import Tools import Prime n = 10**7 Prime.prime_seive(n) print min( [ (n/float(t),n,t) for n,t in Prime.totient(n) if Tools.is_perm(n,t) ])
#!/usr/bin/python2
import Prime
import math
def corners(max_n):
for n in xrange(1,max_n+1):
odd = 2*n+1
d = 2*n
for i in xrange(odd**2 - 3*d, odd**2+1, d):
yield i
n = 13500
Prime.prime_seive((2*n+1)**2)
iprime = 0
n_primes = 0.
total = 0.
for c in corners(n):
for i in xrange(iprime,Prime.n_primes):
if Prime.primes[i] == c:
n_primes += 1.
break
elif Prime.primes[i] > c:
break
iprime = i
#pf = Prime.primeFactors(c)
#if Prime.primeFactors(c).isPrime():
#n_primes += 1.
total += 1.
import Prime
from collections import deque
primeset = set(Prime.prime_seive(1000000))
circulars = set()
for p in primeset:
strp = deque(str(p))
cycles = set()
isCircular = True
for i in range(len(strp)):
strp.rotate(1)
i = int(''.join(map(str, strp)))
if i in primeset:
cycles.add(i)
else:
isCircular = False
if isCircular:
circulars = circulars | cycles
print (circulars, len(circulars))
import Prime as p
primeset = set(p.prime_seive(9999))
def is_permutation(one,two):
return sorted(str(one)) == sorted(str(two))
for i in range(p.n_primes):
if p.primes[i] < 1000 : continue
for j in range(i+1,p.n_primes):
if p.primes[j] < 1000 : continue
if not is_permutation(p.primes[i], p.primes[j]):
continue
third = 2*p.primes[j] - p.primes[i]
if third in primeset and is_permutation(p.primes[j],third):
print p.primes[i], p.primes[j],third
import Prime
primeset = set(Prime.prime_seive(999999))
total = 0
for p in primeset:
#left
pstr = str(p)
if len(pstr) == 1 : continue
truncatable = True
for i in range(1,len(pstr)):
if not int(pstr[-i:]) in primeset : truncatable = False
if not int(pstr[:i]) in primeset : truncatable = False
if truncatable:
print p
total += p
print total
import Prime from time import time s = time() print sum(Prime.prime_seive(2000000)) print time() - s
import Prime
def quad_prime(a,b,prime_set):
n = 0
x = n**2 + a*n + b
while x in prime_set:
x = n**2 + a*n + b
yield x
n+=1
Prime.prime_seive(100000)
prime_set = set(Prime.primes)
maximum = (0, 0, 0)
for b in Prime.primes:
length = 0
if b > 1000:
break
for a in xrange( 1-b, 1000 ):
l = len([p for p in quad_prime(a,b,prime_set) ] )
maximum = max(maximum,(l,a,b))
print maximum, maximum[1]*maximum[2]
for b in np.arange(1,10, dtype = float):
if a == b : continue
if (i*10+a)/(i*10+b) == a/b and (i*10+a)/(i*10+b) < 1:
print (i*10+a),'/',(i*10+b)
numerators.append(i*10+a)
denominators.append(i*10+b)
if (i+a*10)/(i*10+b) == a/b and (i+a*10)/(i*10+b) < 1:
print (i+a*10),'/',(i*10+b)
numerators.append(i+a*10)
denominators.append(i*10+b)
if (i+a*10)/(i+b*10) == a/b and (i+a*10)/(i+b*10) < 1:
print (i+a*10),'/',(i+b*10)
numerators.append(i+a*10)
denominators.append(i+b*10)
if (i*10+a)/(i+b*10) == a/b and (i*10+a)/(i+b*10) < 1:
print (i*10+a),'/',(i+b*10)
numerators.append(i*10+a)
denominators.append(i+b*10)
top = int(np.prod(numerators))
bot = int(np.prod(denominators))
Prime.prime_seive(max(top,bot))
pt = Prime.primeFactors(top)
pb = Prime.primeFactors(bot)
gcd = pt.GCD(pb).getValue()
print top,bot,gcd
print top/gcd, bot/gcd
import Prime
n = 1000000
primeset = set(Prime.prime_seive(n))
total = 0
for max_n,p in enumerate(Prime.primes):
total += p
if total > n:
break
l = max_n
lb = 5
while l > lb:
for i in range(Prime.n_primes - l + 1):
s = sum(Prime.primes[i:i+l])
if s > n :
break
if sum(Prime.primes[i:i+l]) in primeset:
print l,Prime.primes[i:i+l],sum(Prime.primes[i:i+l])
l = lb
break
l -= 1
import Prime
from itertools import permutations
max_prime = 10000000
ps = set(Prime.prime_seive(max_prime))
done = False
for p in Prime.primes:
pstr = str(p)
for d in set(pstr):
family = []
for i in "0123456789":
f = int(pstr.replace(d,i))
if not len(str(f)) == len(pstr):
continue
if f in ps:
family.append(f)
if len(family) == 8:
done = True
print family
break
if done : break
res = a*1000000 + b
elif b > 10000:
res = a*100000 + b
elif b > 1000:
res = a*10000 + b
elif b > 100:
res = a*1000 + b
elif b > 10:
res = a*100 + b
else:
res = a*10 + b
return res
max_n = 99999999
Prime.prime_seive(max_n)
prime_set = set(Prime.primes)
pairs = {}
print "Making pairs"
ttotal = 0
for i in xrange(Prime.n_primes):
p1 = Prime.primes[i]
for j in xrange(i+1, Prime.n_primes):
ttotal += 1
p2 = Prime.primes[j]
#if Prime.isPrime(cat_ints(p1,p2)) and Prime.isPrime(cat_ints(p2,p1)):
new_p1 = cat_ints(p1,p2)
if new_p1 in prime_set:
new_p2 = cat_ints(p2,p1)
if new_p2 in prime_set :
import Prime
from Tools import pandigitals
max_pan = 0
# Note: for n=8,9 all pandigitals are divisible by 9
primeset = set(Prime.prime_seive(int(1e7)))
for i in [7,6,5,4,3,2,1]:
for p in pandigitals(i):
if p in primeset:
max_pan = max(p,max_pan)
if max_pan:
print max_pan
break
