The concrete theory of numbers : Problem of simplicity of Fermat number-twins

2007/07/06 by Boris V. Tarasov, Tarasov, Boris V.
Mathematics · #11A51 #Analytic Number Theory Research #FOS: Mathematics #General Mathematics (math.GM) #History and Theory of Mathematics #Mathematics and Applications #math.GM #msc:11A51

paper · pdf · doi:10.48550/arxiv.0707.0907

6 pages

arxiv created 2007/07/06 · openalex publication_date 2007/07/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The problem of simplicity of Fermat number-twins f_n^±=2²ⁿ±3 is studied. The question for what n numbers f_n^± are composite is investigated. The factor-identities for numbers of a kind x² ± k are found.

Related

• The concrete theory of numbers : New Mersenne conjectures. Simplicity and other wonderful properties of numbers L(n) = 2²ⁿ±2ⁿ±1
• Observations on a certain theorem of Fermat and on others concerning prime numbers
• Arithmetic closed forms count the Mersenne primes, the Fermat primes and the twin-prime pairs
• Regularities of Twin, Triplet and Multiplet Prime Numbers
• ABC Conjecture: ABC = 2^m pⁿ q^r with Fermat or Mersenne Primes