3 ms·
1 is 2 to the power 0 ... 0b0001 shifted left once, it becomes 2 to the power 1 ... 0b0010 shifted left twice, it becomes 2 to the power 2 ... 0b0100 shifted
by nanis 2y ago
1 is 2 to the power 0 ... 0b0001
shifted left once, it becomes 2 to the power 1 ... 0b0010
shifted left twice, it becomes 2 to the power 2 ... 0b0100
shifted left three times, it becomes 2 to the power 3 ... 0b1000
etc until
shifted left 136_279_841 times, it becomes 2 to the power 136_279_84 ... 0b1000...many zeros...0000
subtract 1, it becomes
0b0111...many ones...1111
- schoen 2y agoOne funny thing about Mersenne primes is that, as a result of what you describe, they are exactly those primes whose binary representation consists of a prime number of ones! The smallest Mersenne prime, three, is binary 11, while the next largest is seven (111), then 31 (11111), then 127 (1111111). The next candidate, 2047 (11111111111), is not prime.