FOM: a "hard" problem?
Harvey Friedman
friedman at math.ohio-state.edu
Wed Jul 12 01:55:16 EDT 2000
PROBLEM: Is the number of primes less than 2^100 even? Is the number of
primes less than 2^10,000 even?
I am under the impression that such problems are completely hopeless, even
with the aid of a computer. Hopeless, even if we wish to prove or refute it
with a high degree of certainty. Hopeless even to justify making a
conjecture as to whether it is true or false.
But should we conjecture some sort of formal undecidability of this
question? E.g.,
CONJECTURE?? The version with 2^10,000 cannot be proved or refuted in ZFC
with abbreviations without using more than 2^100 bits.
This leads us to the question of what the best example is of a problem like
this where such a conjecture can be verified?
At the moment, the examples I can think of are hopelessly obnoxious.
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