050.boo

/*
We use a list of primes (generated by sieve). We call it "cache".
We cache the sum of primes upto index "i" in "cache". We call it T[i].

T[j]-T[i] means "the sum of all consecutive primes in the index interval (j,i]"
And, for each pair (i,j) in T, we see if the results in a prime.

Eg.
i,j = (0, 6)
E[6] - E[0] = 41, the sum of primes from indices 1 to 6 
41 is prime, so 41 is a prime that is composed by the sum of 6 (j-1) primes
*/
import System
import System.Linq.Enumerable
import System.Collections.Generic

primes = PrimeNumbers(10**6)
cache = primes.Cache.ToArray()
T = array(long, cache.Length+1)
T[0] = 0

for i in range(1,cache.Length+1):
    T[i] = T[i-1] + cache[i-1]

max = 0
for i in range(T.Length):
    if i+max >= T.Length: continue
    for j in range(i+max, T.Length):
        k = T[j] - T[i]
        if k>=10**6: break
        if primes.IsPrime(k) and j-i > max:
            max = j-i
            answer = k

print answer
assert answer == 997651