The largest prime being 2^57885161 - 1 doesn't say anything about the primes below it. For instance, 31 = 2^5 - 1 is a prime number, but it also is the case that 32 = 29 + 3. And so, perhaps 2^57885161 - 3 is a prime number, implying 2^57885161 = 3 + 2^57885161. But yeah, my main point is that we can't say for certain based solely on the fact 2^57885161 - 1 is prime.

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