A Remarkable Dearth of Primes

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.