def numsubplots(n, recursive=False):
"""
Define the best arrangement of subplots for a
given number of plots.
Parameters:
n:
Number of total plots needed.
recursive:
Whether to return current number of subplots.
Used for recursive calls.
Returns:
p:
A list containing the ideal arrangement
of subplots in the format of [nrows, ncolumns].
n:
Current number of subplots. Returned only
when recursively calling the function.
Ported to Python by Yunus Can Erol on Dec 2017
from mathworks.com/matlabcentral/fileexchange/
26310-numsubplots-neatly-arrange-subplots
Original by Rob Campbell, Jan 2010
Requires prime factorization and checking primality
which is not provided by Python by default; therefore
a custom package (primefac) is required.
"""
import primefac
while primefac.isprime(n) and n > 4:
n += 1
p = primefac.prime_factorize(n)
if len(p) == 1:
p = [1] + p
if recursive:
return p, n
else:
return p
while len(p) > 2:
if len(p) >= 4:
p[0] = p[0] * p[-2]
p[1] = p[1] * p[-1]
del p[-2:]
else:
p[0] = p[0] * p[1]
del p[1]
p = sorted(p)
while p[1] / p[0] > 2.5:
N = n + 1
p, n = numsubplots(N, recursive=True)
if recursive:
return p, n
else:
return p
def main():
print 'starting {}'.format(__file__.split('/')[-1])
startTime = time.time()
numPrime = 0
numCorners = 1
for sideLength in count(3, 2):
# if sideLength > 7:
# break
oddSquare = sideLength**2
corners = []
for x in xrange(1, 4):
corner = oddSquare - (x * (sideLength - 1))
corners.append(corner)
if primefac.isprime(corner):
numPrime += 1
numCorners += 4
percent = numPrime/numCorners
print '{} {} {}: {}/{} ~= {}'.format(
sideLength, oddSquare, corners, numPrime, numCorners, percent)
if percent < 0.1:
break
elapsedTime = time.time() - startTime
print 'elapsedTime: {:.2f} s'.format(elapsedTime)
def num_primes(start, stop, coef): num_primes = 0 for i in xrange(start, stop + 1): if primefac.isprime(coef[0] * i ** 2 + coef[1] * i + coef[2]): num_primes += 1 return num_primes
def gen_jams(N):
for p in itertools.count(2**(N - 1) + 1, 2):
ok = True
for base in xrange(2, 11):
v = to_base(base, p)
if primefac.isprime(v):
ok = False
break
if ok:
yield p
def test_num(potential_coin):
proofs = []
for x in range(2, 11):
coin_in_base = int(potential_coin, x)
if primefac.isprime(coin_in_base):
return []
else:
if coin_in_base > 2**17:
proofs.append(primefac.ecm(coin_in_base))
else:
proofs.append(primefac.pollardRho_brent(coin_in_base))
return proofs
def prove_coin(string):
proof = []
for base in range(2, 11):
number = int(string, base)
factor = primefac.pollardRho_brent(number)
if primefac.isprime(number):
print("wrong number {} base {}: {}".format(
string, base, number), file=sys.stderr)
return None
assert(number % factor == 0)
assert(not (factor == 1 or factor == number))
proof.append(factor)
return proof
def PE_004_no_cheat(n=3):
if n == 1:
return 0
en = 10**n
en1 = 10**(n - 1)
for p in generate_palindromes(n):
p //= 11
if isprime(p):
continue
# Generate numbers such that 11*i has length n
for i in xrange(en // 11, max(p // en, en1 // 11), -1):
if p % i == 0:
return p * 11
def PE_004(n=3):
if n == 1:
return 0
elif n % 2 == 0:
fac_1, fac_2 = cheat_even(n)
palindrome = fac_1 * fac_2
if is_palindrome(palindrome):
return palindrome
en = 10**n
en1 = 10**(n - 1)
for p in generate_palindromes(n):
p //= 11
if isprime(p):
continue
# Generate numbers such that 11*i has length n
for i in xrange(en // 11, max(p // en, en1 // 11), -1):
if p % i == 0:
return p * 11
def f(s, e):
while s < e:
if s % 2 == 0:
s += 1
continue
st = '{0:b}'.format(s)
ll = []
for b in range(2, 11):
cur = int(st, b)
if primefac.isprime(cur):
break
ll.append(cur)
else:
for i in xrange(len(ll)):
ll[i] = primefac.primefac(ll[i]).next()
return (s, ll)
s += 1
window.setworldcoordinates(-500, -500, 500, 500)
window.bgcolor("black")
pen.color("green")
pen.pensize(.000001)
pen.shape("blank")
pen.speed(0)
window.tracer(10000, 0)
pen.up()
# Generates the basic mapping, no prime distinction
# for x in range(0, 20):
# for y in range(0, 25):
# pen.goto(30*x - 500, 30*y - 500)
# num = (x+y)*(x+y+1)/2 + x
# pen.write(num)
# Generating the mapping, coloring in the primes green
for x in range(0, 20):
for y in range(0, 25):
pen.goto(30 * x - 500, 30 * y - 500)
num = (x + y) * (x + y + 1) / 2 + x
if primefac.isprime(num):
pen.color("red")
else:
pen.color("gray")
pen.write(num)
window.exitonclick()
# This works for lines of slope 1 and positive y intercept
primeRate = 10**3
slope = 1 / 5.
intercept = -50000
numLinesToCheck = 50000
data = []
countPrime = 0
for yInt in range(intercept, intercept + numLinesToCheck):
print yInt
# If slope is fractional, need to adjust x step
if slope < 1:
# Slope < 1, yInt is positive, we will start x at 0
if yInt > 0:
for x in range(0, int(1 / slope) * primeRate, int(1 / slope)):
if primefac.isprime(F(x, slope, yInt)):
countPrime += 1
# Slope < 1, yInt is negative, need to change where x starts
else:
for x in range(
int(math.ceil(-yInt / slope)),
int(1 / slope) * primeRate + int(math.ceil(-yInt / slope)),
int(1 / slope)):
if primefac.isprime(F(x, slope, yInt)):
countPrime += 1
# This is for slope > 0, and positive y intercept x starts at 0
elif yInt > 0:
for x in range(0, primeRate):
if primefac.isprime(F(x, slope, yInt)):
countPrime += 1
# Case for slope > 0, negative yInt, needs to start at different x
def F(x):
return int(
c1(x) * G1(x / 2, f1(x / 2)) +
c2(x) * G1(((x - 1) / 2) + 59, f2(((x - 1) / 2) + 59)))
xStart = 0
xEnd = 1000 # 0000
consecutivePrimes = []
consecutiveNonPri = []
while xStart <= xEnd:
print xStart
if primefac.isprime(F(xStart)):
xOrig = xStart
numOrig = F(xOrig)
count = 0
while primefac.isprime(F(xStart + 1)):
xStart += 1
count += 1
consecutivePrimes += [(xOrig, numOrig, count)]
else:
xOrig = xStart
numOrig = F(xOrig)
count = 0
while not primefac.isprime(F(xStart + 1)):
xStart += 1
count += 1
consecutiveNonPri += [(xOrig, numOrig, count)]
import primefac prime = 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print primefac.isprime(prime)
import primefac
# Change the return value to the new function
def base(x):
return x - 1
def mapping(x, y):
return int(((x+y)*(x+y+1)/2) + x)
def integrated(x, shift):
return int(mapping(x + shift, base(x + shift)))
primeRateFactor = 10 ** 6
shift = 1
numPrimes = 0
for x in range(0, primeRateFactor):
print x
if primefac.isprime(integrated(x, shift)):
numPrimes += 1
print "Prime rate out of " + str(primeRateFactor)
print str(float(numPrimes*100)/primeRateFactor) + "%"
print numPrimes
def main():
print 'starting {}'.format(__file__.split('/')[-1])
startTime = time.time()
# CIELING = 100
# CIELING = 1000
CIELING = 1e6
# CIELING = 1e12
# primes_list = primefac.primes(CIELING)
primes_list = list(itertools.islice(primefac.primegen(), int(math.sqrt(CIELING))))
print 'numPrimes: {}'.format(len(primes_list))
print primes_list[:20]
print primes_list[-10:]
print
# get numTerms of 0 to N, sum less than CIELING
numTermsGuess = 0
runningSum = 0
for prime in primes_list:
numTermsGuess += 1
runningSum += prime
if runningSum > CIELING:
runningSum -= prime
break
print 'numTermsGuess = {}, runningSum = {}'.format(numTermsGuess, runningSum)
done = False
result = {}
# maxNumTerms = len(primes_list) # improve?
numTerms = numTermsGuess
while not done:
numTerms -= 1
maxStartIndex = len(primes_list) - numTerms
for startIndex in xrange(0, maxStartIndex):
endIndex = startIndex + numTerms # actually one past end
sumOfTerms = sum(primes_list[startIndex:endIndex])
if sumOfTerms > CIELING:
if numTerms % 25 == 0:
print 'hit CIELING: numTerms = {}, startIndex = {}'.format(numTerms, startIndex)
if startIndex == 0:
done = True
break # go to next numTerms
if primefac.isprime(sumOfTerms):
# print 'RESULT: numTerms = {}, sumOfTerms = {}'.format(numTerms, sumOfTerms)
result = {
'numTerms': numTerms,
'sumOfTerms': sumOfTerms,
'startIndex': startIndex,
}
done = True
# end outer loop
print
print result
if result['numTerms'] < 1e3:
for i in range(result['startIndex'], result['startIndex'] + result['numTerms']):
print primes_list[i],
if i + 1 < result['startIndex'] + result['numTerms']:
print '+',
else:
print '=',
print result['sumOfTerms']
print
elapsedTime = time.time() - startTime
print 'elapsedTime: {:.2f} s'.format(elapsedTime)
def IsPrime(n):
return primefac.isprime(n)
import primefac
is_prime = []
for i in xrange(1, 1000001):
last_digit = i % 10
if last_digit in [4, 6, 8]:
is_prime.append(
(i, 3 * last_digit - 1, primefac.isprime(3 * last_digit - 1)))
elif last_digit in [1, 3, 7, 9]:
is_prime.append(
(i, 3 * last_digit - 10, primefac.isprime(3 * last_digit - 10)))
elif last_digit == 2:
is_prime.append(
(i, 3 * last_digit + 1, primefac.isprime(3 * last_digit + 1)))
elif last_digit == 5:
is_prime.append(
(i, 3 * last_digit + 2, primefac.isprime(3 * last_digit + 2)))
is_prime.append(
(i, 3 * last_digit - 2, primefac.isprime(3 * last_digit - 2)))
elif last_digit == 0:
is_prime.append(
(i, 3 * last_digit + 1, primefac.isprime(3 * last_digit + 1)))
is_prime.append(
(i, 3 * last_digit - 1, primefac.isprime(3 * last_digit - 1)))
import primefac
num_odd = 10000000
num_primes = 0
for i in xrange(1, num_odd, 2):
if primefac.isprime(i):
num_primes += 1
print(2.0 * num_primes) / num_odd
C = 1
for i in d_b:
C = C**2 % n
if (i == 1):
C = (C * M) % n
return C
if __name__ == "__main__":
i = 10**7
while i < 10**9:
# Calculate time required to compute the numbers for enciphering
nums_start_time = time.time()
# Calculate p
p = random.randint(i - 1000, i)
while not (primefac.isprime(p)):
p = random.randint(i - 1000, i)
# Calculate q
q = random.randint(i - 1000, i)
while not (primefac.isprime(q)):
q = random.randint(i - 1000, i)
# Calculate n and phi(n)
n = p * q
phi = (p - 1) * (q - 1)
# Calculate d
d = max(p, q)
while not primefac.isprime(d):
d += 1
import primefac
from fibonacci import fibonacci
import math
num_primes = 0
for i in range(1, 10000):
if primefac.isprime(int(round(math.log(fibonacci(i))))):
num_primes += 1
print num_primes
# sortedData = sorted(data, key=lambda s: s[1], reverse=True)
# print slope
# print data[:20]
# print sortedData[:20]
consecutivePrimes = []
consecutiveNonPri = []
slope = 1
intercept = -254
numToCheck = 100000
xStart = 254
count = 0
while xStart <= numToCheck:
print xStart
if primefac.isprime(F(xStart, slope, intercept)):
xOrig = xStart
numOrig = F(xOrig, slope, intercept)
count = 1
while primefac.isprime(F(xStart + 1, slope, intercept)):
count += 1
xStart += 1
consecutivePrimes += [(xOrig, numOrig, F(xStart, slope,
intercept), count)]
else:
xOrig = xStart
numOrig = F(xOrig, slope, intercept)
count = 1
while not primefac.isprime(F(xStart + 1, slope, intercept)):
count += 1
xStart += 1
context.log_level = "critical"
host, port ="2018shell.picoctf.com", 18148
con = remote(host, port)
if context.log_level != 50: # "critical"
print("#### Q1")
output = con.recvuntil("IS THIS POSSIBLE and FEASIBLE? (Y/N):")
p = int(re.findall(r"p : (.*)", output)[0])
q = int(re.findall(r"q : (.*)", output)[0])
is_feasible = "Y" if primefac.isprime(p) and primefac.isprime(q) else "N"
con.sendline(is_feasible)
if is_feasible == "Y":
con.recv()
n = int(p)*int(q)
con.sendline(str(n))
# t.sleep(0.5)
if context.log_level != 50:
print("#### Q2")
output = con.recvuntil("IS THIS POSSIBLE and FEASIBLE? (Y/N):")
p = int(re.findall(r"p : (.*)", output)[0])
n = int(re.findall(r"n : (.*)", output)[0])
# we already have p