def primeSet(primes, n):
#print(primes, n)
if n < 1:
print("n must be greater than 1")
return
if n == 1:
returnSet = [[primes[i]] for i in range(len(primes))]
return returnSet
else:
print(n, "start")
returnSet = []
pSets = primeSet(primes, n - 1)
Timer.startTimer()
for i in range(len(pSets)):
for j in range(i, len(pSets)):
if pSets[i][1:] == pSets[j][:-1]:
if Primes.isPrime(concat(
pSets[i][0], pSets[j][-1])) and Primes.isPrime(
concat(pSets[j][-1], pSets[i][0])):
temp = list(pSets[i])
temp.append(pSets[j][-1])
returnSet.append(temp)
Timer.endTimer()
Timer.printTime()
print("Sets of", n, ":", len(returnSet))
return returnSet
return
def Program(nMax=100, GRAPHICS=False):
primes = Primes.MakePrimeList(nMax)
primeGraph = Networks.UndirectedGraph()
for p in primes:
primeGraph.AddNode(p)
for p2 in primeGraph.GetNodes():
if Primes.isPrime(concatenateIntegers(p, p2), primes):
if Primes.isPrime(concatenateIntegers(p2, p), primes):
primeGraph.AddEdge(p, p2)
for p1 in primes:
possibles = primeGraph.GetNeighbors(p1)
for p2 in possibles:
possibles2 = listIntersection(possibles,
primeGraph.GetNeighbors(p2))
for p3 in possibles2:
possibles3 = listIntersection(possibles2,
primeGraph.GetNeighbors(p3))
for p4 in possibles3:
possibles4 = listIntersection(possibles3,
primeGraph.GetNeighbors(p4))
for p5 in possibles4:
print(p1, p2, p3, p4, p5), p1 + p2 + p3 + p4 + p5
if GRAPHICS:
NetGraphics.DisplayCircleGraph(primeGraph)
return primeGraph
def eightDivisorCount(n):
ps = Primes.MakePrimeList(int(n**0.5)+2)
primePi = Primes.Prime_Pi()
f = 0
for p in ps:
if p**7 > n:
break
#print p
f += 1
for p in ps:
if 2*p**3 > n:
break
f += primePi(n//(p**3), ps)
print p,f,len(primePi.restricted_memo)
if (n//(p**3)) >= p:
f -= 1
#print p, primePi(n//(p**3), ps)
for n1,p1 in enumerate(ps):
if p1**3 >= n:
break
for p2 in ps[n1+1:]:
if p1*p2*p2 >= n:
break
f += primePi(n//(p1*p2),ps) - primePi(p2,ps)
#print p1,p2,primePi(n//(p1*p2),ps),primePi(p2,ps)
if p2 < 10000:
print p1,p2,f,len(primePi.restricted_memo)
print p1,f,len(primePi.restricted_memo)
return f
def new_432(m):
#primes = Primes.MakePrimeList(int(1.2*m**(1./2))+100)
primes = Primes.MakePrimeList(int(1.2 * m**(1. / 2)) + 120)
prime_pi = Primes.Prime_Pi()
ans = sum_range(1, 18) + func(m, 7, primes, prime_pi)
ans *= 510510
for ix in range(7):
ans *= (primes[ix] - 1)
ans /= primes[ix]
return ans
def Euler131(N):
primes = Primes.MakePrimeList(int(sp.sqrt(N))+4)
x = 1
p = 3*x*x+3*x+1
count = 0
while p <= N:
if Primes.isPrime(p, primes):
count += 1
x += 1
p = 3*x*x + 3*x + 1
return count
def highly_divisible(n):
numfactors = 0
i = n
ti = triangle_num (i)
while numfactors <= n:
if not Primes.isPrime(ti):
numfactors = Primes.get_num_factors(ti)
if numfactors <= n:
i += 1
ti = triangle_num (i)
#print (ti)
else:
return ti
def main(): truncPrimes = getTruncPrimes(Primes.getPrimes(1000000)); truncSum = 0; for p in truncPrimes: truncSum += p print truncSum
def primeFrogProbability(N, croak_string):
ps = Primes.MakePrimeList(N)
ans = Fraction(0)
memo = {}
for position in range(1, N + 1):
ans += calcCroakProbability(N, position, croak_string, ps, memo)
return ans / N
def calcCroakProbability(N, position, croak_string, ps, memo):
if len(croak_string) == 0:
return 1
key = (N, position, croak_string)
try:
return memo[key]
except KeyError:
pass
prob_croak_correct = Fraction(1, 3)
is_prime = Primes.isPrime(position, ps)
if ((is_prime and croak_string[0] == 'P')
or (not is_prime and croak_string[0] == 'N')):
prob_croak_correct *= 2
if position == 1:
memo[key] = calcCroakProbability(N, 2, croak_string[1:], ps, memo)
elif position == N:
memo[key] = calcCroakProbability(N, N - 1, croak_string[1:], ps, memo)
else:
memo[key] = (
calcCroakProbability(N, position - 1, croak_string[1:], ps, memo) +
calcCroakProbability(N, position + 1, croak_string[1:], ps, memo))
memo[key] /= 2
memo[key] *= prob_croak_correct
return memo[key]
def compute_jamcoins(digits, n):
b2_max = int("1"*digits,2)
b2_min = int("1" + (digits-2)*"0" + "1", 2)
primes = Primes.primes
jamcoins = {}
i = b2_min
while len(jamcoins) < n:
potential = bin(i)[2:]
value = 0
factors = [potential]
for j in range(2, 11):
value = 0
value = Primes.isPrime(int(potential,j))
if not value:
break
factors.append(str(value))
if value:
jamcoins[potential] = factors
print(' '.join(factors))
i += 2
return jamcoins
def Euler118_2():
primes = Primes.MakePrimeList(100000000)
print 'Primes Calculated'
primes = [p for p in primes if not repeats_digits(p)]
print 'Primes with repeated digits eliminated'
num_sets = build_sets(0,[], primes)
print 'Number of Pandigital Prime Sets: '+str(num_sets)
return num_sets
def PossiblePrimesList(N):
# Get all the candidates for primes changing 3 digits
ps = Primes.PrimeList(N)
possList = []
for p in ps:
if Has3sameDigits(p):
possList.append(p)
return possList
def Euler484a(N):
start = time.clock()
p_max = int(sp.sqrt(N) + 1000)
primes = Primes.MakePrimeList(p_max)
print 'Primes up to %d calculated. %d primes' % (p_max, len(primes))
ans = F(N, 0, primes)
end = time.clock()
print '%f seconds' % (end - start, )
return ans
def Euler118_1():
permutes = itertools.permutations([1,2,3,4,5,6,7,8,9])
primes = Primes.MakePrimeList(10000)
prime_sets = set()
for digit_list in permutes:
find_prime_sets(digit_list, set(), prime_sets, primes)
print 'Number of Pandigital Prime Sets: '+str(len(prime_sets))
return prime_sets
def make_dfact(n, primes):
dfact = {}
r = 1
while r <= len(primes) and sp.prod(primes[:r]) <= n:
for c in Primes.combProdLessThan(primes, r, n):
d = int(round(sp.prod(c)) + 0.01)
dfact[d] = c
r += 1
return dfact
def Euler77(numWays):
"""
Finds the first number that can be partitioned into primes in numWays.
"""
primeList = Primes.MakePrimeList(max(numWays, 100))
partialPrimeMemo = {}
n = 2
while primePartition(n, primeList, partialPrimeMemo) < numWays:
n += 1
return n
def old_432(m):
primes = Primes.MakePrimeList(int(m * 2))
ans = sum_range(1, 18)
ans += weird_sum_tot(m, 7, primes)
ans *= 510510
for ix in range(7):
ans *= (primes[ix] - 1)
ans /= primes[ix]
return ans
def Euler231(n, m):
""" n choose m
"""
pList = Primes.MakePrimeList(n + 1)
summ = 0
for p in pList:
summ += p * (Number_Ps_in_N_factorial(n, p) - Number_Ps_in_N_factorial(
m, p) - Number_Ps_in_N_factorial(n - m, p))
return summ
def main():
try:
os.remove('output.txt')
print('removed output file!')
except Exception as e:
print(f'Error: {e}')
if sys.argv[1] == "--sequence":
start = time.time()
processes = []
video = cv2.VideoCapture('video_sample.mp4')
w, h = int(video.get(3)), int(video.get(4))
for i in range(int(sys.argv[4])):
video.set(cv2.CAP_PROP_POS_FRAMES,
time.time() * 1000 % video.get(cv2.CAP_PROP_FRAME_COUNT))
res, frame = video.read()
p = multiprocessing.Process(target=worker,
args=(
frame,
w,
h,
int(sys.argv[2]),
int(sys.argv[3]),
int(sys.argv[4]),
))
processes.append(p)
p.start()
for process in processes:
process.join()
end = time.time()
with open('output.txt') as f:
print(
f'{sys.argv[2]} random numbers sequence generated in {end - start}\nentropy: {entropy_handler([int(line.strip()) for line in f if line.strip()], base=2)}'
)
f.close()
elif sys.argv[1] == "--single":
primes = Primes.Primes()
rng = RNGutils.RNGutils()
print("Single mode\n")
video = cv2.VideoCapture('video_sample.mp4')
seed = get_seed_from_pixel()
video.release()
with open("output.txt", "w+") as file:
string = f'{rng.single(primes=primes, pixel_seed=seed, rnd_range=int(sys.argv[2]))}\n'
if "-" not in string:
file.write(string)
print(string)
file.close()
def find_prime_sets(digit_list, current_set, prime_sets, primes):
'''
Recursively finds the prime sets.
digit_list: The digits to make primes of
current_set: The set of primes found so far
prime_sets: The set of all the pandigital prime_sets found so far
primes: A list of primes
'''
if len(digit_list) != 9: # Nine digit lists are composite. Don't check.
num = make_num_from_list(digit_list)
if Primes.isPrime(num):
current_set.add(num)
prime_sets.add(frozenset(current_set))
for ix in range(1,len(digit_list)):
num = make_num_from_list(digit_list[:ix])
if Primes.isPrime(num):
next_set = current_set.copy()
next_set.add(num)
find_prime_sets(digit_list[ix:], next_set, prime_sets, primes)
return
def main(): maxN = 0; nums = [1,2,3,4,5,6,7] nums.reverse(); print nums for perm in itertools.permutations(nums): #print perm num = getListNumber(perm) #print num if(num > maxN and Primes.isPrime(num)): maxN = num print maxN print maxN
def prepareGrid(self, page):
exportGrid = ExportGrid()
try:
with UnstartedRaceWrapper():
if self.pageInfo[page][0] == 'Primes':
exportGrid = ExportGrid(**Primes.GetGrid())
else:
exportGrid.setResultsOneList(self.pageInfo[page][0],
True,
showLapTimes=False)
except KeyError:
return ExportGrid()
exportGrid.title = u'\n'.join(
[_('Podium Results'), u'', exportGrid.title])
return exportGrid
def prepareGrid(self, page):
showLapTimes = (not Model.race) or getattr(
Model.race, 'includeLapTimesInPrintout', True)
try:
with UnstartedRaceWrapper():
if self.pageInfo[page][0] == 'Primes':
exportGrid = ExportGrid(**Primes.GetGrid())
else:
exportGrid = ExportGrid()
exportGrid.setResultsOneList(self.pageInfo[page][0],
True,
showLapTimes=showLapTimes)
except KeyError:
return ExportGrid()
return exportGrid
def worker(seed, length, threads, rnd_range):
primes = Primes.Primes()
rng = RNGutils.RNGutils()
with open("output.txt", "a+") as file:
[
file.write(f'{number}\n')
for number in rng.sequence(primes=primes,
pixel_seed=seed,
length=int(length / threads),
rnd_range=rnd_range)
]
file.close()
return
def calc_mobius(n):
primes = Primes.MakePrimeList(n)
mu = [1]*(n+1)
mu[0] = 0
mu[1] = 1
for p in primes:
mu[p] = -1
i = 2
while p * i <= n:
mu[p*i] *= -1
i += 1
i = 1
while p*p*i <= n:
mu[p*p*i] = 0
i += 1
return mu
def generate_keys(k):
p, g1, g2 = Primes.prime_and_generators(k)
rand = SystemRandom()
x1 = rand.randint(2, p)
x2 = rand.randint(2, p)
y1 = rand.randint(2, p)
y2 = rand.randint(2, p)
w = rand.randint(2, p)
X = (pow(g1, x1, p) * pow(g2, x2, p)) % p
Y = (pow(g1, y1, p) * pow(g2, y2, p)) % p
W = pow(g1, w, p)
private_key = [p, x1, x2, y1, y2, w, k]
public_key = [p, g1, g2, X, Y, W, k]
return private_key, public_key
def worker(frame, w, h, length, rnd_range, threads):
primes = Primes.Primes()
rng = RNGutils.RNGutils()
with open("output.txt", "a+") as file:
seed = get_seed_from_pixel(frame=frame, w=w, h=h)
[
file.write(f'{number}\n')
for number in rng.sequence(primes=primes,
pixel_seed=seed,
length=int(length / threads),
rnd_range=rnd_range)
]
file.close()
return
def Euler268(N, M=100):
primes = Primes.MakePrimeList(M)
#return f(primes, 4, N)
added = [0] * (len(primes) + 1)
ans = 0
for r in range(4, len(primes) + 1):
print N, r, ans
if prod(primes[:r]) > N:
break
multiplier = 1 - added[r]
# Update how many times we have added numbers divisible by
# exactly x primes in the list.
for x in range(r, len(primes) + 1):
added[x] += multiplier * comb(x, r, True)
# Actually add them
ans += multiplier * sum(N // prod(c) for c in combinations(primes, r))
return ans
def Euler351(N):
M = N / 2
primes = Primes.MakePrimeList(M)
ans = 0
r = 1
while r < len(primes) and prod(primes[:r]) <= M:
sign = int((-1)**(r + 1))
count = 0
for c in combProdLessThan(primes, r, M):
count += 1
x = prod(c)
p = int(N // x)
q = int(N // (2 * x))
ans += sign * (p * q - q * (q + 1))
print '%d from list of len %d: %d times; \ttotal %d' % (r, len(primes),
count, ans)
r += 1
return 6 * (2 * ans + M + N - 2)
def Euler122():
primes = Primes.MakePrimeList(200)
m = {}
m[1] = 0
for x in range(2, 201):
if x in primes:
m[x] = m[x - 1] + 1
else:
m[x] = 0
y = x
for p in primes:
while y % p == 0 and y > 0:
m[x] += m[p]
ans = 0
for x in range(1, 201):
ans += m[x]
print 'Sum: ', ans
return ans
def lcm(integerlist):
"""
lcm stands for least common multiple.
this function calculate the lcm of some integers.
"""
lcmdict = {}
for i in integerlist:
factorslist = Primes.factors(i)
factorsdict = {}
for k in factorslist:
factorsdict.setdefault(k, 0)
factorsdict[k] += 1
for afactor in factorsdict:
lcmdict.setdefault(afactor, 0)
if lcmdict[afactor] < factorsdict[afactor]:
lcmdict[afactor] = factorsdict[afactor]
mylcm = 1
for afactor in lcmdict:
mylcm *= afactor ** lcmdict[afactor]
return mylcm, lcmdict
def Euler193(N):
'''
Calculates the number of squarefree numbers less than N
'''
root = round(sp.sqrt(N))
primes = Primes.MakePrimeList(root)
num = 0
n = 1
min_prod = 2
#---------------------------------------#
# Loop over the number of primes to use #
# in the inclusion-exclusion principle. #
#---------------------------------------#
while min_prod <= root:
#-----------------------------------------#
# Iterate over all the combinations of n #
# primes, adding or subtracting according #
# to the inclusion-exclusion principle. #
#-----------------------------------------#
ix_list = range(n)
done = False
while not done:
# Calculate the number of square including numbers
p = sp.product([primes[ix]*primes[ix] for ix in ix_list])
#print [primes[i] for i in ix_list]
if n % 2 == 0:
num -= (N-1) / p
#print '-'+str(N / p)
else:
num += (N-1) / p
#print '+'+str(N/p)
done = not ix_combo(ix_list, primes, root)
n += 1
min_prod = sp.product(primes[:n])
num = N - num - 1
#print 'Number of squarefree numbers below '+str(N)+': '+str(num)
return num
def Euler122(N):
primes = Primes.MakePrimeList(N+2)
m = {}
m[1] = 0
for x in range(2, N+1):
if x in primes:
#print x, m[x-1]
m[x] = m[x-1] + 1
else:
m[x] = 0
y = x+0
for p in primes:
while y%p == 0 and y > 0:
m[x] += m[p]
y /= p
ans = 0
for x in range(1, N+1):
ans += m[x]
print 'Sum: ', ans
print m
return ans
def Euler87(n):
ps = Primes.MakePrimeList(int(scipy.sqrt(n))*2)
nF = 0
nums = []
count = 0
while ps[nF]**4 <= n:
nC = 0
while ps[nF]**4 + ps[nC]**3 <= n:
nS = 0
while ps[nF]**4 + ps[nC]**3 + ps[nS]**2 <= n:
a = ps[nF]**4 + ps[nC]**3 + ps[nS]**2
count += 1
nums.append(a)
nS += 1
nC += 1
nF += 1
nums.sort()
for x in range(1,len(nums)):
if nums[x]==nums[x-1]:
count -= 1
return count
import itertools
import Primes
# awesome.
# 1+2+3+4+5+6+7+8+9=45
# 1+2+3+4+5+6+7+8=36
for aper in itertools.permutations(range(7, 0, -1)):
candidate = int(''.join([str(x) for x in list(aper)]))
if Primes.isPrime(candidate):
print(candidate)
break
# booltemp = False
# break
# if booltemp == True:
# print(ap)
# break
for ap in Primes.primes:
print(ap)
mylist = [[ap]]
found = False
while True:
templist = []
for a in mylist:
for b in Primes.primes[Primes.primes.index(a[-1]) + 1:]:
booltemp = True
for i in a:
if Primes.isPrime(int(str(i) + str(b))) == False or Primes.isPrime(int(str(b) + str(i))) == False:
booltemp = False
break
if booltemp == True:
templist.append(a + [b])
mylist = templist
if mylist == []:
break
print(len(mylist[0]))
if len(mylist[0]) == 5:
print(mylist)
found = True
break
if found == True:
break
def getListNumber(listN): num = listN[0]; for part in range(1,len(listN)): num = Pandigital.appendNums(num, listN[part]); return num def main(): maxN = 0; nums = [1,2,3,4,5,6,7] nums.reverse(); print nums for perm in itertools.permutations(nums): #print perm num = getListNumber(perm) #print num if(num > maxN and Primes.isPrime(num)): maxN = num print maxN print maxN if __name__ == "__main__": if(len(sys.argv) > 1 and sys.argv[1] == "test"): assert True print Primes.getPrimes(1000000000)[1000] else: main()
import Primes print(Primes.factors(600851475143))
def find_sum_primes(n):
#getPrimes gets all primes up to, but not including the passed in value
#primeslist = Primes.getPrimes(n + 1)
primeslist = Primes.prime_sieve(n)
return sum(primeslist)
import Primes
n = 1
while True:
found = True
if n % 100 == 0:
print(n)
print(Primes.factors(n + 1))
step = 0
for i in range(n, n + 4):
tempset = set(Primes.factors(i))
if len(tempset) != 4:
found = False
step = i - n
break
if found == True:
print(n)
break
n += step + 1
import Primes
Primes.extendTo(2000000)
print(sum([int(line.strip()) for line in open('Primes.txt').readlines()]))