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Balum is equal to $$f_2(10)$$ using the fast-growing hierarchy.[1] The term was coined by wiki user Denis Maksudov. It is equal to $$10 \times 2^{10} = 10,240$$. The name "bultun" is also equal to this number using Maksudov's system of naming googolisms, although this name isn't explicitly mentioned. This number belongs to the Alpha series.

## Approximations

Notation Lower bound Upper bound
Scientific notation $$1.024\times10^4$$
Arrow notation $$10\uparrow4$$ $$22\uparrow3$$
Steinhaus-Moser Notation 5[3] 6[3]
Copy notation 9[4] 1[5]
Chained arrow notation $$10\rightarrow4$$ $$22\rightarrow3$$
Taro's multivariable Ackermann function A(3,10) A(3,11)
Pound-Star Notation #*(2)*10
PlantStar's Debut Notation [2] [3]
BEAF & Bird's array notation {10,4} {22,3}
Hyper-E notation E4 E[22]3
Bashicu matrix system (0)[101] (0)[102]
Hyperfactorial array notation 7! 8!
Hardy hierarchy $$H_{\omega^2}(10)$$
Slow-growing hierarchy $$g_{\omega^{\varphi(\omega,0)+\varepsilon_0}+\varphi(\omega,0)}(2)$$

## Etymology

The two parts of the name, "bi" and "alum", mean 2 and "a finite ordinal" respectively. So the full name indicates the ordinal index of the FGH.

## Sources

Numbers by Denis Maksudov
Alpha series
Epsilon series
Epsilon(0)-multiplication series: Bultep · Trultep · Quadrultep · Quintultep · Sextultep · Septultep · Octultep · Nonultep · Dekultep · Hektultep · Kilultep · Megultep · Gigultep · Terultep · Petultep · Exultep · Zettultep · Yottultep
Epsilon(0)-exponentiation series: Bexep · Trexep · Quadrexep · Quintexep · Sextexep · Septexep · Octexep · Nonexep · Dekexep · Hektexep · Kilexep · Megexep · Gigexep · Terexep · Petexep · Exexep · Zettexep · Yottexep
Epsilon(0)-tetration series: Bitetrep · Tritetrep · Quadritetrep · Quintitetrep · Sextitetrep · Septitetrep · Octitetrep · Nonitetrep · Dekotetrep · Hektotetrep · Kilotetrep · Megotetrep · Gigotetrep · Terotetrep · Petotetrep · Exotetrep · Zettotetrep · Yottotetrep
Inserted epsilon series: Uninep · Binep · Trinep · Quadrinep · Quintinep · Sextinep · Septinep · Octinep · Noninep · Dekinep · Hektinep · Kilinep · Meginep · Giginep · Terinep · Petinep · Exinep · Zettinep · Yottinep
Inserted zeta series
Inserted eta series
Phi series
Inserted gamma series
Theta series
Psi series
$$I_\alpha$$ series
$$I(\alpha,\beta)$$ series
Initial $$I(\alpha,\beta)$$ series: Unimah · Bimah · Trimah · Quadrimah · Quintimah · Sextimah · Septimah · Octimah · Nonimah · Dekimah · Hektimah · Kilimah · Megimah · Gigimah · Terimah · Petimah · Eximah · Zettimah · Yottimah
Inserted $$I(\alpha,\beta)$$ series: Uninimah · Binimah · Trinimah · Quadrinimah · Quintinimah · Sextinimah · Septinimah · Octinimah · Noninimah · Dekinimah · Hektinimah · Kilinimah · Meginimah · Giginimah · Terinimah · Petinimah · Exinimah · Zettinimah · Yottinimah
M-series