Sam's Number

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Sam's Number is an ill-defined number described in an article written on Googology Wiki in February 2014 by a user under the name "SammySpore":

Sam's number is so gigantically huge it cannot be described. It boggles the mind. Actually, it would boggle a megafugafzgargoogolplex minds.

If you want a small glimpse of how big it is, here. Sam's Number is enormously larger than Rayo's Number. It can fill a greagol multiverses. Actually it can fill so much more than that, it is undescribable.

The article was quickly deleted due to the site's restrictions regarding unsourced original content, but grew into an inside joke within the googology community as an example of lazy and poorly defined googology.

Since, Sam's Number has been assigned a multitude of possible defined values by many sources and thus, is an ill-defined number which cannot be defined using any typical notations. It remains a completely undefined number as of now. In addition, DeepLineMadom eventually suggested under his blog post that Sam's Number should no longer be intended to have a value larger than that of Oblivion or Utter Oblivion as previously suggested by the List of googolisms/Uncomputable numbers, considering it is not actually treated in the context of a defined number to begin with, and could hypothetically be assigned any number of definitions. (See also List of googolisms/Uncomputable numbers#Warning.)

Sam's Number was mentioned in a joke article written by Sbiis Saibian about Easter bunnies.

Sam's Number has also appeared in the salad number Croutonillion.

Definitions and analyses from other users

Googology Wiki user I am a McCree God claimed on his site that he calculated Sam's Number, and the result was equal to \(10^{((10\uparrow\uparrow)^{202}(10\uparrow)^{96}8.0291 \times 10^{218})-1}\).

Googology Wiki user DeepLineMadom claimed on his site that he again calculated Sam's Number using a different method, and the result was a salad number. \(\mathrm{Sam}_{\omega_{\varepsilon_{\omega_1^{\mathrm{CK}}\times f_{\psi(K)\times \mathrm{E}100\#100\#100}(\mathrm{Rayo}(10^{100}))}}^{\mathrm{CK}}}(\)\(\text{Large Number Garden Number}\)\()\), using \(\mathrm{Sam}\) function. The definition and its ill-definedness can be found here.

Googology Wiki user HaydenTheGoogologist2009 claimed on his site that he calculated Sam's Number using another method, and the result also turned out to be a salad number.

\(M_{\omega^{\text{CK}}_{\psi_0(\varepsilon_{\Omega_{\Omega_{\Omega_{\Omega_{\Omega_{\omega_1^{\text{CK}}}}}}} * \Phi_1(1) + 1}) * f_{\psi(K(2;0) * M(2;0) * I(1, 0, 0, 0) * \Omega(1, 0, 0)) * \text{E}100*(*(*(*(*(*(\#))))))\{\&(\&(\&(\#))),\#+1,1,2}\text{^^^^^}\#\text{^^^^^}\#>\#\text{^^^^^}\#>\#\text{^^^^^}\#>\#\text{^^^^^}\#>\#\text{^^^^^}\#>\#\text{^^^^^}(\#+\#+\#+\#+\#)\text{^^^^^}\#\#\#\#\#*\#*\#*\#*\#*\#\text{**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^**^^}\#\#\#\#\#\#\#\#\#\#\#\{\#\{\#\{\#\{\#\{\#\{\#\{\#\{\#\{\#\{\#\text{^^^^^}\#\text{^^^^}\#\text{^^^}\#\text{^^}\#\text{^}\#*\#\#+\#\}\#\}\#\}\#\}\#\}\#\}\#\}\#\}\#\}\#\}\#\#\#\#\#\#\#\#\#\#\#*\#\#\#\#\#\#\#\#\#\#100\#\#\#\#\#\#\#\#\#\#100\#\#\#\#\#\#\#\#\#100\#\#\#\#\#\#\#\#100\#\#\#\#\#\#\#100\#\#\#\#\#\#100\#\#\#\#\#100\#\#\#\#100\#\#\#100\#\#100\#100\#\#1\#2}(\text{FOOT}^{10}(10^{100}) + \text{Rayo}(10^{100})) + \{10, 100 / 2\}}(\text{Ultimate oblivion} + \text{large number garden number})\)

using the \(M\) function. Furthermore, HaydenTheGoogologist2009 claimed on his site that he made 12 variations on his version of Sam's Number, which was inspired by W. A. Mozart's “Twelve Variations on 'Ah vous dirai-je, Maman'".

Googology wiki user Nihilustheabsolutist “calculated” Sam’s number on his site which turned out to be a salad number.

(((E@((E#(((F_M(Sam^{Megafugafzgargoogolplex}(无S(Large number garden number^{INSANE FOOT})))#¹⁰⁰Hyper oblivion))Large number garden number)) X fish number 8 (yes, legit fish number 8) + Cramog = Sam’s number. using Sam’s function, Strong entropic function, Cascading E notation, and hyper E notation (Also F_M is Mahlo cardinal in fgh) It was updated later to

Sam number =(((E@((E#((Fm(Sam^Megafugafzgargoogolplex(无S(Large number garden numberINSANE FOOT)))#100Hyper oblivion))Large number garden number)) X fish number 8 (yes, legit fish number 8)

Googology Wiki user DeepLineMadom also called this number Dead Sam, Death Sam, Sammy Pranker, Sammy Hoaxer, Derpy Sam, Sammy Rayo, Ultra Sam, The Dead Jokers, and S.A.M Number, and also referenced different capitalizations of the number in his list of alternate capitalizations of Sam's Number, most notably the all-capital SAM'S NUMBER meant to serve as a joke with stronger irony.

Nihilustheabsolutist coined Spore’s number, the true hyper start of all salads, Sammyspores number, Sammy's number, Large Number Sam Number, Boggle-megafugafzgargoogolplex, END SAM, and Sammy and friends (episode 1) which are equal to Sam's number.

Googology Wiki user HaydenTheGoogologist2009 determined that there are at least \(10! = 3,628,800\) arrangements for the capitalizations for the number Sam's Number.