  This paper is example 5 in chapter 5. Let H be an n-cycle. A permutation s is
H-admissible if Hs = H' where H' is an n-cycle. Here we define a 19 X 19
matrix, M, in the following way: We obtain the remainders modulo 100 of each of
the smallest 342 odd primes. we obtain the remainders modulo 100 of each of the
primes. They are placed in M according to the original value of each prime.
Thus their placement depends on the the original ordinal values of the primes
according to size. We use this ordering to place the primes in M. Let H_0 be an
initial 19 cycles arbitrarily chosen. We apply a sequence of up to [ln(n)+1]
H_0 3-cycles to obtain a 19-cycle of smaller value than H_0, call the new
19-cycle H_1. We follow this procedure to obtain H_1. We call [ln(n)] + 1 a
chain. We add up the values of the 19-cycles in each chain. This procedure
continues until we cannot obtain a chain the sum of whose values is not
negative. COMMENT. I've renamed the document "Yhe General Traveling Salesman
Problem, Version 5". I preciously named it "The Traveling Salesman, Version 5".
Although the algorithms work on the GTSP, I thought that more people would
google it if it was named "The Traveling Salesman Problem." Rhar qas because my
work is only available through arxiv.org,
