7 ms·
What’s the significance of primes being one less than large powers of 2? Does this mean base-2 is the most natural base?
by throwacide 9y ago
What’s the significance of primes being one less than large powers of 2? Does this mean base-2 is the most natural base?
- Someone 9y ago2 is the only integer n such that n-1 = 1. That’s significant because (n^m) - 1 is divisible by n - 1. So, for example, 125320078^35785332 - 1 is divisible by 125320077 and, hence, not a prime. So, this problem has been solved for all n>2. n^m + 1 is a more difficult problem. For example, for n=10, we get 2: prime, 11: prime, 101: prime, 1001: composite, 10001: composite, etc (at least the 8,000 following are composite. See https://math.stackexchange.com/questions/2108085/is-there-a-prime-which-is-the-form-of-10n-1-except-2-11-101 https://math.stackexchange.com/questions/2108085/is-there-a-...)
- throwacide 9y agoOh, neat. Thanks.