Calculating Tetration

[bo198214]

Sorry, you wanted to know \( {}^{4}{3}\text{ mod } 10^8 \). Using this information, the last few digits are ...30214289387

Slowly, slowly, this contradicts my result 00739387.
As it seemed not to be explicit enough, I reexplain:

To get 3^(3^27) % 100000000 I just take 27 times the cube:
\( a_0 = 3 \)
\( a_{n+1} = {a_n} ^ 3 \) % 100000000
then \( a_{27}=3^{3^{27}} \) % 100000000 by the law \( (a\%m)^b=a^b\% m \).

We can also shorten this to 3^(3^27)=((3^19683)^19683)^19683, where 19683=3^9. Lets compute again this way:
3^19683 % 100000000 = 17859227
17859227^19683 % 100000000 = 384483
384483 ^ 19683 % 100000000 = 739387

So I come again to 3^(3^27) % 100000000 = 00739387.