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I'm curious if there are any known examples of proofs using a computer which after being published, (in a journal or otherwise) turned out to have bugs in the software which invalidated the proof. I'm particularly interested in examples where the "proved" conjecture turned out to be false.

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Not exactly the answer you are looking for but still interesting, from “New Scientist”:

In 1998 Thomas Hales submitted a computer-assisted proof of the Kepler conjecture, a theorem dating back to 1611. This describes the most efficient way to pack spheres in a box, wasting as little space as possible. It appears the best arrangement resembles the stacks of oranges seen in grocery stores.

Hales’ proof is over 300 pages long and involves 40,000 lines of custom computer code. When he and his colleagues sent it to a journal for publication, 12 reviewers were assigned to check the proof. “After a year they came back to me and said that they were 99% sure that the proof was correct,” Hales says. But the reviewers asked to continue their evaluation.

However, this tiny uncertainty did not disappear with time. “After four years they came back to me and said they were still 99% sure that the proof was correct, but this time they said were they exhausted from checking the proof.”

As a result, the journal then took the unusual step of publishing the paper without complete certification from the referees (Annals of Mathematics Vol. 162, p. 1063-1183, 2005).

Also a fun to read: https://phys.org/news/2016-05-math-proof-largest-terabytes.html

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