How many numbers of the form 2^n-1 and less than 2000 are prime?

Explanation

For 2^n-1 to be a prime number (Mersenne prime), n itself must be prime. Testing prime values: 2^2-1=3, 2^3-1=7, 2^5-1=31, and 2^7-1=127 are all prime. For n=11, 2^{11}-1 = 2047, which exceeds 2000. Thus, there are 4 such primes.

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