restart;second:=evalf(5^(3125));
# This we can calculate...mult:=evalf(%/3125);
# Next, we can take that huge number and divide it to
# parts by 3125 (that we can calculate).
# That way we get how many numbers 1.911e2184 needs to be
# multiplied by theirself.n1:=6.115*1.911*10^2180;
n2:=2184*2180;third:=n1*10^n2;# We have an aproximation of 3rd step. Now we can say
# something about a power of 5^(5^(5^(5^5))) = 5^third
# Like before, we can take 'third' number and divide it
# into parts that we know, what power they are.
mult2:=third/3125;f1:=1.911*3.739445*10^2180;
f2:=2184*4763297;fourth:=f1*10^f2;10403040648+2180;# It's huge. Number itself would fit in 10.5GB of diskspace
# if my thinking was good. PLEASE check it and write if any mistake
# (in method) occured.
# If You're interresed in large prime numbers, the biggest I know
# is in power of 10^24...
2^30*3^30+7;
isprime(%);# It's PROPABLY prime, test is propabilistic...