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The pentaelgathor regiment is a series of numbers from E100#^#^#####100 to E100(#^#^#^6)90 defined using Cascading-E notation (i.e. beginning from pentaelgathor and up to pentaelgathornonagintice).[1] The numbers were coined by Sbiis Saibian.

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## List of numbers of the regiment Edit

 Name of number Cascading-E notation (definition) Fast-growing hierarchy (approximation) pentaelgathor E100#^#^#####100 $$f_{\omega^{\omega^{\omega^5}}}(100)$$ grand pentaelgathor E100(#^#^#^5)100#2 $$f_{\omega^{\omega^{\omega^5}}}^2(100)$$ grangol-carta-pentaelgathor E100(#^#^#^5)100#100 $$f_{\omega^{\omega^{\omega^5}}+1}(100)$$ pentaeltrigathor E100(#^#^#^5)100(#^#^#^5)100 $$f_{\omega^{\omega^{\omega^5}}2}(100)$$ pentaeltergathor E100(#^#^#^5)100(#^#^#^5)100(#^#^#^5)100 $$f_{\omega^{\omega^{\omega^5}}3}(100)$$ pentaelgathor-by-hyperion E100(#^#^#^5)*#100 $$f_{\omega^{\omega^{\omega^5}+1}}(100)$$ pentaelgathor-by-godgahlah E100(#^#^#^5)*#^#100 $$f_{\omega^{\omega^{\omega^5}+\omega}}(100)$$ pentaelgathor-by-godgathor E100(#^#^#^5)*#^#^#100 $$f_{\omega^{\omega^{\omega^5}+\omega^\omega}}(100)$$ pentaelgathor-by-gralgathor E100(#^#^#^5)*#^#^##100 $$f_{\omega^{\omega^{\omega^5}+\omega^{\omega^2}}}(100)$$ pentaelgathor-by-thraelgathor E100(#^#^#^5)*#^#^###100 $$f_{\omega^{\omega^{\omega^5}+\omega^{\omega^3}}}(100)$$ pentaelgathor-by-terinngathor E100(#^#^#^5)*#^#^####100 $$f_{\omega^{\omega^{\omega^5}+\omega^{\omega^4}}}(100)$$ deutero-pentaelgathor E100(#^#^#^5)*(#^#^#^5)100 $$f_{\omega^{\omega^{\omega^5}2}}(100)$$ trito-pentaelgathor E100(#^#^#^5)*(#^#^#^5)*(#^#^#^5)100 $$f_{\omega^{\omega^{\omega^5}3}}(100)$$ teterto-pentaelgathor E100(#^#^#^5)*(#^#^#^5)*(#^#^#^5)*(#^#^#^5)100 $$f_{\omega^{\omega^{\omega^5}4}}(100)$$ pepto-pentaelgathor E100#^(#^#^5*#)5 $$f_{\omega^{\omega^{\omega^5}5}}(100)$$ exto-pentaelgathor E100#^(#^#^5*#)6 $$f_{\omega^{\omega^{\omega^5}6}}(100)$$ epto-pentaelgathor E100#^(#^#^5*#)7 $$f_{\omega^{\omega^{\omega^5}7}}(100)$$ ogdo-pentaelgathor E100#^(#^#^5*#)8 $$f_{\omega^{\omega^{\omega^5}8}}(100)$$ ento-pentaelgathor E100#^(#^#^5*#)9 $$f_{\omega^{\omega^{\omega^5}9}}(100)$$ dekato-pentaelgathor E100#^(#^#^5*#)10 $$f_{\omega^{\omega^{\omega^5}10}}(100)$$ hecato-pentaelgathor E100#^(#^#^5*#)100 $$f_{\omega^{\omega^{\omega^5+1}}}(100)$$ pentaelgridgathor E100#^(#^#^5*##)100 $$f_{\omega^{\omega^{\omega^5+2}}}(100)$$ pentaelkubikgathor E100#^(#^#^5*###)100 $$f_{\omega^{\omega^{\omega^5+3}}}(100)$$ pentaelquarticgathor E100#^(#^#^5*####)100 $$f_{\omega^{\omega^{\omega^5+4}}}(100)$$ pentaelgodgathgathor E100#^(#^#^5*#^#)100 $$f_{\omega^{\omega^{\omega^5+\omega}}}(100)$$ pentaelgralgathgathor E100#^(#^#^5*#^##)100 $$f_{\omega^{\omega^{\omega^5+\omega^2}}}(100)$$ pentaelthraelgathgathor E100#^(#^#^5*#^###)100 $$f_{\omega^{\omega^{\omega^5+\omega^3}}}(100)$$ pentaelterinngathgathor E100#^(#^#^5*#^####)100 $$f_{\omega^{\omega^{\omega^5+\omega^4}}}(100)$$ pentaelgathordeus E100#^(#^#^5*#^#^5)100 $$f_{\omega^{\omega^{\omega^52}}}(100)$$ pentaelgathortruce E100#^(#^#^5*#^#^5*#^#^5)100 $$f_{\omega^{\omega^{\omega^53}}}(100)$$ pentaelgathorquad E100#^(#^#^5*#^#^5*#^#^5*#^#^5)100 = E100(#^#^#^6)4 $$f_{\omega^{\omega^{\omega^54}}}(100)$$ pentaelgathorquid E100(#^#^#^6)5 $$f_{\omega^{\omega^{\omega^55}}}(100)$$ pentaelgathorsid E100(#^#^#^6)6 $$f_{\omega^{\omega^{\omega^56}}}(100)$$ pentaelgathorseptuce E100(#^#^#^6)7 $$f_{\omega^{\omega^{\omega^57}}}(100)$$ pentaelgathoroctuce E100(#^#^#^6)8 $$f_{\omega^{\omega^{\omega^58}}}(100)$$ pentaelgathornonice E100(#^#^#^6)9 $$f_{\omega^{\omega^{\omega^59}}}(100)$$ pentaelgathordecice E100(#^#^#^6)10 $$f_{\omega^{\omega^{\omega^510}}}(100)$$ pentaelgathorvigintice E100(#^#^#^6)20 $$f_{\omega^{\omega^{\omega^520}}}(100)$$ pentaelgathortrigintice E100(#^#^#^6)30 $$f_{\omega^{\omega^{\omega^530}}}(100)$$ pentaelgathorquadragintice E100(#^#^#^6)40 $$f_{\omega^{\omega^{\omega^540}}}(100)$$ pentaelgathorquinquagintice E100(#^#^#^6)50 $$f_{\omega^{\omega^{\omega^550}}}(100)$$ pentaelgathorsexagintice E100(#^#^#^6)60 $$f_{\omega^{\omega^{\omega^560}}}(100)$$ pentaelgathorseptuagintice E100(#^#^#^6)70 $$f_{\omega^{\omega^{\omega^570}}}(100)$$ pentaelgathoroctogintice E100(#^#^#^6)80 $$f_{\omega^{\omega^{\omega^580}}}(100)$$ pentaelgathornonagintice E100(#^#^#^6)90 $$f_{\omega^{\omega^{\omega^590}}}(100)$$

## Sources Edit

1. Saibian, Sbiis. Cascading-E Numbers. Retrieved 2017-10-13.