A coNP witness must be both unique-enough to be convincing and polynomially bounded in size; the prime factorization of n can require exponentially many bits relative to log n when n has many small factors.

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Exponentially(as used in mathematics and chaos theory): Growing or increasing at an accelerating rate, like doubling again and again—so small differences become huge ones very quickly.
Polynomially bounded(in complexity analysis): Growing at a controlled, predictable rate—specifically, not faster than a mathematical formula involving powers (like doubling or tripling), as opposed to exploding exponentially.
Prime factorization(as used in the Fundamental Theorem of Arithmetic): Breaking a number down into its prime number building blocks—for example, 12 breaks down into 2 × 2 × 3. Every number has exactly one way to do this.
bits(Information theory): Units of code length resulting from the use of base-2 logarithms in the entropy formula
coNP witness(computational complexity theory): In computer science, a piece of evidence or proof that demonstrates something is NOT true or NOT solvable in a certain way—think of it like showing a counterexample to prove someone wrong.
log n(mathematics and computer science): A mathematical shorthand for the logarithm of a number, which is roughly how many times you need to multiply a base number (usually 10 or 2) to reach that number.

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