It is one program. If P=NP then the body of the program consists of "print(P=NP)". And otherwise it consists of "print(P!=NP)". [1]
Similarly for every hash function there exists a program that outputs a hash collision in well under a second. Just hardcore any collision and print it to the screen. [2]
[1] If you want to be pedantic then there's a third option that prints some more complicated statement about the relationship between standard axioms and P?=NP.
[2] Please don't ruin my short argument by pointing out that someone can create a hash function with output size in the petabytes range :)
Similarly for every hash function there exists a program that outputs a hash collision in well under a second. Just hardcore any collision and print it to the screen. [2]
[1] If you want to be pedantic then there's a third option that prints some more complicated statement about the relationship between standard axioms and P?=NP.
[2] Please don't ruin my short argument by pointing out that someone can create a hash function with output size in the petabytes range :)