Legion's Numbers

Legion's number of the first kind is defined as

			(1)
			(2)

where 666 is the beast number. It has 1881 decimal digits.

Legion's number of the second kind is defined as

			(3)
			(4)

It has approximately  digits, and ends with  trailing zeros.

REFERENCES:

Pickover, C. A. "Legion's Number." Ch. 28 in The Mathematics of Oz: Mental Gymnastics from Beyond the Edge. New York: Cambridge University Press, pp. 64-65 and 269-274, 2002.