The Sierpinski Problem
| Is 78,557 the smallest Sierpinski number? |
The Sierpinski problem is: "What is the smallest Sierpinski number?"
In 1967, Sierpiński and Selfridge conjectured that 78,557 is the smallest Sierpinski number, and thus the answer to the Sierpinski problem.
To show that 78,557 really is the smallest Sierpinski number, one must show that all the odd numbers smaller than 78,557 are not Sierpinski numbers. That is, for every odd k below 78,557 there exists a positive integer n such that k2n+1 is prime. As of September 2012, there are only six candidates:
- k = 10223, 21181, 22699, 24737, 55459, and 67607
which have not been eliminated as possible Sierpinski numbers. Seventeen or Bust (with PrimeGrid), a distributed computing project, is testing these remaining numbers. If the project finds a prime of the form k2n+1 for every remaining k, the Sierpinski problem will be solved.
Read more about this topic: Sierpinski Number
Famous quotes containing the word problem:
“The government is huge, stupid, greedy and makes nosy, officious and dangerous intrusions into the smallest corners of life—this much we can stand. But the real problem is that government is boring. We could cure or mitigate the other ills Washington visits on us if we could only bring ourselves to pay attention to Washington itself. But we cannot.”
—P.J. (Patrick Jake)