Odd perfect numbers have a prime factor exceeding $10^{7}$

DOI10.1090/S0025-5718-03-01496-0zbMath1126.11304WikidataQ114093886 ScholiaQ114093886MaRDI QIDQ4806405

Paul M. Jenkins

Publication date: 14 May 2003

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

Mathematics Subject Classification ID

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

Related Items (5)

Odd perfect numbers have a prime factor exceeding $10^{7}$ ⋮ Odd perfect numbers have a prime factor exceeding $10^8$ ⋮ Computers as a novel mathematical reality. III: Mersenne numbers and sums of divisors ⋮ Odd perfect numbers have at least nine distinct prime factors ⋮ On the largest prime divisor of an odd harmonic number

Cites Work

• Unnamed Item
• Outline of a Proof that Every Odd Perfect Number has at Least Eight Prime Factors
• Improved Techniques for Lower Bounds for Odd Perfect Numbers
• On the Largest Prime Divisor of an Odd Perfect Number. II
• The second largest prime divisor of an odd perfect number exceeds ten thousand
• Every odd perfect number has a prime factor which exceeds 10⁶
• Odd perfect numbers have a prime factor exceeding $10^{7}$
• The third largest prime divisor of an odd perfect number exceeds one hundred
• Odd perfect numbers are divisible by at least seven distinct primes

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