Sierpiński number

In 1960 Waclaw Sierpinski proved that there exists infinetly many odd integers, k, such that k2ⁿ +1 contains no prime numbers for all n in the natural numbers

However, two years later, John Selfridge found that k = 78557 was a number that gave a sequence of composite numbers. - He then conjectured that the number he had found, was the smallest fulfilling this property.

To this day, the conjecture still stands; but the distributed project Seventeen or bust, has startet searching for primes in the remaining seventeen sequences on the form k2ⁿ +1 where k < 78557, and no prime has been found in the sequence.