The legendary math Universalist, Henri Poincare, once said, “ Mathematicians do not study objects, but relations between objects.” Inspired by subtle patterns that emanate from an abyss of ostensible chaos, mathematicians manifest these words by exploring relations within algebraic and geometric structures. These edifices, upon occasion, reveal intricate beauty buried deep in a profusion of symbols etched on the tablet of logical thought. Problems requiring various degrees of acumen have been presented in an assortment of publications over the course of modern history. From the field of Number Theory, problems are often innocently conveyed, but cloaked behind a veil of extensive logic that guards them from any immediate proof. Some problems call for a deep understanding harnessed only after years of study. However, others are immediately accessible with a little mathematical maturity. One such conundrum can be stated in terms of Sierpiński numbers of the second kind. A Sierpiński number of the second kind (henceforth, just Sierpiński number) is an odd positive integer such that is a composite number for every positive integer . In 1960, Wacław Sierpiński proved that there are infinitely many such . To eliminate a given positive integer from Sierpiński number candidacy, one only needs to show a prime number of the form for some positive integer . On the other hand, to prove that is a Sierpiński number, the convention is to show that there exists a covering set of primes such that every member of the set divides for every positive integer . The smallest Sierpiński number currently known is 78557 and was proven by the mathematician John Selfridge in 1962 with the covering set { 3, 5, 7, 13, 19, 37, 73 }. Therefore, a fundamental open question arises: Out of the set of all Sierpiński numbers, is 78557 the smallest? To answer this question in the affirmative, one has to eliminate all positive integers less than 78557 from Sierpiński number candidacy. Mathematical proof and computational methods have eliminated all but six remaining candidates: 10223, 21181, 22699, 24737, 55459, and 67607. The website Seventeen or Bust is a distributed computing project dedicated to the goal of eliminating these remaining six. When the project first started there were seventeen (hence the name), but since then, eleven have been eliminated by finding the desired prime. Anyone can join the search. It could be you that proves that 78557 is the smallest Sierpiński number. All one needs is a computer and a willingness to give up a small amount of computational power. So plug in and discover.

Opinions expressed on these pages were the views of the writers and did not necessarily reflect the views and opinions of the American Mathematical Society.
Categories
 Academic Skills
 Advice
 Algebra
 Algebraic Geometry
 AMS
 Analysis
 Announcement
 Arts & Math
 Biology
 Book Reviews
 Conferences
 Crossword Puzzles
 Diversity
 Ecology
 Editorial Statement
 Firstgeneration
 General
 Grad School
 Grad student advice
 Grad student life
 Interview
 Interviews
 JMM
 Jobs
 Linear Algebra
 MAM
 Math
 Math Education
 Math Games
 Math History
 Math in Pop Culture
 Math Teaching
 Mathematicians
 Mathematics in Society
 Mathematics Online
 News
 Number Theory
 Publishing
 puzzles
 Social Justice
 Starting Grad Schol
 Statistics
 staying organized
 Teaching
 Technology & Math
 Topology
 Uncategorized
 Voting Theory
Archives
 December 2021
 November 2021
 October 2021
 September 2021
 April 2021
 January 2021
 November 2020
 July 2020
 June 2020
 May 2020
 March 2020
 February 2020
 January 2020
 December 2019
 November 2019
 October 2019
 September 2019
 August 2019
 November 2018
 September 2018
 June 2018
 May 2018
 March 2018
 February 2018
 January 2018
 December 2017
 November 2017
 October 2017
 September 2017
 August 2017
 July 2017
 June 2017
 April 2017
 March 2017
 February 2017
 January 2017
 December 2016
 November 2016
 October 2016
 September 2016
 August 2016
 July 2016
 June 2016
 May 2016
 April 2016
 March 2016
 February 2016
 January 2016
 December 2015
 November 2015
 October 2015
 September 2015
 July 2015
 June 2015
 May 2015
 April 2015
 March 2015
 January 2015
 December 2014
 November 2014
 October 2014
 September 2014
 August 2014
 July 2014
 June 2014
 May 2014
 April 2014
 March 2014
 February 2014
 January 2014
 December 2013
 November 2013
 October 2013
 September 2013
 August 2013
 July 2013
 June 2013
 May 2013
 April 2013
 March 2013
 February 2013
 January 2013
 December 2012
 November 2012
 October 2012
 September 2012
 August 2012
 July 2012
 June 2012
 May 2012
 April 2012
 March 2012
 February 2012
 January 2012
 December 2011
 November 2011
 October 2011
 September 2011
 August 2011
 July 2011
 June 2011
 May 2011
 April 2011
 March 2011
 February 2011
 January 2011
 December 2010
 November 2010
 October 2010
 September 2010
 August 2010
 July 2010
 June 2010
 May 2010
 April 2010
 March 2010
 February 2010
 January 2010
 December 2009
 November 2009
 October 2009
 September 2009
 August 2009
 July 2009
 June 2009
 May 2009
 April 2009
 March 2009
 February 2009
Meta