Odd perfect numbers are greater than $10^{1500}$
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Publication:2894538
DOI10.1090/S0025-5718-2012-02563-4zbMath1263.11005WikidataQ55898614 ScholiaQ55898614MaRDI QIDQ2894538
Publication date: 29 June 2012
Published in: Mathematics of Computation (Search for Journal in Brave)
Arithmetic functions; related numbers; inversion formulas (11A25) Factorization; primality (11A51) Values of arithmetic functions; tables (11Y70)
Related Items (12)
On the number of total prime factors of an odd perfect number ⋮ ON PRIME FACTORS OF ODD PERFECT NUMBERS ⋮ On the number of prime factors of an odd perfect number ⋮ Arithmetic, enumerative induction and size bias ⋮ Computers as a novel mathematical reality. III: Mersenne numbers and sums of divisors ⋮ On a sequence of densities generated by the greedy algorithm ⋮ Unnamed Item ⋮ Perfect and Deficient Perfect Numbers ⋮ Odd perfect numbers: a triptych ⋮ IMPROVED UPPER BOUNDS FOR ODD MULTIPERFECT NUMBERS ⋮ Unnamed Item ⋮ Odd perfect numbers, Diophantine equations, and upper bounds
Cites Work
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- Approximate formulas for some functions of prime numbers
- Odd perfect numbers have a prime factor exceeding $10^8$
- Odd perfect numbers have at least nine distinct prime factors
- New techniques for bounds on the total number of prime factors of an odd perfect number
- Improved Techniques for Lower Bounds for Odd Perfect Numbers
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