def check_fraction(n1,n2):
d1 = mwmath.get_digits(n1)
d2 = mwmath.get_digits(n2)
if d1[1]==0:
if d2[1]==0:
return [1,1]
init_frac = 1.0*n1/n2
common = get_common_digit(n1,n2)
if len(common)==0:
return [1,1]
[new_1,new_2,new_frac] = remove_common_digit(n1,n2,common[0])
#print new_1
#print new_2
#print 'init:', init_frac
#print 'new:', new_frac
if init_frac==new_frac:
print 'hit'
print n1,' ',n2
print new_1,' ',new_2
return [new_1,new_2]
else:
return [1,1]
def get_common_digit(n1,n2):
d1 = mwmath.get_digits(n1)
d2 = mwmath.get_digits(n2)
common = []
for digit in d1:
if digit in d2:
common.append(digit)
return common
def is_permute(a,b):
if not len(str(a))==len(str(b)):
return False
b_dig = mwmath.get_digits(b)
for dig in mwmath.get_digits(a):
if dig in b_dig:
b_dig.remove(dig)
else:
return False
return True
def is_permute(a, b):
if not len(str(a)) == len(str(b)):
return False
b_dig = mwmath.get_digits(b)
for dig in mwmath.get_digits(a):
if dig in b_dig:
b_dig.remove(dig)
else:
return False
return True
def find_truncatable_primes(prime_list):
truncatable_count = 0
trunc_sum = 0
kk = 0
while truncatable_count<11:
new_p = prime_list[kk]
if new_p<11:
kk+=1
continue
digits = mwmath.get_digits(new_p)
check = True
if digits[0]==1 or digits[0]==9:
check=False
if new_p%10==1 or new_p%10==9:
check=False
for digit in digits:
if (digit!=2) and (digit%2==0):
check=False
#try to truncate from rinth
while check:
if len(mwmath.get_digits(new_p))==1:
break
new_p = int(str(new_p)[1:])
if not new_p in prime_list:
check=False
#truncate from left
new_p = prime_list[kk]
while check:
if len(mwmath.get_digits(new_p))==1:
break
new_p = int(str(new_p)[:len(mwmath.get_digits(new_p))-1])
if not new_p in prime_list:
check=False
new_p = prime_list[kk]
if check:
truncatable_count+=1
trunc_sum+=new_p
print "Found one: " +str(new_p)
kk+=1
return trunc_sum
def find_truncatable_primes(prime_list):
truncatable_count = 0
trunc_sum = 0
kk = 0
while truncatable_count < 11:
new_p = prime_list[kk]
if new_p < 11:
kk += 1
continue
digits = mwmath.get_digits(new_p)
check = True
if digits[0] == 1 or digits[0] == 9:
check = False
if new_p % 10 == 1 or new_p % 10 == 9:
check = False
for digit in digits:
if (digit != 2) and (digit % 2 == 0):
check = False
#try to truncate from rinth
while check:
if len(mwmath.get_digits(new_p)) == 1:
break
new_p = int(str(new_p)[1:])
if not new_p in prime_list:
check = False
#truncate from left
new_p = prime_list[kk]
while check:
if len(mwmath.get_digits(new_p)) == 1:
break
new_p = int(str(new_p)[:len(mwmath.get_digits(new_p)) - 1])
if not new_p in prime_list:
check = False
new_p = prime_list[kk]
if check:
truncatable_count += 1
trunc_sum += new_p
print "Found one: " + str(new_p)
kk += 1
return trunc_sum
def get_next_term(n, fact_dict):
d = mwmath.get_digits(n)
s = 0
for ii in d:
s += fact_dict[ii]
return s
def get_next_term(n,fact_dict):
d = mwmath.get_digits(n)
s = 0
for ii in d:
s+=fact_dict[ii]
return s
def get_next_term(n):
d = mwmath.get_digits(n)
s = 0
for ii in d:
s+=ii**2
return s
def remove_common_digit(n1, n2, common):
d1 = mwmath.get_digits(n1)
d2 = mwmath.get_digits(n2)
for digit in d1:
if not int(digit) == common:
new_1 = float(digit)
for digit2 in d2:
if not int(digit2) == common:
new_2 = float(digit2)
if new_2 == 0:
return [new_1, new_2, 0]
else:
return [1, 0, 0]
return [new_1, new_2, new_1 / new_2]
def remove_common_digit(n1,n2,common):
d1 = mwmath.get_digits(n1)
d2 = mwmath.get_digits(n2)
if d1[0]==common:
new_1 = d1[1]
else:
new_1 = d1[0]
if d2[0]==common:
new_2 = d2[1]
else:
new_2 = d2[0]
if new_2==0:
return [1,0,0]
else:
return [new_1,new_2,1.0*new_1/new_2]
def remove_common_digit(n1,n2,common):
d1 = mwmath.get_digits(n1)
d2 = mwmath.get_digits(n2)
for digit in d1:
if not int(digit)==common:
new_1 = float(digit)
for digit2 in d2:
if not int(digit2)==common:
new_2 = float(digit2)
if new_2==0:
return [new_1,new_2,0]
else:
return [1,0,0]
return [new_1,new_2,new_1/new_2]
def main():
fact_sum = []
for ii in range(3, 2903040):
digits = mwmath.get_digits(ii)
m_d = max(digits)
if m_d < 4 and ii > 100:
continue
if m_d < 6 and ii > 10000:
continue
if m_d < 9 and ii > 1000000:
continue
if m_d < 8 and ii > 100000:
continue
if sum(map(mwmath.nr_factorial, digits)) == ii:
fact_sum.append(ii)
return sum(fact_sum)
def main():
fact_sum = []
for ii in range(3,2903040):
digits = mwmath.get_digits(ii)
m_d = max(digits)
if m_d<4 and ii>100:
continue
if m_d<6 and ii>10000:
continue
if m_d<9 and ii>1000000:
continue
if m_d<8 and ii>100000:
continue
if sum(map(mwmath.nr_factorial,digits))==ii:
fact_sum.append(ii)
return sum(fact_sum)
def check_substring_properties(n):
digits = mwmath.get_digits(n)
prime_list = [2,3,5,7,11,13,17]
if len(digits)==10:
for ii in range(7,0,-1):
d = 100*digits[ii]+10*digits[ii+1]+digits[ii+2]
if d%prime_list[ii-1]==0:
continue
else:
return False
if len(digits)==9:
for ii in range(6,-1,-1):
d = 100*digits[ii]+10*digits[ii+1]+digits[ii+2]
if d%prime_list[ii-1]==0:
continue
else:
return False
return True
def check_substring_properties(n):
digits = mwmath.get_digits(n)
prime_list = [2, 3, 5, 7, 11, 13, 17]
if len(digits) == 10:
for ii in range(7, 0, -1):
d = 100 * digits[ii] + 10 * digits[ii + 1] + digits[ii + 2]
if d % prime_list[ii - 1] == 0:
continue
else:
return False
if len(digits) == 9:
for ii in range(6, -1, -1):
d = 100 * digits[ii] + 10 * digits[ii + 1] + digits[ii + 2]
if d % prime_list[ii - 1] == 0:
continue
else:
return False
return True
n = 10000
potential_primes = [2, 3]
ii = 1
while 6 * ii <= (n):
potential_primes.append(6 * ii - 1)
potential_primes.append(6 * ii + 1)
ii += 1
prime_list = []
for jj in potential_primes:
if mwmath.is_prime(jj):
prime_list.append(jj)
new_p = 37
digits = mwmath.get_digits(new_p)
check = True
for digit in digits:
if (digit % 2 == 0):
check = False
print "Contains an even digit"
#try to truncate from right
while check:
if len(mwmath.get_digits(new_p)) == 1:
break
new_p = int(str(new_p)[1:])
if not new_p in prime_list:
print "Breaking " + str(new_p) + " is not prime"
check = False
def main():
s = time.time()
return [sum(mwmath.get_digits(mwmath.nr_factorial(100))),time.time()-s]
def main():
Fact = mwmath.nr_factorial(100)
return sum(mwmath.get_digits(Fact))
def main():
s = time.time()
return [sum(mwmath.get_digits(mwmath.nr_factorial(100))), time.time() - s]
potential_primes=[2,3]
ii = 1
while 6*ii<=(n):
potential_primes.append(6*ii-1)
potential_primes.append(6*ii+1)
ii+=1
prime_list=[]
for jj in potential_primes:
if mwmath.is_prime(jj):
prime_list.append(jj)
new_p = 37
digits = mwmath.get_digits(new_p)
check = True
for digit in digits:
if (digit%2==0):
check=False
print "Contains an even digit"
#try to truncate from right
while check:
if len(mwmath.get_digits(new_p))==1:
break
new_p = int(str(new_p)[1:])
if not new_p in prime_list:
print "Breaking "+str(new_p)+" is not prime"
def digit_sum(n):
return sum(mwmath.get_digits(n))
def digit_sum(n):
return sum(mwmath.get_digits(n))