def Primedivisors(N):
"""return the list of Primedivisors for natural number N"""
import Primelist
import math
import itertools
import P3
primediv=[]
div_num=1
divs=[1,N]
if P3.IsPrime(N)==True:
#return ([],2,divs)
return []
a=Primelist.primes(N/2)
#return primedivisors
while(N!=1):
for i in a:
while N%i==0:
N=N/i
primediv.append(i)
#return divisors number
#for i in set(primediv):
#div_num=div_num*(primediv.count(i)+1)
##return divisors
#for i in range(1,len(primediv)+1,1):
#b=itertools.combinations(primediv,i)
#for j in b:
#prod=1
#for k in j:
#prod=prod*k
# divs.append(prod)
#return (primediv,div_num,set(divs))
return primediv
def CG_conjecture(N):
"""docstring for CG_conjecture"""
a=Primelist.primes(N)
for i in a[1:]:
if IsSquareNum((N-i)/2):
#print N,'=',i,'+','2*',math.sqrt((N-i)/2),'**2'
return True
return False
import Primelist
from P3 import IsPrime
listb = Primelist.primes(1000)
lista = range(-999, 1000, 2)
def f1(a, b):
return lambda n: n ** 2 + a * n + b
def Nprime(c):
n = 0
nprime = 0
while c(n) > 0:
if IsPrime(c(n)):
n += 1
nprime += 1
else:
break
return nprime
res = []
for a in lista:
for b in listb:
c = f1(a, b)
n = Nprime(c)
# print n,a,b
res.append((n, a, b))
print max(res)
import Primelist
import P3
def TruncatablePrime(N):
"""docstring for TruncatablePrime"""
N=str(N)
tmplist=[]
for i in range(1,len(N)):
tmplist.append(N[i:])
tmplist.append(N[0:len(N)-i])
#print tmplist
tmplist=map(int,tmplist)
for TruncatedNum in tmplist:
if not(P3.IsPrime(TruncatedNum)):
return False
return True
if __name__ == '__main__':
inilist=Primelist.primes(1000000)
result=[]
for i in inilist:
if TruncatablePrime(i):
print i
result.append(i)
print sum(result[4:]),len(result)-4
results.append(N)
return results
def cyclic(N):
"""docstring for cyclic"""
results=[]
if len(str(N))==1:
return [N]
for i in str(N):
if int(i) not in [1,3,7,9]:
return []
return map(int,RingRotate(N))
def cyclicPrime(N):
if cyclic(N)==[]:
return []
for i in cyclic(N):
if not(P3.IsPrime(i)):
return []
return N
if __name__ == '__main__':
prims=Primelist.primes(1000000)
result=[]
for i in prims:
if cyclicPrime(i):
result.append(i)
print result,len(result)
import math
import itertools
import Primelist
if __name__ == '__main__':
num=[]
a=Primelist.primes(9999)
a=[i for i in a if i>1000]
for i in a:
b=itertools.permutations(str(i))
for c in b:
d=[map(int,x) for x in c]
if d[0]!=0:
k=d[0][0]*1000+d[1][0]*100+d[2][0]*10+d[3][0]
if k in a:
num.append(k)
a.pop(a.index(k))
#print count,k
if len(set(num))>=3:
tmp=itertools.combinations(num,2)
for comb in tmp:
#print comb,sum(comb),num
if sum(comb)/2 in num:
print num,comb,sum(comb)/2
num=[]