def find_perms(): primes.init(10**7) big_primes = [p for p in reversed(primes.primes_list)] min = 10**7 minval = 10**7 start = cfn.binary_search(primes.primes_list, math.sqrt(10**7), len(primes.primes_list)-1,0) print start big_primes = [p for p in reversed(primes.primes_list[:start+1])] for p in big_primes: for bp in reversed(big_primes): if bp > p: break for bp2 in reversed(big_primes): if bp2 > bp: break print p,bp,bp2 comp = int(p)*int(bp)*int(bp2) ep = int(p-1)*int(bp-1)*int(bp2-1) if comp/(ep*1.) >= minval: break if (cfn.digit_hash(comp)==cfn.digit_hash(ep) and comp/(ep*1.) < minval): min = comp minval = comp/(ep*1.) print comp,p,bp,bp2,ep,comp/(ep*1.) break #biggest for this p
def main(n): primes.init(10**6) nums = [1,3,7,9,13,27] offnums = [11,17,19,21,23] total = 0 failure = False #below is the only intelligent part #look at each of the numbers modulo 5 #and we can eliminate all possibilities for #n^2 except for n mod 5 = 0. for x in xrange(10,n,10): square = x*x if (((x % 3) not in (1,2)) or ((x % 7) not in (3,4))): continue for offset in nums: if not primes.is_prime(square+offset): failure = True break if failure: failure = False continue for offset in offnums: if primes.is_prime(square+offset): failure = True break if not failure: print "Yay",x total += x failure = False print total
def main(): primes.init(10**6) sums = [0]*(10**6+1) for x in range(1,10**6): primes.factor(x) print x print x
def find_all(max): result = [] primes.init(max) for p in primes.primes_list: divides = is_prime_divider(int(p)) if divides: result.append(p) return result
def main(): sol = [] prime_length = 10**8 pr.init(prime_length) primes = 1 while sol == []: if primes > prime_length: pr.init(primes) sol = solutions(1200,5) print sol print "answer:",sum(sol)
def main(): primes.init(1000*1000+10) cur = 2 total = 0 while cur <= 1000*1000: total+= int(primes.euler_phi(cur)) if cur % 1000 == 0: print cur if total < 0: print type(total),type(cur) break cur +=1 print total
def main(): primes.init(10**7) pl = primes.primes_list start = bisect(pl,10**5) print start for n,p in enumerate(pl[start:]): p = int(p) p2 = p**2 rem = (fmp(p-1,n+1+start,p2)+fmp(p+1,n+1+start,p2) )% p2 if rem > 10**10: break print p,rem,n+start+1
def main(max): primes.init(2*max+1) k = 89 results = [] while len(results) <25: k+=2 if k % 5 == 0: k+=2 if primes.is_prime(k): continue small = smallest_k(k) if small and ((k-1) % small) == 0: print small results.append(k) print results print sum(results)
def main(max): primes.init(2*max+1) #A(n) < n. Apparently, the pigeonhole principle can be pulled out #but I'm a bit confused as to how, as the number of states #the sum can be in is dependent not only on the current sum #but also the number of possible increments. Both of these #potentially are n, so it seems the A(n) is only bounded by n^2. #for non-zero divisors, this can be immediately shown. k = 10**6-1 small = None while small == None: k+=2 if k % 5 == 0: k+=2 small = smallest_k(k) if small < max: small = None print k
#So, assuming we have an array with all primes less than 100 million #(roughly 10 million I believe), how do we quickly find the reduced #multiples? I'm not going to bother actually. I'm just going to run #through it. It'll be slow at first, but the difference between #6th and the 7th smallest isn't that big, and we're just iterating #through the array downwards, so the entire algorithm will be O(n) #(roughly, not paying to much attention) import math import primes def down_count(prime_array): total = 0 index_left = 0 index_right = len(prime_array)-1 while index_left <= index_right: if ((prime_array[index_left]* prime_array[index_right]) <= 10**8): total += index_right-index_left+1 print "total",total index_left +=1 else: index_right -= 1 return total if __name__=="__main__": print "Beginning Count!" primes.init(10**8/2) print down_count(primes.primes_array)
def main(): primes.init(100) sum_fixed_n(10)
memo[special]= None result = None for prime in p.primes_list: count = 0 if prime in special: continue for s in special: if p.is_prime(p.concat_nums(prime,s)): if p.is_prime(p.concat_nums(s,prime)): count +=1 if count == len(special): result = special+(prime,) break if result == None: for i in range(len(special)): for prime in p.primes_list[1:]: if prime not in special: result = tryit(special[:i]+(prime,) +special[i+1:]) if result: print result break if result: break memo[special] = result return memo[special] if __name__=="__main__": p.init(1*10**4) print sum(tryit((3,7,109,673)))
#sum of prime factors of #20*10**6, 15*10**6 import numpy as np import primes def somewhat_smaller_binom(n,k): z = np.arange(k,n+1) #for i in np.arange(2,(n-k)+1): z[:-2] /= np.arange(2,(n-k)+1) map(primes.factor,z) primes.init(10**7) print somewhat_smaller_binom(20*10**6,15*10**6)
import primes import itertools as it import sys def spiral(n): sum = 1 for side in range(2,n,2): for corner in range(4): sum += side yield sum,side+1 def prime_percent(n): prime_count = 0 percent = 1 for i,(s,side) in it.izip(it.count(2),spiral(n)): if primes.is_prime(s): prime_count += 1 percent = (prime_count*1.0)/i percent = (prime_count*1.0)/i if percent < .1: #print i,percent,side print side break if __name__=="__main__": primes.init(10**6) n = 10**6 if len(sys.argv) > 1: n = eval(sys.argv[1]) prime_percent(n)
return p
def pyramid_enumerate(n, options, f):
result = []
index = 0
for i in range(n):
while f(result + [options[index]]) < f(result + [options[index + 1]]):
print index
index += 1
result.append(options[index])
index = 0
return result
def combinations_distinct(alist):
total = 0
for x in range(1, len(alist) + 1):
total += choose_degen(alist, x) * 2 ** (x - 1)
return total + 1
primes.init(1000)
nums = [2 * 3 * 2 * 3 * 5 * 5]
for x in nums:
res = reciprocals(x)
print res, map(lambda x: Frac(x[1]) / Frac(x[0]), res)
print len(res), x
print combinations_distinct([(2, 2), (3, 2), (5, 2)])
def main(): primes.init(50*10**6) print number_of_ways(50*10**6)
def main(): primes.init(10**7) brute_force()
import primes primes.init(10**4) for x in range(2,10**4): primes.factor(x)
def main():
primes.init(1000)
print "hi"
enumerate_min(4 * 10 ** 6)