A proof of cases of de Polignac's conjecture

Mbakiso F. Mothebe, Dintle N. Kagiso, Ben T. Modise

For $n\ge 1$ let $p_n$ denote the $n^{\mathrm{th}}$ prime number. Let $$S=\{1,7,11,13,17,19,23,29\},$$ the set of positive integers which are both less than and relatively prime t…