import q27
import math
if __name__ == '__main__':
primes = q27.generatePrimeList(1000000)
l = list(primes)
l.sort()
for x in range(9, 1000001, 2):
if x in primes:
continue
flag = False
for p in l:
if p >= x:
break
y = math.sqrt((x - p) / 2)
print(y)
if y == int(y):
flag = True
break
if not flag:
print(x)
break
import q27
if __name__ == '__main__':
denom = sorted(list(q27.generatePrimeList(5000)))
n = 2
while (1):
total = [[0] * len(denom) for _ in range(n + 1)]
total[0] = [1] * len(denom)
#print(total)
for i in range(1, n + 1):
for j, x in enumerate(denom):
x = total[i - x][
j] if i - x >= 0 else 0 #if the number includes the denominator x
y = total[i][j - 1] if j >= 1 else 0
total[i][j] = x + y
print(n, total[n][len(denom) - 1])
ways = total[n][len(denom) - 1]
if ways >= 5000:
break
n += 1
import q72
import q27
if __name__ == '__main__':
n = 10**7
primes = q27.generatePrimeList(n)
spf = q72.seiveSpf(n)
print("primes and seive calculation finished")
mind = 10**99
minN = 0
for x in range(2, n + 1):
if x in primes:
continue
y = q72.totient(x, spf)
if sorted(str(x)) == sorted(str(y)):
if x / y < mind:
print(x, y)
mind = x / y
minN = x
import q27
import itertools
def isArithmeticSeq(arr):
return arr[0] + arr[2] == 2 * arr[1]
if __name__ == '__main__':
l = q27.generatePrimeList(10000)
r = q27.generatePrimeList(1000)
primeSet = l.difference(r)
primes = list(primeSet)
primes.sort()
print(len(primes))
permutes = list(
map(int,
[''.join(x) for x in list(itertools.permutations(str(1487)))]))
print(permutes)
for x in primes:
permutes = list(
map(int,
[''.join(x) for x in list(itertools.permutations(str(x)))]))
count = 0
seq = set()
for y in permutes:
if y in primeSet:
count += 1
seq.add(y)
if len(seq) >= 3:
def checkP(n, primes, maxPrime):
if n < maxPrime:
return n in primes
return is_prime(n)
def checkCartConcatPrimes(a, b, primes, maxPrime):
ij = int(str(a) + str(b))
ji = int(str(b) + str(a))
if not checkP(ij, primes, maxPrime) or not checkP(ji, primes, maxPrime):
return False
return True
if __name__ == '__main__':
primeset = q27.generatePrimeList(10000000)
maxP = max(primeset)
primes = sorted(list(q27.generatePrimeList(8500)))
primes = primes[:8400]
print(primes[:5])
print(len(primes))
pd = dict()
for i in range(len(primes)):
for j in range(i + 1, len(primes)):
if checkCartConcatPrimes(primes[i], primes[j], primeset, maxP):
if primes[i] in pd:
pd[primes[i]].add(primes[j])
else:
pd[primes[i]] = set()
pd[primes[i]].add(primes[j])
