Determine the largest even positive integer that cannot be written as the sum of two odd composite positive integers.
38 is the answer
For an even integer over 38:
If it's 0 mod 3, then it equals 3*3+ an odd
multiple of 3;
If it's 1 mod 3, then it equals 5*5 + an
odd multiple of 3;
If it's 2 mod f 3, then
it's 35 plus an odd multiple of 3.
In all those cases there exist two composite addends.
Therefore the largest
possible one is 38.
38=1+37=3+35=5+33=7+31=9+29=11+27=13+25=
=15+23=17+21=19+19
In each of the above couples at least one number is a
prime.
solution
