Here's the challenge: Find a counterexample of XGC(c, m)

i.e. find at least a natural n, multiple of m, not less than m * ( c + m ), such that it cannot be written as the sum of m numbers taken from the Euclid(c, m) set.
A Euclid(c, m) set is defined as the set of naturals of the form c + m * k which are all prime to each other, starting with k = 1, and being c prime to m.

Greatest Hits

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In the following table are reported all the known greatest hits achieved in the search for a counterexample of XGC, along with the name of the person who did it and an URL to her/his internet page or e-amil, whenever available.