def solution():
N = 10000
primes = []
for p in prime_start():
primes.append(p)
if p > N:
break
print(len(primes), 'primes generated')
lowSum = 5 * primes[-1]
pairs = {}
startTime = time.time()
# a, b, c, d, e are primes array index
for a in range(1, len(primes)):
if primes[a] * 5 > lowSum: break
if primes[a] not in pairs:
pairs[primes[a]] = findPairs(a, primes)
for b in range(a+1, len(primes)):
if primes[a] + primes[b] * 4 > lowSum: break
if primes[b] not in pairs[primes[a]]:
# print(primes[a], primes[b], 'no match found')
continue
if primes[b] not in pairs:
pairs[primes[b]] = findPairs(b, primes)
for c in range(b+1, len(primes)):
if primes[a] + primes[b] + primes[c] * 3 > lowSum: break
if primes[c] not in pairs[primes[a]] or primes[c] not in pairs[primes[b]]:
continue
if primes[c] not in pairs:
pairs[primes[c]] = findPairs(c, primes)
for d in range(c+1, len(primes)):
if primes[a] + primes[b] + primes[c] + primes[d] * 2 > lowSum: break
if primes[d] not in pairs[primes[a]] or primes[d] not in pairs[primes[b]] or primes[d] not in pairs[primes[c]]:
continue
if primes[d] not in pairs:
pairs[primes[d]] = findPairs(d, primes)
for e in range(d+1, len(primes)):
if primes[a] + primes[b] + primes[c] + primes[d] + primes[e] > lowSum: break
if primes[e] not in pairs[primes[a]] or primes[e] not in pairs[primes[b]] or primes[e] not in pairs[primes[c]] or primes[e] not in pairs[primes[d]]: continue
if lowSum > primes[a] + primes[b] + primes[c] + primes[d] + primes[e]:
lowSum = primes[a] + primes[b] + primes[c] + primes[d] + primes[e]
print('found', primes[a], primes[b], primes[c], primes[d], primes[e])
print('search accomplished in {0} seconds'.format(time.time() - startTime))
return lowSum
def bruteForce(target):
n = 1
for p in util.prime_start():
# reminder is always 2 when n is even number
if n % 2 == 0:
n += 1
continue
r = calculateR_v2(p, n)
if r > target:
break
n += 1
return n
def solution():
N = 5000
primes = []
for p in prime_start():
primes.append(p)
target = p
ways = [0] * (target + 1)
ways[0] = 1
for i in primes:
for j in range(i, target + 1):
ways[j] += ways[j - i]
if ways[j] > N:
return j
def solution():
primes = []
for p in prime_start(2000):
if p > 4500: break
primes.append(p)
N = 10000000
minResult = N
index = 0
for i in range(0, len(primes)):
for j in range(i, len(primes)):
n = primes[i] * primes[j]
if n > N: break
phi_n = (primes[i] - 1) * (primes[j] - 1)
ratio = float(n) / float(phi_n)
if isPermutation(n, phi_n) and ratio < minResult:
minResult = ratio
index = n
print('found {}, phi_i: {}, min: {}, prime factors: {}'.format(n, phi_n, minResult, (primes[i], primes[j])))
return index