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50-consecprimes.py
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50-consecprimes.py
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#Problem 50
#May 17, 2011
#Which prime, below one-million, can be written as the sum of the most consecutive primes?
import math
BELOW_WHAT = 1000000
def isPrime(n):
if n==0:
return False
if n==1:
return False
elif n<4:
return True
elif n%2 == 0:
return False
elif n<9:
return True
elif n%3 == 0:
return False
else:
r = int(math.sqrt(n)+1)
f=5
while f<=r:
if n%f == 0:
return False
if n%(f+2) == 0:
return False
f=f+6
return True
#Generate a prime
def primeGen():
n = 1
while 1:
n += 1
if(isPrime(n)):
yield n
sos = {} #sums of sequences
def sumOfSequence(start,end,seq):
outerkey = start
innerkey = end
if outerkey in sos:
if (innerkey-1) in sos[outerkey]:
val = sos[outerkey][innerkey-1] + seq[innerkey]
d = {innerkey:val}
sos[outerkey] = d
return val
val = sum(seq[start:end])
d = {innerkey:val}
sos[outerkey] = d
return val
g = primeGen()
primelist = []
while True:
p = g.next()
if(p>=BELOW_WHAT):
break
primelist.append(p)
mx = 0
manchurian_candidate = 0
for i in range(len(primelist)):
if(i%1000==0):
print '.',
for j in range(len(primelist)):
if(i > j): continue
sm = sumOfSequence(i,j,primelist)
if(sm > BELOW_WHAT):
break
if(isPrime(sm)):
l = len(primelist[i:j])
if(l > mx):
mx = l
manchurian_candidate = sm
print
print manchurian_candidate