A test method is described for determining the divisibility of non-negative integers by a prime number. The test uses an integer multiplying factor that is defined for each prime, designated as [beta], to reduce the non-negative integer that is being tested by an order of magnitude in each of a sequence of steps to obtain a series of new numbers. The test is repeated until a new number is obtained that is either an obvious multiple of the prime number, which indicates that the original integer being tested is a multiple of the particular prime, or is not such a multiple, indicating that the original integer is not a multiple of the particular prime. The values of [beta] for successive prime numbers are defined by arithmetic progressions.