def make_pairs(N):
"""Makes a prime pairs graph.
Args:
N: Largest possible prime in the prime pairs graph.
Returns:
A dictionary.
"""
g = defaultdict(lambda: [])
for i in range(3, N):
if not utils.isPrime(i):
continue
for j in range(i+1, N+1):
if not utils.isPrime(j):
continue
ij = int(str(i) + str(j))
if not utils.isPrime(ij):
continue
ji = int(str(j) + str(i))
if not utils.isPrime(ji):
continue
g[i].append(j)
g[j].append(i)
return g
def solve():
p = 223
condition = True
l = getSubsets(len(str(p)))
lastLength = len(str(p))
while (condition):
print(p)
st = str(p)
if (lastLength != len(str(p))):
l = getSubsets(len(str(p)))
lastLength = len(str(p))
for i in l:
count = 0
z = []
for j in range(0, 10):
newSt = st
for k in i:
newSt = newSt[:k] + str(j) + newSt[k+1:]
num = int(newSt)
if (num != 0 and math.floor(math.log(num, 10)) + 1 != len(newSt)):
continue
if (u.isPrime(int(newSt))):
count = count + 1
z.append(newSt)
if (j > 2 and count < j - 2):
break
if (count == 8):
condition = False
print(p, z)
p = u.nextPrime(p)
def solve():
p = 223
condition = True
l = getSubsets(len(str(p)))
lastLength = len(str(p))
while (condition):
print(p)
st = str(p)
if (lastLength != len(str(p))):
l = getSubsets(len(str(p)))
lastLength = len(str(p))
for i in l:
count = 0
z = []
for j in range(0, 10):
newSt = st
for k in i:
newSt = newSt[:k] + str(j) + newSt[k + 1:]
num = int(newSt)
if (num != 0
and math.floor(math.log(num, 10)) + 1 != len(newSt)):
continue
if (u.isPrime(int(newSt))):
count = count + 1
z.append(newSt)
if (j > 2 and count < j - 2):
break
if (count == 8):
condition = False
print(p, z)
p = u.nextPrime(p)
def solve():
for i in range(0, 9):
l = getPandigitalList(i+1)
for j in l:
if (utils.isPrime(int(j))):
print(j)
break
print(i)
def solve():
for i in range(0, 9):
l = getPandigitalList(i + 1)
for j in l:
if (utils.isPrime(int(j))):
print(j)
break
print(i)
def solve():
i = 1001
while (i < 9999):
if (p.isPrime(i)):
ll = l.getListOfPermutations(str(i))
diff = 0
num = 0
for n in ll:
num = int(n)
if (num != i and p.isPrime(num)):
diff = num - i
last = num + diff
try:
if (ll.index(str(last)) >= 0 and p.isPrime(last)):
print(i, num, last)
except ValueError:
continue
i = i + 2
def solve():
i = 1001
while (i < 9999):
if (p.isPrime(i)):
ll = l.getListOfPermutations(str(i))
diff = 0
num = 0
for n in ll:
num = int(n)
if (num != i and p.isPrime(num)):
diff = num - i
last = num + diff
try:
if (ll.index(str(last)) >= 0 and p.isPrime(last)):
print(i, num, last)
except ValueError:
continue
i = i + 2
def solve():
count = 0
for i in range (2, 1000000) :
l = getListOfRotations(i)
flag = True
for n in l:
if (not utils.isPrime(n)):
flag = False
break
if (flag == True):
count = count + 1
return count
def solve():
conjecture = True
n = 9
while (conjecture == True):
conjecture = False
while (utils.isPrime(n)):
n = n + 2
for i in range(2, n - 1):
if (utils.isPrime(i)):
twice = n - i
j = 1
difference = twice - 2 * j**2
while (difference >= 0):
if (difference == 0):
conjecture = True
print(n, '=', i, '+2*', j, '^2')
break
j = j + 1
difference = twice - 2 * j**2
if (conjecture == True):
break
if (conjecture == False):
return n
n = n + 2
def solve():
conjecture = True
n = 9
while (conjecture == True):
conjecture = False
while (utils.isPrime(n)):
n = n + 2
for i in range(2, n - 1):
if (utils.isPrime(i)):
twice = n - i
j = 1
difference = twice - 2*j**2
while (difference >= 0):
if (difference == 0):
conjecture = True
print(n, '=', i, '+2*', j, '^2')
break
j = j + 1
difference = twice - 2*j**2
if (conjecture == True):
break
if (conjecture == False):
return n
n = n + 2
def solve():
count = 1
summ = 0
i = 11
while (count <= 11):
l = getListOfTruncations(i)
flag = True
for n in l:
if (not utils.isPrime(int(n))):
flag = False
break
if (flag == True):
summ = summ + i
count = count + 1
i = i + 1
return summ
def solve():
count = 1
summ = 0
i = 11
while (count <= 11):
l = getListOfTruncations(i)
flag = True
for n in l:
if (not utils.isPrime(int(n))):
flag = False
break
if (flag == True):
summ = summ + i
count = count + 1
i = i + 1
return summ
def solve():
bestL = 0
bestP = 0
p = 2
length = 2
bound = 1000000
while (p < bound):
s = 0
last = p
length = 2
while (s < bound):
s = s + last
last = u.nextPrime(last)
if (u.isPrime(s) and length > bestL):
bestL = length
bestP = s
if (bestP > bound):
break
else:
print(p, bestL, bestP)
length = length + 1
p = u.nextPrime(p)
print(bestL, bestP)
def solve():
bestL = 0
bestP = 0
p = 2
length = 2
bound = 1000000
while (p < bound):
s = 0
last = p
length = 2
while (s < bound):
s = s + last
last = u.nextPrime(last)
if (u.isPrime(s) and length > bestL):
bestL = length
bestP = s
if (bestP > bound):
break
else:
print(p, bestL, bestP)
length = length + 1
p = u.nextPrime(p)
print(bestL, bestP)