			\|"Wythagoras"
			\|[https://googology.fandom.com/wiki/User_blog:Wythagoras/NEWS!_I_found_a_22-state_machine_that_beats_G! Googology Post]
	\|		\|
	\|-		\|-