Question

P=2^(43112609)-1 Suppose you have traveled to a faraway place where the base of the number system is 37 . (The inhabitants of that country are fond of prime numbers.) So it has 37 symbols in place of our 10 digits, but otherwise it works just like the decimal system. Expressed in that system P,has(.........) digits.?

Answer 1

Answer:

  8,275,842 digits

Step-by-step explanation:

One more than the floor of the logarithm to the base 37 gives the number of digits. The change of base formula can be used.

  $\log_{37}{(2^{43112609}-1)}\approx\dfrac{43112609\log{2}}{\log{37}}\approx 8275841.2$

Expressed in the base-37 number system, P has 8275842 digits.