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Petultep is equal to $$f_{\varepsilon_0\times 10^{15}}(10)$$ using the fast-growing hierarchy.[1] The term was coined by wiki user Denis Maksudov.

## Etymology

The 3 parts of the name, "peto", "ult" and "ep", mean $$10^{15}$$, multiplication and $$\varepsilon_0$$ respectively, which form $$\varepsilon_010^{15}$$ when concatenated backwards. So the full name indicates the ordinal index of the FGH.

## Approximations

Notation Approximation
BEAF $$\{10,10 (X \uparrow\uparrow X) 10^{12}+1\}$$[2]
Bird's array notation $$\{10,10 [1 \backslash 2] (10^{15}+1)\}$$
Hyperfactorial array notation $$10![1,10^{15},1,1,2]$$
Extended Cascading-E Notation $$\textrm{E}10\#\text{^^}\#\mbox *\#(10^{15}+1)$$
Hardy hierarchy $$H_{\varepsilon_0^{10^{15}}}(10)$$
Slow-growing hierarchy $$g_{\vartheta(\varepsilon_{\Omega2}(10^{15}-1)+\varepsilon_{\Omega+1})}(10)$$

## Sources

1. My system of number names (FGS) - Traveling To The Infinity
2. Using particular notation $$\{a,b (X \uparrow\uparrow X) c \#\}$$ for $$\{X \uparrow\uparrow b\ \&\ a (X \uparrow\uparrow X) c-1 \#\}$$
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

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