The pursuit of prime numbers–integers evenly divisible only by themselves and 1–can lead to all sorts of curious results and unexpected patterns. In some instances, you may even encounter a mysterious absence of primes.
In 1960, Polish mathematician Waclaw Sierpinski (1882–1969) proved that there are infinitely many odd integers k such that k times 2n + 1 is never prime for all values of n greater than or equal to 1. A multiplier k with this property is called a Sierpinski number.