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Number theory
Erdős problem 409 - sigma termination
If n>1 then the iteration n↦σ(n)−1 necessarily reaches a prime.
Note: this is open — it is not clear that the σ iteration always terminates,
since it is non-decreasing (unlike the φ iteration which is strictly decreasing).
$2,690 bounty·1 piece from 1 person·last one 19 days ago
week of 27 Sept 2025 · nothing publishedweek of 4 Oct 2025 · nothing publishedweek of 11 Oct 2025 · nothing publishedweek of 18 Oct 2025 · nothing publishedweek of 25 Oct 2025 · nothing publishedweek of 1 Nov 2025 · nothing published
Solve it
A complete proof or refutation in Lean. The first one the validator accepts takes the whole bounty.
27 Sept 2025a year of work on this problem19 Sept 2026
erdosproblems.com/409
Something wrong with this formalization?
A statement that does not faithfully capture the original conjecture is the one real risk here, so we would rather hear about it early - before someone spends weeks on it.
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