Christian Goldbach was an 18th century mathematician who is best known for the Goldbach Conjecture which states that any even integer greater than two can be written as a sum of two primes. A prime is an integer greater than one which is evenly divisible only by one and by itself, viz.
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 ...
For the first few even integers greater than two we have
4 = 2+2
6 = 3+3
8 = 3+5
10 = 5+5 = 3+7
This partitioning into two primes is often not unique. For example for 100 there are six distinct ways:
100 = 3+97 = 11+89 = 17+83 = 29+71 = 41+59 = 47+53
In 1742, Goldbach proposed his conjecture to Leonhard Euler (pronounced "oiler") who was one of the most prolific mathematicians not only of his day but of all time. Euler tested the conjecture up to 2500 or so; he concluded that it was probably true but was beyond the capabilities of mathematics of the day, a status it has maintained for 270 years.
You can validate your puzzle solution with certitude.
More than you need to know:
- The conjecture has been verified up to at least 1018.
- For more on Goldbach and his times, see Goldbach.
- For an interesting novel based on the conjecture read Uncle Petros and Goldbach's Conjecture.
- At the time of publication of the novel there was a $1,000,000 award offered for a proof of the conjecture.
Some Links:
The first ten solvers are:
1. pfalstad Fri, 10 Aug 2012 21:39:44
2. Nylimb Sat, 11 Aug 2012 0:39:27
3. turuthok Sat, 11 Aug 2012 1:57:14
4. foundinthewild Fri, 21 Dec 2012 11:46:08
5. Essap Sun, 24 Feb 2013 19:24:30
6. dmneiman Mon, 24 Feb 2014 18:04:16
7. pcc322 Sun, 9 Mar 2014 20:39:09
8. Red_Devil35 Sun, 9 Mar 2014 21:07:07
9. Hives Thu, 17 Apr 2014 14:47:35
10. leopold22 Thu, 17 Apr 2014 15:07:25