Mathematician Conditionally Disproves Prime SHA256 Hash Conjecture
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Ha, neat! Adam seems to have conditionally disproven my absurd conjecture, in its most natural 1980's vintage big-endian form. So we have to modify it! "All but finitely many primes have the same little-endian SHA256* hash." *Assuming a reasonable arbitrary-length extension.
@geoffreyirving Ignoring for the moment that SHA256 is only defined on inputs of fewer than 2^64 bits, a proof of the first Hardy-Littlewood conjecture would allow you to construct a bunch of nearby primes that differ only in the last message block where they can be whatever you want up to [1/2]
Important edit! This is very likely disprovable if the hash is big-endian, per @apgox. Shame on me for leaning too hard on the random oracle model. :)
Ha, neat! Adam seems to have conditionally disproven my absurd conjecture, in its most natural 1980's vintage big-endian form. So we have to modify it! "All but finitely many primes have the same little-endian SHA256* hash." *Assuming a reasonable arbitrary-length extension. https://twitter.com/apgox/status/2079976467090325952