def p27():
global sieve
testSieve = get_sieve_erosthane(15000)
testSieve.sort()
sieve = set(testSieve)
primes = get_sieve_erosthane(1000)
primes.sort()
max, a, b = 0, 0, 0
for j in primes:
# A must be prime too
for i in primes:
# i + j > 0
if not i + j > 0 : pass
# 1 + i + j is also a prime
if not 1+i+j in sieve : pass
n = check(i, j)
if n > max :
max, a, b = n, i, j
n = check(-i, j)
if n > max :
max, a, b = n, -i, j
# skipping -j as -ve numbers are not considered primes
return (max, a, b)
def p49():
s = get_sieve_erosthane(9999, sort = True)
sieve = [n for n in s if n >= 1000]
sieveSet = set(sieve)
answers = set()
for n in sieve:
perm = permutations(str(n))
num = set([list_to_int(i) for i in perm if list_to_int(i) in sieveSet])
if len(num) < 3 : continue
num = list(num)
num.sort()
l = len(num)
for i in range(0, l):
for j in range(i+1, l):
diff = num[j] - num[i]
if num[i] + diff not in num or num[i] + 2 * diff not in num :
continue
answers.add((num[i], num[i]+diff, num[i]+diff+diff))
return answers
def p41():
numbers = ['0', '1', '21', '321', '4321', '54321', '654321', '7654321']
# sqrt(999999999) = 31622
sieve = get_sieve_erosthane(32000, sort = True)
for i in range(7, 1, -1):
perm = permutations(numbers[i])
for p in perm:
num = list_to_int(p)
if pTest_sieve(num, sieve) :
return num
def p46():
n = 10000
sieve = get_sieve_erosthane(n, method='set')
for i in range(3, n, 2):
# Since only composite numbers
if i in sieve : continue
# Count down from the number to 2 (smallest prime)
success = False
for j in range(1, i):
# 2 x (j ^ 2)
diff = i - (2 * j * j)
if diff in sieve:
#print i, diff, j
success = True
break
if not success : return i
def p37():
limit = 740000
sieve = get_sieve_erosthane(limit)
sieve.sort()
sieve_set = set(sieve)
answer = []
for n in sieve[4:]:
ns = str(n)
# Any number with a 0, 2, 5 cannot be a truncatable prime
if '0' in ns or '2' in ns or '5' in ns : continue
flag = True
for i in range(1, len(ns)):
if int(ns[i:]) not in sieve_set or int(ns[:i]) not in sieve_set :
flag = False
break
if flag : answer.append(n)
print answer
return sum(answer)
def p35():
sieve = get_sieve_erosthane(1000000, 'set')
# Starting with the obvious ones
circularPrimes = [2, 3, 5, 7]
for i in list(sieve)[4:]:
flag = True
si = str(i)
if '2' in si or '5' in si or '0' in si:
flag = False
else:
for j in rotate(si):
# Converts a list of digits to a single integer
n = reduce(lambda rst, d: int(rst) * 10 + int(d), j)
if n not in sieve :
flag = False
break
if flag :
circularPrimes.append(i)
#print i
return len(circularPrimes)
