The largest known prime number has emerged. It has more than 23M digits

Re:The largest known prime number has emerged. It has more t... by throwacide on Monday January 15, 2018 @07:15PM (#16154690)

What’s the significance of primes being one less than large powers of 2? Does this mean base-2 is the most natural base?

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Re:The largest known prime number has emerged. It has more t... by Someone on Tuesday January 16, 2018 @02:39AM (#16156469)

2 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-...)

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