Finding prime desert N-tuplets

• Main Authors: Candoleta, Herbert H., Muhi, Liza Marie T.
• Format: text
• Language: English
• Published: Animo Repository 1994
• Subjects: Numbers, Prime; Numbers, Theory of; Programming (Mathematics); Prime numbers
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/16166
• Institution: De La Salle University

Although the number of primes is infinite, one can still find as many consecutive integers as one pleases. This study concerns itself with sets of consecutive integers. Regions of n consecutive composite integers where no prime is present are called prime desert n-tuplets. In order for a prime desert of length k to exist, k must be odd. The existence of prime desert twins and triplets of length k implies that k = 5(mod 6). Moreover, for prime desert quadruplets and quintuplets of length k to exist, k = 29(mod 30). This paper also provides a computer program which will generate all possible prime desert n-tuplets. However, the language is up to maximum value of 2,147,483,647.