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odd_perfect_number.lower_bound

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A known result: If an odd perfect number exists, it must be greater than $10^{1500}$ and must have at least 101 prime factors (including multiplicities). *Reference:* Pascal Ochem, Michaël Rao (2012). "Odd perfect numbers are greater than 10^1500"

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Lean 4 Statement 
theorem odd_perfect_number.lower_bound (n : ℕ) (hn : Odd n) (hp : Perfect n) :
    n > 10^1500 ∧ (n.primeFactorsList).length ≥ 101
ID: Wikipedia__PerfectNumbers__odd_perfect_number.lower_bound
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