Werner Hürlimann

Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132

Volume 21, 2015, Number 4, Pages 22—29

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## 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 8*n* ± 1 are obtained. Their use yield a new Diophantine approach to the existence of an infinite number of twin primes of the form (8*n*−1, 8*n*+1).

### Keywords

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

### AMS Classification

- 11A51
- 11B25
- 11D85

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*Zahlentheorie*, Mathematik für Lehrer, Band 19, VEB Deutscher Verlag für Wissenschaften, Berlin. - Dilcher, K. & Stolarsky, K.B. (2005) A Pascal-type triangle characterizing twin primes,
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## Cite this paper

APAHürlimann, W. (2015). Two triangular number primality tests and twin prime counting in arithmetic progressions of modulus 8. Notes on Number Theory and Discrete Mathematics, 21(4), 22-29.

ChicagoHürlimann, Werner. “Two Triangular Number Primality Tests and Twin Prime Counting in Arithmetic Progressions of Modulus 8.” Notes on Number Theory and Discrete Mathematics 21, no. 4 (2015): 22-29.

MLAHürlimann, Werner. “Two Triangular Number Primality Tests and Twin Prime Counting in Arithmetic Progressions of Modulus 8.” Notes on Number Theory and Discrete Mathematics 21.4 (2015): 22-29. Print.