# Problem 569: Prime Mountain Range
A mountain range consists of a line of mountains with slopes of exactly
45°, and heights governed by the prime numbers, pn. The up-slope of the
kth mountain is of height p2k−1, and the downslope is p2k. The first few
foot-hills of this range are illustrated below. Tenzing sets out to
climb each one in turn, starting from the lowest. At the top of each
peak, he looks back and counts how many of the previous peaks he can
see. In the example above, the eye-line from the third mountain is drawn
in red, showing that he can only see the peak of the second mountain
from this viewpoint. Similarly, from the 9th mountain, he can see three
peaks, those of the 5th, 7th and 8th mountain. Let P(k) be the number of
peaks that are visible looking back from the kth mountain. Hence P(3)=1
and P(9)=3. Also \$\\displaystyle \\sum\_{k=1}\^{100} P(k) = 227\$. Find
\$\\displaystyle \\sum\_{k=1}\^{2500000} P(k)\$.