def solve(num,remaining):
#base case.
#Recheck that the number is valid
if len(num) == 10 and len(remaining) == 0:
valid = True
primes = cf.generate_primes_less_than(20)
#this loop makes sure that each candidate substring is divisible by
#the prime as defined by the problem (d2d3d4 % 2 == 0 and d3d4d5 %3 == 0, etc...)
for j in range(1,7):
substr = num[j:j+3]
prime = primes[j-1]
if int(substr) % prime != 0:
valid = False
break
#if indeed we pass the check, return the number
if valid:
return int(num)
else:
return 0
#as we flesh out the number, make sure it's valid before we move onto
#further ones.
sum = 0
for i in range(len(remaining)):
temp = num + remaining[i]
length = len(temp)
if temp[0] != '0' and (length < 4 or
length == 4 and int(temp[3]) % 2 == 0 or
length == 5 and int(temp[2:5]) % 3 == 0 or
length == 6 and int(temp[3:6]) % 5 == 0 or
length == 7 and int(temp[4:7]) % 7 == 0 or
length == 8 and int(temp[5:8]) % 11 == 0 or
length == 9 and int(temp[6:9]) % 13 == 0 or
length == 10 and int(temp[7:10]) % 17 == 0):
sum += solve(temp, remaining[0:i] + remaining[i+1:len(remaining)])
return sum
"""
Created on 2013-01-23
@author: paymahn
"""
import CommonFunctions as cf
import itertools as it
import time
t = time.time()
primes = cf.generate_primes_less_than(10000) # generate primes less than 10000
primes = set(x for x in primes if x > 1000) # remove primes less than 1000 (we only have 4 digit primes now)
for i in primes:
permutations = [
cf.tuple_to_num(x) for x in it.permutations(str(i))
] # get all the permutations of the digits of the current prime
permutations = set(
x for x in permutations if x in primes
) # remove duplicate permutations and non prime permutations
triplets = [x for x in it.permutations(permutations, 3)] # it's hard to explain this one succintly, use a debugger
for x in triplets: # test each triplet and print the triplet if it's valid
sorted_triplet = sorted(x)
if sorted_triplet[2] - sorted_triplet[1] == sorted_triplet[1] - sorted_triplet[0]:
print sorted_triplet
print time.time() - t
def replace(num, digit, locations):
result = num
for i in locations:
result -= num % 10**(i+1)
result += digit*10**i
result += num % 10**i
return result
t = time()
LIMIT = 1000000
primes = cf.generate_primes_less_than(LIMIT)
prime_set = set(primes)
valid_primes = [x for x in primes if x > 100109]
for p in primes:
length = int(math.log10(p)) + 1
for x in it.combinations(range(length),3): #not sure why the 3 works, but it does
primes_created = []
for r in range(10):
new_num = replace(p,r,x) #replaces digits indicated by x with the digit r in the number p
if new_num > 0 and int(math.log10(new_num)) + 1 == length and new_num in prime_set:
primes_created.append(new_num)
if len(primes_created) == 8 and p in primes_created:
@author: paymahn
'''
'''
f**k this, it's not working. I'm gonna try something different
'''
import CommonFunctions as cf
import itertools as it
import time
t = time.time()
pandigitals = [cf.tuple_to_num(x) for x in it.permutations(range(10))]
primes= cf.generate_primes_less_than(20)
tally = 0
for i in pandigitals:
i = str(i)
if len(i) == 10:
valid = True
for j in range(1,7):
substr = i[j:j+3]
prime = primes[j-1]
if int(substr) % prime != 0:
valid = False
break
if valid:
tally += int(i)
@author: paymahn
'''
'''
Can't find the 11th prime
'''
import CommonFunctions as cf
import time
import math
t = time.time()
primes = cf.generate_primes_less_than(1000000)
#remove primes that have even numbers
#turn into set for quick lookups
usable_primes = set([x for x in primes if not cf.contains_even_digit(x)])
tally = 0
count = 0
for x in usable_primes:
if x > 7 and count < 11:
#test left trucation
left = True
temp = x
''' Created on Jan 18, 2013 @author: PaymahnMoghadasian ''' # this was made better by implement the sieve of Erastothene in CommonFunctions.py import CommonFunctions as cf print sum(cf.generate_primes_less_than(2000000))
'''
Created on 2013-01-22
@author: paymahn
'''
import itertools as it
import CommonFunctions as cf
pan9 = [int(''.join(map(str,x))) for x in it.permutations(range(1,8),7)]
pan9.sort(reverse=True)
primes = cf.generate_primes_less_than(int(7654321**0.5))
for i in pan9:
if cf.is_prime(i, primes):
print i
break
print "finished"
'''
Note that b must be prime and positive (I'm not sure if there's such a thing as a negative prime)
|a| must be bigger than b because primes can't be negative. If |a| < b and b is prime then f(1) is negative, which is not prime
EX: let f(n) = n*n + a*n + b
f(1) = 1 + a + b
If |a| < b then f(1) < 2
'''
import CommonFunctions as cf
import time
t = time.time()
values_of_b = cf.generate_primes_less_than(1000)
primes = set(cf.generate_n_primes(300))
best_a, best_b = None, None
best_n = 0
print time.time() - t
for b in values_of_b:
for a in range(-b + 1, 10000):
n = 0
while n * n + a * n + b in primes:
n += 1
if n > best_n:
best_n = n
best_a = a
'''
Created on 2013-01-21
@author: paymahn
'''
import CommonFunctions as cf
import math
primes = set(cf.generate_primes_less_than(1000000))
count = 0
for i in primes:
#print "Testing prime", i
len = int(math.log10(i) + 1)
temp = i
valid = True
for j in range(len):
temp = (temp % 10**(len-1)) * 10 + temp/10**(len-1)
if temp not in primes:
valid = False
break
if valid:
print i
count += 1
print count
'''
Created on 2013-01-23
@author: paymahn
'''
import CommonFunctions as cf
MAX = 10000
primes = set(cf.generate_primes_less_than(MAX))
odd_composite = [x for x in range(1,MAX) if x%2==1 and x not in primes and x > 1]
squares = [x*x for x in range(1,MAX) if x*x <= MAX/2]
for i in odd_composite:
goldbach = False
for j in squares:
if i - 2*j in primes and not goldbach:
goldbach = True
break
if not goldbach:
print i
break
