Every odd perfect number has a prime factor which exceeds 10⁶

DOI10.1090/S0025-5718-98-00982-XzbMath0973.11110WikidataQ114093826 ScholiaQ114093826MaRDI QIDQ4396467

Graeme L. Cohen, Peter Hagis jun.

Publication date: 14 June 1998

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

zbMATH Keywords

largest prime factorodd perfect number

Mathematics Subject Classification ID

Arithmetic functions; related numbers; inversion formulas (11A25) Values of arithmetic functions; tables (11Y70)

Related Items (8)

The second largest prime divisor of an odd perfect number exceeds ten thousand ⋮ Odd perfect numbers have a prime factor exceeding $10^{7}$ ⋮ On the number of distinct prime factors of an odd perfect number ⋮ Odd perfect numbers have a prime factor exceeding $10^8$ ⋮ Computers as a novel mathematical reality. III: Mersenne numbers and sums of divisors ⋮ Unnamed Item ⋮ The third largest prime divisor of an odd perfect number exceeds one hundred ⋮ On the largest prime divisor of an odd harmonic number

Cites Work

• New Solutions of a p - 1 ≡1 (mod p 2 )
• On Multiple Prime Divisors of Cyclotomic Polynomials
• On the Largest Prime Divisor of an Odd Perfect Number. II
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• Unnamed Item

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