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I like the bald guy in the comments idea golfing and posting his own numbers.

For a limit of 10,000⁵. Reading https://www.ams.org/journals/mcom/1967-21-097/S0025-5718-196... the original search seems to have gone up to 250⁵. That’s a search space that’s 40⁵ ≈ 10⁸ larger.

They also forget to break out of the loops when the sum of, say, the first three fifth powers already is larger than 10,000⁵.

It's likely that the original search also used strength reduction to save a lot of cycles (effectively replacing all multiplications with additions):