##
Three Unique Primes

What is the largest integer less than 100 which cannot be written as the sum
of three unique prime numbers? Less than 1000? Less than 1 million?
For example,

10 = 5+3+2, all unique.

11 = 7+2+2 = 5+3+3, but neither sum has
all three primes unique.

*Extension*: The problem above actually has been investigated
thoroughly. Try also finding the largest integer in each range which
can be written as exactly one such sum.

Source: Original.

Solution

Mail to Ken