Problem: How many different prime numbers are factors of NNN if
2(3(5(7N)))=11?\log _{2}\left(\log _{3}\left(\log _{5}\left(\log _{7} N\right)\right)\right)=11 ? log2​(log3​(log5​(log7​N)))=11?
Answer Choices:
A. 111
B. 222
C. 333
D. 444
E. 777
Solution:
Note that N=753211N=7^{5^{3^{2^{11}}}}N=753211, which has only 777 as a prime factor.