How Large Are Mersenne Primes in Decimal Digits?

[anil]

A prime number is a positive ineger greater than 2 whose only integer divisors are itself and 1. A Mersenne prime in of the form 2^(n) - 1 where p is a prime. For example 2^(5) - 1 = 31 is a Mersenne prime. One of the larger Mersenne prime is 2^(216091) - 1. Estimate the number of decimal digits in this number.

Please post your explanation and your answer. No this problem needs no calculus. Got guts[?]

 

[jcsd]

Okay it's not my job to do your homework, so I will only give you a few pointers:

The -1 is unimortant to your estimate, so ignore that for the minute:

You can then construct this equation:

2^(216091) = 10^x

From here it should be very easy to solve.

 

[anil]

Kiddo: this is not my HW

This is not my homework. LoL this is a "challenge problem" they give in my college to exercise brain. I got the answer I just want to see my asnwer is right. 72030

 

[jcsd]

No your answer is wrong, look at the equation I gave again, you may of made a simple error.