六道语言模型自信却答错的题，与引擎算出的结果并列。
靠模式作答的助手，出错的频率足以造成影响，而且错得有规律：答案的形状是对的。级数的前几项是对的；积分是一个著名的值，却配上了错误的积分限；因式分解停在肉眼看不出的地方。下面每一行展示模式给出的答案、它出错的那一项，以及引擎真正计算时返回的结果。
本页不点名任何模型。左栏是模式匹配在这些题目上普遍会给出的结果，任何一个模型一旦进步，它就过时了；右栏在每次构建时都重新对照引擎验证，若有偏差，本页就无法发布。
出错的一项： 31x^9/2835
构建时已对照引擎验证
The first four coefficients are common enough to be recalled correctly; the fifth is not. The true coefficient is 62/2835. A series that is right to four terms and wrong at the fifth looks like knowledge and is the shape of a guess.
出错的一项： -1
构建时已对照引擎验证
A 4x4 characteristic polynomial has enough terms for one sign to go wrong on the way to the answer, and a wrong sign produces a wrong eigenvalue that still looks like one. Here the matrix decouples into two 2x2 blocks; the engine finds all four exactly rather than approximating the quartic.
出错的一项： Pi
构建时已对照引擎验证
The Dirichlet integral is famous enough to be recalled, and famous enough to be recalled with the wrong limits: the value over (-inf, inf) is Pi, over (0, inf) it is Pi/2. Both facts are true; attaching the right one to the limits written down is the computation.
出错的一项： 329218123329 declared prime
构建时已对照引擎验证
Dividing out the 3 is easy; deciding whether the twelve-digit cofactor is prime is not something inspection can do, so a plausible answer stops there and calls it prime. The engine factors it, and it is not.
出错的一项： 1
构建时已对照引擎验证
The theorem is real and the shape of the problem invites it, but 10^6 is not 10^9+6. The correct residue is reached only by actually reducing, which is a few hundred squarings - trivial for an engine and impossible by inspection.
出错的一项： Pi^4/96
构建时已对照引擎验证
zeta(2) = Pi^2/6 is remembered by everyone; zeta(4) is remembered as 'Pi^4 over something', and the something is where a recalled answer diverges from a computed one. 90 is right; 96 and 45 both appear in nearby identities and are both wrong here.
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