<P> where the number of 3s in each successive tower is given by the tower just before it . Note that the result of calculating the third tower is the value of n, the number of towers for g . </P> <P> The magnitude of this first term, g, is so large that it is practically incomprehensible, even though the above display is relatively easy to comprehend . Even n, the mere number of towers in this formula for g, is far greater than the number of Planck volumes (roughly 10 of them) into which one can imagine subdividing the observable universe . And after this first term, still another 63 terms remain in the rapidly growing g sequence before Graham's number G = g is reached . To illustrate just how fast this sequence grows, while g is equal to 3 ↑ ↑ ↑ ↑ 3 (\ displaystyle 3 \ uparrow \ uparrow \ uparrow \ uparrow 3) with only four up arrows, the number of up arrows in g is this incomprehensibly large number g . </P> <P> Graham's number is a "power tower" of the form 3 ↑ ↑ n (with a very large value of n), so its rightmost decimal digits must satisfy certain properties common to all such towers . One of these properties is that all such towers of height greater than d (say), have the same sequence of d rightmost decimal digits . This is a special case of a more general property: The d rightmost decimal digits of all such towers of height greater than d + 2, are independent of the topmost "3" in the tower; i.e., the topmost "3" can be changed to any other non-negative integer without affecting the d rightmost digits . </P> <P> The following table illustrates, for a few values of d, how this happens . For a given height of tower and number of digits d, the full range of d - digit numbers (10 of them) does not occur; instead, a certain smaller subset of values repeats itself in a cycle . The length of the cycle and some of the values (in parentheses) are shown in each cell of this table: </P>

What is the value of graham's number