Odd perfect numbers are greater than 10¹⁵⁰⁰

2012/01/30 by Pascal Ochem, Michaël Rao · 5 citations
Mathematics · Computer Science · #Analytic Number Theory Research #History and Theory of Mathematics #Computability, Logic, AI Algorithms

paper · pdf · doi:10.1090/s0025-5718-2012-02563-4

openalex publication_date 2012/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/22

Abstract

Brent, Cohen, and te Riele proved in 1991 that an odd perfect number N is greater than 10³⁰⁰. We modify their method to obtain N>10¹⁵⁰⁰. We also obtain that N has at least 101 not necessarily distinct prime factors and that its largest component (i.e. divisor p^a with p prime) is greater than 10⁶².

Citations

• Approximate formulas for some functions of prime numbers
• Odd perfect numbers have a prime factor exceeding 10⁸

Cited by

• Odd perfect numbers, Diophantine equations, and upper bounds
• On the number of prime factors of an odd perfect number
• IMPROVED UPPER BOUNDS FOR ODD MULTIPERFECT NUMBERS
• Bi-unitary multiperfect numbers, I
• Perfect number [wikipedia]

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