def p60():
""" The 5-prime set with the least sum s.t concatenation
of any pair of primes in any order results in a prime"""
# we start with n = 100000
pslist = primes.getPrimeList(100000)
matchingPrimes = {}
def add(p, q):
if p not in matchingPrimes:
matchingPrimes[p] = set()
matchingPrimes[p].add(q)
return
def recurse(ps):
if len(ps) == 5:
return sum(ps)
ret = 10**100
p1 = ps[0]
if p1 not in matchingPrimes:
return ret
for q in matchingPrimes[p1]:
matchesAll = True
for p in ps[1:]:
if q not in matchingPrimes[p]:
matchesAll = False
break
if matchesAll:
ret = min(ret, recurse(ps + [q]))
return ret
for p in pslist:
for q in pslist:
if p >= q:
break
pq = int(str(p) + str(q))
qp = int(str(q) + str(p))
if primes.checkIfPrime(qp) and primes.checkIfPrime(pq):
add(p, q)
add(q, p)
ret = 1 << 100
for p in pslist:
if p in matchingPrimes:
ret = min(ret, recurse([p]))
return ret
def p3():
""" Largest prime factor of the number 600851475143"""
number = 600851475143
squareRoot = int(number**0.5)
ret = 0
for s in xrange(2, squareRoot + 1):
if number % s == 0:
if primes.checkIfPrime(s):
ret = max(ret, s)
while number % s == 0:
number = number / s
if number != 1 and primes.checkIfPrime(number):
ret = max(ret, number)
return ret
def testFewKnownPrimes(self):
known_primes = [
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61,
67, 71, 73, 79, 83, 89, 97
]
for n in xrange(1, 101):
inclusion = n in known_primes
primality = primes.checkIfPrime(n)
self.assertTrue(not (inclusion ^ primality))
def p41():
""" Largest pandigital prime """
res = 0
for d in xrange(4, 9):
digits = range(1, d + 1)
allPerms = combinatorics.genAllPerms(digits)
for perm in allPerms:
num = 0
for d in perm:
num = 10 * num + d
if primes.checkIfPrime(num):
res = max(res, num)
return res
def getLen(a, b):
n = 0
while primes.checkIfPrime(n * n + a * n + b):
n = n + 1
return n