Journal of Integer Sequences, Vol. 4 (2001), Article 01.2.3

Prime Pythagorean triangles

Harvey Dubner
449 Beverly Road
Ridgewood, New Jersey 07450

Tony Forbes
Department of Pure Mathematics
The Open University
Walton Hall, Milton Keynes MK7 6AA, United Kingdom

Email addresses: hdubner1@compuserve.com and tonyforbes@ltkz.demon.co.uk

Abstract: A prime Pythagorean triangle has three integer sides of which the hypotenuse and one leg are primes. In this article we investigate their properties and distribution. We are also interested in finding chains of such triangles, where the hypotenuse of one triangle is the leg of the next in the sequence. We exhibit a chain of seven prime Pythagorean triangles and we include a brief discussion of primality proofs for the larger elements (up to 2310 digits) of the associated set of eight primes.

1991 Mathematics Subject Classification: Primary 11A41
Keywords: Pythagorean triangles, prime numbers, primality proving

(Mentions sequences A048161 A048270 A048295)

Received May 6, 2001; revised version received Sept. 3, 2001. Published in Journal of Integer Sequences Sept. 13, 2001.