Formula to obtain the next prime in an arithmetic progression
Sebastián Martín Ruiz · Smarandache Notions Journal archive · 2004
In this article, a formula is given to obtain the next prime in an arithmetic progression. Theorem: We consider the arithmetic progression di a + 0 ≥ i of positive integers with 1 ) , ( = d a GCD and considering that the final term is dM a + is to say M i ≤ ≤ 0 . Let p a term in the arithmetic progression (it doesn’t have to be prime). Then the next prime in the arithmetic progression is: ∑ ∏ ∑ − + = − + = + =