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* 2^{n} + 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* 2^{n} + 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* 2^{n} + 1. Primes below approximately 10^{15} 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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