UNSOLVED PROBLEMS 
In Number Theory, Logic, and Cryptography 
What’s New 
This page lists recent developments, and changes to the website. If you intend to be a regular user of the site, you might like to bookmark this page so that you can see at a glance what has changed since your last visit.
January 2019: The prize for any valid solution now stands at US$3,000 and a bottle of champagne. Ten new contributions were received in 2018. March 2018: A bottle of champagne is on offer for a neat closedform approximation to the Apery Constant. For details, please see here February 2018: Nineteen contributions were published on the site in 2017. Hopefully some will prove useful to those looking at one or more of the problems. Prizes for any correct solution remain at US$2,500 and a bottle of champagne! July 2017: All fees for publication and donations to the UP site received between 24th July and 31st August 2017 will be donated to the Against Malaria Foundation (AMF). March 2017: A proposed proof of the nonexistence of a Perfect Cuboid by Dr William Wyss has been found to have flaws and has been withdrawn. October 2015: Contributions published during the period 1st October 2015 to 31st December 2015 will be eligible for prizes of US$5000. August 2015: New contributions this month include one addressing the search for a Perfect Cuboid, and another looking at some of the puzzles behind Elgar’s Enigma Variations. July 2015: A new contribution to the Riemann Hypothesis can be found on the Solutions page. April 2015: The problem of finding a semimagic square of cubes has been added to the site. Any fees received for articles published on the Solutions page between 5th April and 25th June 2015 will be donated to the MakeAWish Foundation. March 2015: Brocard’s Problem has been added to the site. Thanks to Scott Hampton for the suggestion. February 2015: Eight of the last ten contributions have been related to the Perfect Cuboid problem. They can be found on the Solutions page. Following further testing, the new lower bound for the odd side of a perfect cuboid has been raised to 25 trillion. November 2014: New contributions to various problems including the Riemann Hypothesis can be found on the Solutions page, and there’s a new link to an excellent article re the Zodiac Cipher. September 2014: New contributions to the Odd Perfect Number problem and the Beal Conjecture can be found on the Solutions page. July 2014: Simon Donaldson, Maxim Kontsevich, Jacob Lurie, Richard Taylor, and Terence Tao are the recipients of the first Breakthrough Prize in Mathematics. Each of the five mathematicians will receive US$3 million. For more details see here. May 2014: A new contribution to the DLP and DiffieHellman problems can be found on the Solutions page. April 2014: Several items this month. First, there are several new contributions on the Solutions page, including one which raises the lower bound for the odd side of a perfect cuboid to 8*10^{12}. Second, the developer of this web site is now offering US$1000 for valid solutions to 19 of the 22 problems listed  details on the Prizes page. Third, thanks to various contributors, A$329 is being donated to the MakeAWish Foundation. March 2014: Contributions to the Rational Distance problem and the Perfect Cuboid problem, and revised versions of the papers relating to the decryption of the Dorabella Cipher, have been added to the Solutions page. December 2013: All fees received between 1st October 2013 and 31st March 2014 will be donated to the MakeAWish Foundation. Additionally, the rules governing the $500 prizes have been relaxed so that prior publication on some other sites will not render the author(s) ineligible, and the time limit for acceptance has been extended to 18 months. November 2013: An update to the Dorabella Cipher solution, and a contribution to the Magic Square of Squares problem, can both be found on the Solutions page.. September 2013: A new contribution to the Riemann Hypothesis has been added to the Solutions page, and some findings related to the Magic Square of Squares problem are reported here. July 2013: The Rational Distance problem has been added to the site. June 2013: Andrew Beal has raised his prize for a proof of, or counterexample to, the Beal Conjecture to one million dollars. See for example here. May 2013: A very interesting article discussing the possible proof of the ABC Conjecture can be found here. April 2013: A contribution to the Riemann Hypothesis has been added to the Solutions page March 2013: A proposed solution to Fermat’s Last Theorem has been added to the Solutions page. February 2013: This site will now offer prizes of US $500 for the solution to most of the problems listed on the site. For details, please see the Prizes page. January 2013: A new unsolved problem, the Lonely Runner conjecture, has been added to the site. December 2012: Lists of Euler bricks, edge cuboids, and face cuboids are available from the Solutions page. October 2012: There’s currently much excitement in the professional mathematics community about Kyoto mathematician Shinichi Mochizuki’s claim to have proved the ABC conjecture. Unfortunately, the mathematics in his proof is so cryptic that a decision on its validity is unlikely for some time. August 2012: The Dorabella Cipher decryption is referred to by Robert Padgett here, and contributions to the Perfect Cuboid problem and the Riemann Hypothesis have been added to the Solutions page. March 2012: Seventh place in the Intel Science Talent Search 2012 was awarded to Anirudh Prabhu of Indiana, who received $25,000 for his investigation of the Odd Perfect Number problem, and his suggestion that odd perfect numbers do not exist. February 2012: A paper describing the solution to the Dorabella Cipher can be found on the web site of the National Cryptologic Museum Foundation (NCMF).
Some earlier items have now been removed ——————————– This web site developed and maintained by Tim S Roberts Email: timro21@gmail.com
