April 19th 2006

# Seventeen or Bust

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Seventeen or Bust is a distributed internet project to solve the Sierpinsky problem. It differs from almost all comparable distributed internet projects in one point: It is clearly defined when the project is finished. The Sirpinsky problem is:
What is the smallest number k so that N = k 2n + 1 is composite for all n?
Since 1962 it is know that k = 78.557 is such a number. This can be shown with the related covering set (see The Prime Glossary). At the beginning of the project the number of possible k < 78.557 was 17 - that's where the name of the project comes from. As in April 2006 for 9 of these 17 numbers an exponent n was found so that p = k 2n + 1 is prime. Consequently there are only 8 numbers to go.

Similiar to GIMPS there is also some trial and p-1 prefactoring work done (see the factoring forum). Additionally in the All Things SoB Sieving - project there is another approach sieving out numbers. This project systematically goes thru all prime numbers and checks wheather they factor one of the remaining canditates k 2n + 1. Primes below approximately 1015 have been exhausted finished for exponents n < 20.000.000 and the 8 remaining k. In 2004 I could find 76 such factors.

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