Andrew Granville, Carl Pomerance
Abstract
We find infinitely many pairs of coprime integers, a and q, such that the least prime congruent to a (modulo q) is unusually large. In so doing we also consider the question of approximating rationals by other rationals with smaller and coprime denominators.
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We find infinitely many pairs of coprime integers, a and q, such that the least prime congruent to a (modulo q) is unusually large. In so doing we also consider the question of approximating rationals by other rationals with smaller and coprime denominators.
Key concepts: Coprime integers, Rational number, Modulo, Primitive root modulo n, Mathematics, Prime (order theory), Arithmetic, Prime number