Odd perfect numbers are greater than $10^{1500}$

DOI10.1090/S0025-5718-2012-02563-4zbMath1263.11005WikidataQ55898614 ScholiaQ55898614MaRDI QIDQ2894538

Pascal Ochem, Michaël Rao

Publication date: 29 June 2012

Published in: Mathematics of Computation (Search for Journal in Brave)

Mathematics Subject Classification ID

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

• Unnamed Item
• Unnamed Item
• 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

This page was built for publication: Odd perfect numbers are greater than $10^{1500}$