Two triangular number primality tests and twin prime counting in arithmetic progressions of modulus 8

Werner Hürlimann
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 21, 2015, Number 4, Pages 22–29
Full paper (PDF, 103 Kb)

Details

Authors and affiliations

Werner Hürlimann
Swiss Mathematical Society, University of Fribourg
1700 Fribourg, Switzerland

Abstract

Two triangular number based primality tests for numbers in the arithmetic progressions 8n ± 1 are obtained. Their use yield a new Diophantine approach to the existence of an infinite number of twin primes of the form (8n−1, 8n+1).

Keywords

• Primality test
• Compositeness test
• Triangular number
• Arithmetic progression
• Diophantine curve of degree two
• Divisor function
• Twin prime

AMS Classification

• 11A51
• 11B25
• 11D85

References

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