Alphabet & Epstein Numbers

The third phase of Counting really,Really,REALLY High


Copyright 2016-2017 by Louis Epstein,All Rights Reserved

A power-tower of a Zurvanic Absolute Number POPBLED the Zurvanic Absolute Number popbled the Zurvanic Absolute Number times, times
Zurvanic Absolute Numbers,
each surrounded by Moser polygons of a number equal to
the Zurvanic Absolute Number times the Zurvanic Absolute Number power of its upward-counting ordinal as every term in a Zurvanic-Absolute-Number-per-dimension, Zurvanic Absolute Number dimensional Bowers array,
each polygon having a number of sides equal to the number of Zurvanic Absolute Numbers,raised to itself the-Zurvanic-Absolute-Number-popbled Zurvanic Absolute Numbers of times, popbled a number of times equal to the Zurvanic Absolute Number in a Zurvanic-Absolute-Number-in-a-Zurvanic-Absolute-Number-gon-gon times a power tower of the number of polygons surrounding that particular Zurvanic Absolute Number raised to the Zurvanic Absolute Number times its Zurvanic Absolute Number power in a number of layers equal to the Zurvanic Absolute Number times the Zurvanic Absolute Number power of the Zurvanic Absolute Number times itself-raised-to-the-Zurvanic-Absolute-Number-times-its-Zurvanic-Absolute-Number-in-a-Zurvanic-Absolute-Number-gon-power,
the whole popbled the Zurvanic Absolute Number times the number of times expressed by a chain of Conway arrows between every number rising from twenty-nine to the Zurvanic Absolute Number power of the Zurvanic Absolute Number power of the Zurvanic Absolute Number, plus the Zurvanic Absolute Number ultrexed the Zurvanic Absolute Number of times to the Zurvanic Absolute Number, each number repeated the Zurvanic Absolute Number of times,
is defined as "the Number a", first of The Alphabet Numbers.

The convoluted collection of operations described above is the Alphabet Number function.
Perform the Alphabet Number Function on The Number a (substituted in each instance for the Zurvanic Absolute Number) and repeat a times,and you reach the Number A,perform it on A repeating A times and you reach The Number b, and so on through the alphabet.
Performing the function on the Number Z that many times yields the Number aa,followed in sequence by aA,ab,and so forth...after aZ comes Aa,after ZZ comes aaa,and so on.

In this terminology,we quickly realize that TWO plus TWO is a lot less than FOUR, which is more than SIX but much less than ZERO,while every number discussed so far is a great deal less than NOTHING.
We also discover that SOMETHING is much greater than INFINITY even though it doesn't come close to CHUMPCHANGE.What's more,BIGGERTHANINFINITY is way less than MUCHTOOSMALLTOMENTION.
And we realize that we need even more methods of conveying numbers much larger.

Bracket colon notation

The Number expressed by the Number Z Z's is expressed in shorthand as
{Z:Z}
and that expressed by THAT many Zs is
{Z:Z:Z}
while the number expressed by repeating the single-colon-separated Zs Z times is
{Z::Z}
.

The number expressed by THAT many Zs is
{Z:Z::Z}
while the number expressed by using that many colons to separate Zs is
{Z[Z::Z]Z}
Alphabet Numbers separated by N colons convert to
{(first alphabet number)((N-1 colons,second alphabet number -1) repeated second alphabet number -1 times)}

To convey using that many layers of square brackets use
{Z{[Z::Z]Z}}.
Brackets resolve from inside to out and right to left.
{ONE:TWO:THREE:FOUR}
means FOUR repetitions of THREE is the number of repetitions of TWO needed to express the number of repetitions of ONE to express the intended number,while
{ONE[TWO:THREE]FOUR}
means THREE repetitions of TWO is the number of colons to calculate with in repeating FOUR repetitions of FOUR (working leftward and repeating FOUR each successively calculated number of times) to get the number of repetitions of ONE.
The rightmost bracket closes all unclosed pairs,if any are outstanding.

Epstein's First Number

With this groundwork laid,it is finally possible to express numbers big enough to put my name on.

The Number

{GREATERTHANYOUCOULDPOSSIBLYDESCRIBEORIMAGINE
(GREATERTHANYOUCOULDPOSSIBLYDESCRIBEORIMAGINE colons)
{[GREATERTHANYOUCOULDPOSSIBLYDESCRIBEORIMAGINE
(GREATERTHANYOUCOULDPOSSIBLYDESCRIBEORIMAGINE colons)
{[GREATERTHANYOUCOULDPOSSIBLYDESCRIBEORIMAGINE
(GREATERTHANYOUCOULDPOSSIBLYDESCRIBEORIMAGINE colons)
.
.
.
(repeated GREATERTHANYOUCOULDPOSSIBLYDESCRIBEORIMAGINE! layers)
.
.
.
ISAIDGREATERTHANYOUCOULDPOSSIBLYDESCRIBEORIMAGINE!}
Zs express Epstein's First Number,or E(1)... in full "E(1,0,0,0,0...)" as explained hereafter.

The Epstein Number Function

E(n) is graduated to E(n+1) as follows.

1.Popble E(n) E(n) times.
2.Perform the Alphabet Number Function on the number resulting from Step 1,that many times.
3.The Number expressed by the number resulting from Step 2 Zs is then substituted for GREATERTHANYOUCOULDPOSSIBLYDESCRIBEORIMAGINE in every appearance in the expression defining E(1) (retaining the two factorials),and this is repeated that many times.
4.Steps 1-3 are repeated E(n) times.

E(E(E(E(E(...E(n) layers...(n))))))
is also E(n,1).
E(E(E(E(E(...E(n,1) layers...(n,1))))))
is also E(n,2).
E(E(E(E(E(...E(E(n),E(n)layers) layers...(E(n),E(n)))))))
is also E(n,1,1).
E(E(E(E(E(...E(E(E(n),E(n),E(n)),(E(n),E(n),E(n) layers)layers) layers...(E(n),E(n),E(n))))))))
is also E(n,1,1,1).
etc.

The Nominated Epstein Numbers

Epstein's First (Unofficially) NOMINATED Number

And so,the first number I will use in offering a nomination for biggest named number is
E(I,SAID,GREATER,THAN,ANY,OF,YOU,COULD,POSSIBLY,DESCRIBE,OR,IMAGINE!,NOT,IN,SEVENTY,{OCTO:YOTTILLIARD},TIMES,AS,MANY,FORTNIGHTS,AS,THERE,HAVE,BEEN,PLANCK,TIMES,SINCE,THE,BIG,BANG!)

Of course that's so easily beatable...

Epstein's SECOND (Unofficially) Nominated Number

E(THIS,NUMBER,IS,SO,MUCH,BIGGER,THAN,MY,FIRST,NOMINATED,NUMBER,IT,WILL,BOGGLE,ALL,OF,YOUR,MINDS!,SEVENTEEN,{OCTO:YOTTILLIO:ILLIARDS},OF,BUSY,BEAVERS,COULD,NEVER,EVER,COME,ANYWHERE,NEAR,TO,THIS,HUUGE!...repeated Epstein's First Nominated Number,popbled,times...I,MEAN,THIS,NUMBER,IS,TRULY,GARGANTUANLY,TREMENDOUS!)

Epstein's THIRD (Unofficially) Nominated Number

My third nominated number is

the Second Nominated Number with
the Number expressed by
the Second Nominated Number,with the Alphabet Number function performed upon it
the number of times expressed by a chain of Conway arrows between ten repetitions of every number from five to itself ultrexed twice to its factorial,
Zs repetitions
of this number of repetitions
interpolated after the first "THIS",and E(that number of repetitions) repetitions of that number interpolated after the first "NUMBER",and the number of layers of E-subscripting before the immediately preceding number is used to to get the number and its number of repetitions raised to itself in a power-tower of the immediately preceding number of times after every succeeding array generation(Alphabet Number in the specification).

This is the embryo of the Epstein Number Nominating Function.
From this point,to get from Unofficially Nominated Number n to Unofficially Nominated Number n+1,a similar interpolation of additional generations is performed as follows.

1.After the first specified generation in EUNN n,
add the Alphabet Number described by
EUNN n with the Alphabet Number Function performed upon it
E(1,2,3,...E(EUNN n)) times,
Z's,
repetitions of that Alphabet Number.
2.After each succeeding generation,interpolate
EE(...number of layers of subscripting equal to number interpolated after preceding generation raised to itself in a power tower of a number of layers equal to itself)(number interpolated in previous generation))) repetitions of this new number of repetitions.

3.Repeat steps 1 and 2,substituting the entire number achieved after step 2 for EUNN n in step 1,
E(1,2,3,4,...E(E(EUNN n layers of subscripting)(EUNN n))) times.

When EUNN n reaches E(1,2,3,...EE(Epstein's Third Unofficially Nominated number of layers of subscripts)(Epstein's Third Unofficially Nominated Number))) we have reached Epstein's One Step Toward A Little Bit Seriously Nominated Number.

The increment in EUNN n to take ESTALBSNN n to n + 1 is the
E(1,1,2,2,3,3...EE(ESTALBSNN n layers of subscripts)(ESTALBSNN n,repeated ESTALBSNN n times))) power of the previous number.

When ESTALBSNN n reaches E((every integer from 1 repeated twice its square times)...E(E(EEpstein's Fourth Step Toward A Little Bit Seriously Nominated Number) layers of subscripts)(Epstein's Fourth Step Toward a Little Bit Seriously Nominated Number,repeated E(Epstein's Fourth Step Toward a Little Bit Seriously Nominated Number) times))) we have reached Epstein's First A Little Bit Seriously Nominated Number.

The increment in ESTALBSNN n to tale EALBSNN n to n+1 is a power tower of the previous increment raised to E((every integer from 1 repeated thrice its cube times)...E(E(EALBSNN n,repeated E(EALBSNN n layers of subscripts) layers of subscripts)(EALBSNN n), repeated that many times)))) that many times.

When EALBSNN n reaches E((every integer from 1 repeated four times its fourth power times)...E(E(EEpstein's Fifth A Little Bit Seriously Nominated Number,repeated Epstein's Fifth A Little Bit Seriously Nominated Number times ) layers of subscripts)(E(Epstein's Fifth A Little Bit Seriously Nominated Number,repeated Epstein's Fifth A Little Bit Seriously Nominated Number times),repeated E(Epstein's Fifth A Little Bit Seriously Nominated Number) times))) we have reached Epstein's First Step Toward Semi-Seriously Nominated Number.

The increment in EALBSNN n to take ESTSSNN n to n + 1 is a power tower of E(the previous increment raised to E((every integer from 1 repeated four times its fifth power times)...E(E(ESTSSNN n,repeated E(E(ESTSSNN n,repeated ESTSSNN n times) layers of subscripts) layers of subscripts)(ESTSSNN n), repeated that many times)))) that many times) raised to itself that many times.

When ESTSSNN n reaches EE((every integer from 1 repeated four times its sixth power times)...E(E(E(Epstein's Sixth Step Toward Semi-Seriously Nominated Number,repeated E(Epstein's Sixth Step Toward Semi-Seriously Nominated Number) times ) layers of subscripts)(E(Epstein's Sixth Step Toward Semi-Seriously Nominated Number,repeated E(Epstein's Sixth Step Toward Semi-Seriously Nominated Number) times),repeated E(Epstein's Sixth Step Toward Semi-Seriously Nominated Number) times)))) we have reached Epstein's First Semi-Seriously Nominated Number.

The increment in ESTSSNN n to take ESSNN n to n + 1 is a power tower of E(the previous increment raised to E((every integer from 1 repeated four times its seventh power times)...E(E(ESSNN n,repeated E(E(ESSNN n,repeated E(E(ESSNN n,repeated ESSNN n times) times) layers of subscripts) layers of subscripts)(E(ESSNN n,repeated ESSNN n times)), repeated that many times)))) that many times) raised to itself E(that many times) times.

When ESSNN n reaches EE((every integer from 1 repeated four times its eighth power times)...E(E(E(Epstein's Seventh Semi-Seriously Nominated Number,repeated E(Epstein's Seventh Semi-Seriously Nominated Number) times ) layers of subscripts)(E(Epstein's Seventh Semi-Seriously Nominated Number,repeated E(Epstein's Seventh Semi-Seriously Nominated Number) times),repeated E(Epstein's Seventh Semi-Seriously Nominated Number) times))),repeated E(that many times) times) we have reached Epstein's First Step Toward Almost Seriously Nominated Number.

The increment in ESSNN n to take ESTASNN n to n + 1 is a power tower of E(the previous increment raised to E((every integer from 1 repeated four times its ninth power times)...E(E(ESTASNN n,repeated E(E(ESTASNN n,repeated E(E(ESTASNN n,repeated E(ESTASNN n,repeated ESTASNN n times) times) times) layers of subscripts) layers of subscripts)(E(ESTASNN n,repeated E(ESTASNN n) times)), repeated that many times)))) that many times) raised to itself E(that many times,repeated E(that many times) times) times.

When ESTASNN n reaches EE((every integer from 1 repeated five times its tenth power times)...E(E(E(Epstein's Eighth Step Toward Almost Seriously Nominated Number,repeated E(Epstein's Eighth Step Toward AlmostSeriously Nominated Number) times ) layers of subscripts)(E(Epstein's Eighth Step Toward Almost Seriously Nominated Number,repeated E(Epstein's Eighth Step Toward Almost Seriously Nominated Number) times),repeated E (Epstein's Eighth Step Toward Almost Seriously Nominated Number, repeated E(Epstein's Eighth Step Toward Almost Seriously Nominated Number) times) times))),repeated E(that many times,repeated E(that many times)times ) times) we have reached Epstein's First Almost Seriously Nominated Number.

The increment in ESTASNN n to take EASNN n to n + 1 is a power tower of E(the previous increment raised to E((every integer from 1 repeated six times its twelfth power times)...E(E(EASNN n,repeated E(E(EASNN n,repeated E(E(EASNN n,repeated E(EASNN n,repeated E(EASNNN n,repeated EASNN n times) times) times) times) layers of subscripts) layers of subscripts)(E(EASNN n,repeated E(EASNN n,repeated EASNN n times) times)), repeated that many times)))) that many times) raised to itself E(that many times,repeated E(E(that many times)) times) times.

When EASNN n reaches EE((every integer from 1 repeated ten times its twentieth power times)...E(E(E(Epstein's Ninth Almost Seriously Nominated Number,repeated E(Epstein's Ninth Almost Seriously Nominated Number,repeated E(Epstein's Ninth Almost Seriously Nominated Number) times) times ) layers of subscripts)(E(Epstein's Ninth Almost Seriously Nominated Number,repeated E(Epstein's Ninth Almost Seriously Nominated Number) times),repeated E (Epstein's Ninth Almost Seriously Nominated Number, repeated E(Epstein's Ninth Almost Seriously Nominated Number) times) times))),repeated E(that many times,repeated E(that many times)times ) times) we have reached Epstein's First Step Toward Seriously Nominated Number.

The increment in EASNN n to take ESTSNN n to n + 1 is a power tower of E(the previous increment raised to E((every integer from 1 repeated ten times its twenty-fifth power popbled times)...E(E(ESTSNN n,repeated E(E(ESTSNN n,repeated E(E(ESTSNN n,repeated E(ESTSNN n,repeated E(ESTSNN n,repeated E(ESTSNN n) times) times) times) times) layers of subscripts) layers of subscripts)(E(ESTSNN n,repeated E(ESTSNN n,repeated E(ESTSNN n) times) times)), repeated that many times)))) that many times) raised to itself E(E(that many times),repeated E(E(E(that many times))) times) times.

When ESTSNN n reaches EE((every integer from 1 repeated twenty times its thirtieth power popbled times)...E(E(E(Epstein's Tenth Step Toward Seriously Nominated Number,repeated E(Epstein's Tenth Step Toward Seriously Nominated Number,repeated E(Epstein's Tenth Step Toward Seriously Nominated Number) times) times ) layers of subscripts)(E(Epstein's Tenth Step Toward Seriously Nominated Number,repeated E(Epstein's Tenth Step Toward Seriously Nominated Number) times),repeated E (Epstein's Tenth Step Toward Seriously Nominated Number, repeated E(Epstein's Tenth Step Toward Seriously Nominated Number,repeated E(Epstein's Tenth Step Toward Seriously Nominated Number) times) times) times))),repeated E(that many times,repeated E(that many times)times ) times) we have at last reached Epstein's First Seriously Nominated Number.

The increment in ESTSNN n to take ESNN n to n + 1 is a power tower of E(the previous increment raised to E((every integer from 1 repeated twenty-two times its fortieth power,popbled twice,times)...E(E(ESNN n,repeated E(E(ESNN n,repeated E(E(ESNN n,repeated E(ESNN n,repeated E(E(ESNN n),repeated E(ESNN n) times) times) times) times) layers of subscripts) layers of subscripts)(E(E(ESNN n),repeated E(ESNN n,repeated E(ESNN n,repreated ESNN n times)) times) times)), repeated that many times)))) that many times) raised to itself E(E(that many times),repeated E(E(E(that many times))) times) times.

Now that we have defined the Seriously Nominated Numbers...

The Transitional Nominee

What I temporarily consider as the largest named number with a prescribed method of calculation as the never-ending search for more qualifying numbers proceeds is not even an Epstein Number,but an Alphabet Number.

The one expressed by the

E((every integer starting with 1,repeated E(E(nn... in a power tower of nn layers) layers of subscripts)(nn... in a power tower of nn layers)) times...to the last repetition of E(E(Epstein's First Seriously Nominated Number layers of subscripts)(Epstein's First Seriously Nominated Number, repeated E(Epstein's First Seriously Nominated Number) times)) )
Seriously Nominated Number of

Z's,
all bracketed and individually separated by like number of colons in each instance.

Getting Really Serious

It now becomes time to again clean up the function and take it forward.

E(E(E(...(E(Transitional Nominee,repeated E(Transitional Nominee) times) layers of subscripts)...(E(1),E(1,1),etc until we reach E(every integer starting with 1,repeated E(E(nn... in a power tower of nn... in a power tower of E(nn,repeated E(Transitional Nominee) times) layers)
layers of subscripts)(nn... in a power tower of E(nn) layers)) times...to the last repetition of E(E(E(Transitional Nominee) layers of subscripts)(E(Transitional Nominee), repeated E(Transitional Nominee,repeated E(Transitional Nominee) times)))

is Epstein's First Really Seriously Nominated Number,or E1R1SNN.

To increment E1RnSNN to E1Rn+1SNN one must substitute
(E((E1R1SNN)layers of subscripts) (E(every integer starting with 1,repeated E1R1SNN raised to itself in a power tower of E1R1SNN layers,times,to the last repetition of E(E(E(E1R1SNN))layers of subscripts) (E(E1R1SNN), repeated E((E1R1SNN),repeated E(E(E1R1SNN)times)))) for every occurrence of "Transitional Nominee" in the above formula if n=1,and this formula,with every occurrence of E1Rn-1SNN replaced by E1RnSNN, in every amended formula thereafter.

When n of E1RnSNN reaches E(E1RE(E1R1SNN layers of subscripts)((E1R1SNN,repeated E(E1R2SNN) times))SNN) we have reached Epstein's First Really,Really Seriously Nominated Number or E2R1SNN.

Hereafter,EnRE(E(EnRE(n)SNN) layers of subscripts)((EnRE(n)SNN,repeated E(EnRE(n,n)SNN) times))SNN = En+1R1SNN.

The formula for incrementing the subscripted R-number in succeeding generations of the superscripted-prefixed R number is modified by requiring that the substitution of the expanded formula for each occurrence of the subscripted number take place not once,but EnR1SNN times.

Of course n in nR is like the number of an Epstein number just shorthand for (n,0,0,0,0...).
Thus,
EE(E(E(E(E(...E(n) layers...(EnR1SNN))))))R1SNN
is also E(n,1)R1SNN.
EE(E(E(E(E(...E(n,1) layers...(E(n,1)R1SNN)))))R1SNN
is also E(n,2)R1SNN.
EE(E(E(E(E(...E(E(n),E(n)layers) layers...(E(E(n,n)R1SNN), E(E(n,n)R1SNN))))))))R1SNN
is also E(n,1,1)R1SNN.
EE(E(E(E(E(...E(E(E(n),E(n),E(n)),(E(n),E(n),E(n) layers)layers) layers...(E(E(n,n,n)R1SNN), (E(n,n,n)R1SNN),(E(n,n,n)R1SNN))))))))) R1SNN
is also E(n,1,1,1)R1SNN.
etc.

Armed with this escalation formula,we proceed to define the

First Kingmaker Number

As in,not taking the nomination itself,but has a role in defining it. As with the Transitional Nominee,it's an Alphabet Number,expressed by Z's of a quantity expressed by an Epstein Number.

The preceding superscript of R has as its comma-separated generations every integer starting with 1,repeated E(E (every integer from 1 to E(E9R9SNN)R9SNN)R9SNN) raised to itself in a power tower of E (every integer from 1 to EE9R9SNN R9SNN) layers,times,to the last repetition of E(E(E(E(9,9)RE(9)SNN))layers of subscripts) (E(E9R9SNN), repeated E((E9R9SNN),repeated E(E(E9R9SNN)times))times)))
The subscript is E(9,9,9)RE(9,9,9)SNN.
And the First Kingmaker Number is that many Zs individually separated by as many colons within a set of brackets.

Awarding the Next Transitional Nomination....

The superscript of the number that at this point bears my nomination as largest named number is
1.Every integer from 1 to E(First Kingmaker NumberKingmaker Number repetitions of every number from 1 to E(First Kingmaker Number))R(E(First Kingmaker Number))SNN, each number repeated (E(n) layers of subscripts)(E(E(n) repeated E(n) times)).We shall call the designated maximum number here the Terminal Number.
2.Every possible sequence of any two integers,duplication permitted between 1 and the Terminal Number...each sequence ordered in ascending order of Epstein Number value potential,each repeated (E(the sequence) layers of subscripts)(E(E(the sequence) repeated E(the sequence) times)).
Then every possible sequence of three integers between 1 and the Terminal Number,likewise.
Then every possible sequence of four integers between 1 and the Terminal Number,likewise...et cetera.
3.After the last repetition of the entire sequence of integers, repeat steps 1 and 2 working out of the set of integers between 2 and the Terminal Number,with the number of layers of subscripts, and of the repetitions of each E(number) or E(sequence) in defining the number of repetitions,raised to a power tower with the Kingmaker Number as the base,followed by E(n)(or E(sequence)) layers of E(n) (or E(sequence)) followed by a number of ascending layers of First Kingmaker Numbers defined by the value of the E-layers.

4.Repeat step 3 with the set of integers between 3 and the Terminal Number,then the set between 4 and the Terminal Number,etc.
5.Repeat steps 1-4 E(First Kingmaker Number) times,with the number of subscripts/repetitions never resetting but continuing to be exponentiated throughout.

The subscript of this number is E(First Kingmaker Number repetitions of Terminal Number).

Since I was implored by a reader who stayed up until 1 AM reading the previous nomination to keep going...

Getting Extraordinarily Serious

EEE(E(...E(E(last transitional nominee layers of subscripts)(last transitional nominee,repeated E(last transitional nominee) times) layers of subscripts)...(E(Alphabet Number represented by last transitional nominee Zs,repeated E(E(that Alphabet Number,repeated E(that Alphabet Number) times) times) RE(E(last transitional nominee,repeated E(E(last transitional nominee,repeated E(last transitional nominee) times)times)SNN
is Epstein's First Extraordinarily Seriously Nominated Number,or EE1SNN.

EE(E...E(EEnSNN,repeated E(EEnSNN,repeated... (E(EEnSNN,repeated E(EEnSNN)times repetitions of this)...times)times) layers of subscripts) E(EEnSNN,repeated E (EEnSNN,repeated E(EEnSNN, repeated... (E(EEnSNN,repeated E(EEnSNN)times repetitions of this)...times)times) layers of subscripts...(E(E(E(EEnSNN))) times) = EEn+1SNN.

When n reaches E(the following sequence:)
1.Every integer from 1 to E(E(EE1SNNEE2SNN...(power tower rising to EEEE999SNNSNN)) repetitions of every number from 1 to E(E(EE{REALLY::BIG::ALPHABET::NUMBER}SNN,repeated E(EE{AN::EVEN::BIGGER::ALPHABET::NUMBER}SNN times) ))SNN, each number repeated (E(EEnSNN) layers of subscripts) (E(E(EEnSNN) repeated E((EEnSNN) times)). We shall call the designated maximum number here the first terminal number of this specification.
2.Every possible sequence of any two integers,duplication permitted between 1 and the terminal number...each sequence ordered in ascending order of Epstein Number value potential,each repeated (E(the sequence) layers of subscripts)(E(E(the sequence) repeated E(the sequence) times)).
Then every possible sequence of three integers between 1 and the terminal number,likewise.(always no limit on duplicate numbers)
Then every possible sequence of four integers between 1 and the terminal number,likewise...et cetera.
3.After the last repetition of the entire sequence of integers, repeat steps 1 and 2 working out of the set of integers between 2 and the terminal number,with the number of layers of subscripts, and of the repetitions of each E(number) or E(sequence) in defining the number of repetitions,raised to a power tower with the terminal number as the base,followed by E(E(n))(or E(E)sequence))) layers of E(E(n)) (or E(E(sequence))) followed by a number of ascending layers of EEn counting up from 1SNN numbers defined by the value of the E-layers.
4.Repeat step 3 with the set of integers between 3 and the terminal number,then the set between 4 and the terminal number,etc.
5.Repeat steps 1-4 E(first terminal number) times,with the number of subscripts/repetitions never resetting but continuing to be exponentiated throughout.
6.Repeat steps 1-5 E(E...(E(first terminal number) layers of subscripts) (E(first terminal number),repeated E(first terminal number) times) times, substituting the number of repetitions used for the final sequence of numbers in the last cycle of step 5 for the first terminal number.

we have reached Epstein's First Extra Extraordinarily Seriously Nominated Number,or EE1ESNN,which starts a new generation.

Incrementing EEnESNN uses the formula used for incrementing EEnSNN except that EEnESNN is substituted for EEnSNN on every occasion and in the specifications of the numbers of layers of subscripts and of the repetitions,this substitution of the full number of subscripts and repetitions for the specified number is then repeated EEnESNN times.

EEEEEE...EEnESNN layers... EEnESNNESNNESNNESNN =EnE1ESNN.

When this latest n reaches E(the following sequence:)
1.Every integer from 1 to E(E(EE1ESNNEE2ESNN...(power tower rising to EEEE(999 layers of subscripts) EE999ESNNESNNESNN)) repetitions of every number from 1 to E(E(EEEE...E(999) layers of subscripts...EE(999)ESNNESNN,repeated E(EEE E({AN::EVEN::LARGER::ALPHABET::NUMBER}) layers of subscripts...EE(99999)ESNN ESNN times) ))ESNN, each number repeated (E(EEnESNN) layers of subscripts) (E(E(EEnESNN) repeated E((EEnESNN) times)). We again call the designated maximum number here the first terminal number of this specification.
2.Every possible sequence of any two integers,duplication permitted between 1 and the terminal number...each sequence ordered in ascending order of Epstein Number value potential,each repeated (E( EE(the sequence)ESNN) layers of subscripts)(E(E(EE(the sequence)ESNN) repeated E(EE(the sequence)ESNN times)).
Then every possible sequence of three integers between 1 and the terminal number,likewise.(always no limit on duplicate numbers)
Then every possible sequence of four integers between 1 and the terminal number,likewise...et cetera.
3.After the last repetition of the entire sequence of integers, repeat steps 1 and 2 working out of the set of integers between 2 and the terminal number,with the number of layers of subscripts, and of the repetitions of each E(number) or E(sequence) in defining the number of repetitions,raised to a power tower with the terminal number as the base,followed by E(E(EEnESNN)) (or E(E(EEsequenceESNN))) layers of E(E(EEnESNN)) (or E(E(EEsequenceESNN))) followed by a number of ascending layers of EEn counting up from 1ESNN numbers defined by the value of the E-layers.
4.Repeat step 3 with the set of integers between 3 and the terminal number,then the set between 4 and the terminal number,etc.
5.Repeat steps 1-4 E(first terminal number) times,with the number of subscripts/repetitions never resetting but continuing to be exponentiated throughout.
6.Repeat steps 1-5 E(E...(E(EEfirst terminal numberESNN) layers of subscripts)(E(EEfirst terminal numberESNN),repeated (EE(EEfirst terminal numberESNN)ESNN layers of subscripts)(EEfirst terminal numberESNN,repeated (EEfirst terminal numberESNN)times)) times) times, substituting the number of repetitions used for the final sequence of numbers in the last cycle of step 5 for the first terminal number.

we reach another arbitary turning point number.
When we take the Alphabet Number represented by this many Zs each separated by a like number of colons and a layer of nesting curly and square brackets,we plug it into this:

EEE...(repeat this E...(repeat this E this Alphabet NumberE(E(this Alphabet Number)ESNN times) (E(E(this Alphabet Number))EE(This Alphabet Number)ESNN E(E(this Alphabet Number)ESNN times) E(E(this Alphabet Number)ESNN times) E(E(this Alphabet Number)ESNN

(The number of superscripting layers is invoked upon the number of superscripting layers the like number of times) to yield Epstein's First Very Extraordinarily Seriously Nominated Number,or EV1ESNN,

Incrementing EVnESNN uses the formula used for incrementing EEnESNN except that EVnESNN is substituted for EEnESNN on every occasion and in the specifications of the numbers of layers of subscripts and of the repetitions,this substitution of the full number of subscripts and repetitions for the specified number is then repeated EV(EVnESNN layers of subscripts)(E(EVnESNN),repeated E(EVnESNN) times)ESNN times.

When the number of subscripts in EVnESNN and this latest n reaches EV(the following sequence:)ESNN
1.Every integer from 1 to E(E(EV1ESNNEV2ESNN...(power tower rising to EVEV(E(9,9,9) layers of subscripts) EEE(9,9,9)ESNNESNNESNN)) repetitions of every number from 1 to E(E(EVEV...E(9,9,9) layers of subscripts...EVE(9,9,9)ESNNESNN,repeated E(EVE E({AN::ENORMOUSLY::LARGER::ALPHABET::NUMBER}) layers of subscripts...EVE(9,9,9,9,9)ESNN ESNN times) ))ESNN, each number repeated (E(EVnESNN) layers of subscripts) (E(E(EVnESNN) repeated E((EVnESNN) times))times. We again call the designated maximum number here the "first terminal number" of this specification.
2.Every possible sequence of any two integers,duplication permitted between 1 and the terminal number...each sequence ordered in ascending order of Epstein Number value potential,each repeated (E( EV(the sequence)ESNN) layers of subscripts)(E(E(EV(the sequence)ESNN) repeated E(EV(the sequence)ESNN times)).
Then every possible sequence of three integers between 1 and the terminal number,likewise.(always no limit on duplicate numbers)
Then every possible sequence of four integers between 1 and the terminal number,likewise...et cetera.
3.After the last repetition of the entire sequence of integers, repeat steps 1 and 2 working out of the set of integers between 2 and the terminal number,with the number of layers of subscripts, and of the repetitions of each E(number) or E(sequence) in defining the number of repetitions,raised to a power tower with the terminal number as the base,followed by E(E(EVnESNN)) (or E(E(EVsequenceESNN))) layers of E(E(EVnESNN)) (or E(E(EVsequenceESNN))) followed by a number of ascending layers of EVEVn counting up from 1ESNNESNN numbers defined by the value of the E-layers.
4.Repeat step 3 with the set of integers between 3 and the terminal number,then the set between 4 and the terminal number,etc.
5.Repeat steps 1-4 EV(first terminal number)ESNN times,with the number of subscripts/repetitions never resetting but continuing to be exponentiated throughout.
6.Repeat steps 1-5 E(E...(E(EVfirst terminal numberESNN) layers of subscripts)(E(EVfirst terminal numberESNN),repeated (E(EVfirst terminal numberESNN)layers of subscripts) E(EVfirst terminal numberESNN,repeated (EVE(first terminal number,repeated itself ultrexed itself times to itself times)ESNN)times)) times) times, substituting the number of repetitions used for the final sequence of numbers in the last cycle of step 5 for the first terminal number.
7.Repeat steps 1-6 EV(number of subscripts equal to the number of times steps 1-5 were repeated in the previous repetition of step 6)(EVthat number, repeated that many timesESNN,repeated itself cubed times)ESNN times,substituting the number of repetitions used for the final sequence of numbers in the last cycle of step 6 for the first terminal number.
Steps 8- E(E...(E(EVfirst terminal numberESNN) layers of subscripts)(E(EVfirst terminal numberESNN),repeated (E(EVfirst terminal numberESNN)layers of subscripts) E(EVfirst terminal numberESNN,repeated (EVE(first terminal number,repeated itself ultrexed itself times to itself times)ESNN)times)) times) times). These steps follow the pattern laid out in Step 7,relating to Step (Step number -1).

we reach another passing Kingmaker-Number...
The Alphabet Number expressed by that many Zs each separated by colons,the first two by that many,each working rightward by the previous number ultrexed that number of times to itself is another, while if one uses that Alphabet Number as the first terminal number of the specification used to generate the previous Kingmaker-Number and then repeats this process that whole Kingmaker Number of times, one reaches Epstein's first Very,Very Extraordinarily Seriously Nominated Number,or E2V1ESNN.

Incrementing E2VnESNN uses the formula used for incrementing EVnESNN except that E2VnESNN is substituted for EVnESNN on every occasion and in the specifications of the numbers of layers of subscripts and of the repetitions,this substitution of the full number of subscripts and repetitions for the specified number is then repeated EV(E2VnESNN layers of subscripts)(E(E2VnESNN),repeated E(E2VnESNN,repeated E2V(E(n,n,n))ESNN times) times)ESNN times.

E2VE2V (E(2,3,4,...E2V3ESNN, each number repeated E2Vthat numberESNN times) layers of subscripts) (E(2,3,4,...E2V3ESNN, each number repeated E2Vthat number popbled itself timesESNN times) ESNN ESNN

will serve as another passing Kingmaker-Number...
The Alphabet Number expressed by that many Zs each separated by colons,the first two by that many,each working rightward by raising the number of colons to the previous number ultrexed that number of times to (itself popbled itself-Zs ultrexed (itself-{Z:Z}s popbled itself-{Z::Z::Z}s popbled...(that-Kingmaker-Number-popbled of Zs layers of nesting))
was my standard-bearing nominee as highest named calculable number when a disk crash took this page offline in April 2017.

Getting this page back up calls for

The Resurrection Celebration Number

So let's ultrex the Alphabet Number expressed by E(every number from 2 to the previous nominee repeated itself ultrexed itself times to E(E(every number from 1 to itself cubed,repeated E (every number from 1 to itself to the 4th power,repeated...(so on until E(every number from 1 to itself to the E2VE(itself)ESNN power) is reached) layers of subscripts)times) Z's E(WE,ARE,BACK,ONLINE,HALLELUJAH!) times to its E(RESURRECTION,CELEBRATION) power and popble that itself-ultrexed-twice-to-its-cube times.

Resurrection Celebration Number 2

Ultrex the Alphabet Number expressed by E(every number from 2 to the Resurrection Celebration Number repeated itself popbled itself times to E(E(every number from 1 to itself cubed, repeated E(every number from 1 to itself to the 4th power,repeated... (so on until E(every number from 1 to itself to the E2VE(itself)ESNN power) is reached) layers of subscripts)times) Z's each separated by that-many-raised-to-the-popbled-ordinal-of-the-Z colons E(LET,US,ALL,ROW,THE,BOAT,ASHORE,HALLELUJAH!) times to its EV(RESURRECTION,CELEBRATION,QUOTH,THE,RAVEN,FOREVERMORE!) ESNN power and popble that itself-popbled-ten-times-itself-popbled times.

Prove another comparably calculable number is bigger,and I'll go further...


If this number feels too small,popble the number the-number-popbled times, and repeat until the feeling goes away...or

Keep counting...

Louis Epstein


First edition January 4,2016
Second Nominated Number added January 5,2016
HTML tweaks and Third Nominated Number added January 6,2016
Expansion to the Transitional Nominee on January 9th 2016,and new nominee,followed by Extraordinarily Serious extension, January 12th.Further nominees January 13th and 15th. Enhancement with ultrex & nominee tweaks February 4th-11th.
Correction & E2VESNN incrementation added April 4th.
New nominee tweaks July 8th 2016 and March 4th 2017.
Resurrection Celebration September 11th 2017, second celebration on the 18th,some fixes the 21st.

Do you just want a shortcut to the ultimate number? (not computable)
A web project of Putnam Internet Services.