def concatp(p1,p2):
d1=int(log(p1,10)+1)
d2=int(log(p2,10)+1)
if not isprime(p1*10**d2+p2):
return False
if not isprime(p2*10**d1+p1):
return False
return True
def make_prime_list(n):
prime_list = []
for i in range(2, n + 1):
if primes.isprime(i):
prime_list.append(i)
return prime_list
def pp():
start_time = time.time()
digits='123456789'
numbers=[]
for n in product(digits,repeat=4):
if n[-1] not in '24568' and sum([int(x) for x in n])%3 !=0:
numbers.append(int(''.join(n)))
ps=[]
for number in numbers:
if isprime(number):
ps.append(number)
perms=dict()
for prime in ps:
perm=''.join(sorted(str(prime)))
if perm in perms:
perms[perm].append(prime)
else:
perms[perm] = [prime]
for x in perms:
if len(perms[x])<4:
continue
d1=[]
for n in combinations(perms[x],2):
diff=abs(n[1]-n[0])
d1.append([n,diff])
for i in range(len(d1)-1):
if diff == d1[i][1]:
if n[0] in d1[i][0] or n[1] in d1[i][0]:
nums=sorted(list(set([n[0],n[1],d1[i][0][0],d1[i][0][1]])))
concat=str(nums[0])+str(nums[1])+str(nums[2])
print n,d1[i][0],diff,concat
print("--- %s seconds ---" % (time.time() - start_time))
def sumofprimes(n):
primes = []
for i in xrange(n):
if isprime(i):
primes.append(i)
return sum(primes)
def run_length(a,b):
n = 0
while True:
#print n
if isprime(poly(a,b,n)):
n += 1
else:
return n
def sum_of_primes(lista):
total = 0
for i in lista:
if isprime(i):
total += i
return total
def is_circular_prime(p):
rotations = len(str(p))
prime = deque(str(p))
for x in range(rotations):
prime_int = int("".join(prime))
if not isprime(prime_int):
return False
prime.rotate(1)
return True
def consecutive_primes(a,b):
# n^2 + (a*n) + b
n = 0
while True:
p = (n * n) + (a * n) + b
if not isprime(p):
return n
n += 1
def check(n):
if primes.isprime(n): return (n+2)
x=0
while primes.prime(x)<n:
square=math.sqrt((n-primes.prime(x))/2.0)
if square==int(square):
return (n+2)
x+=1
print n
def try_move(self, marker, location):
# full or past 52
if (location.occupied or location.label > self.locations[-1].label):
return
if primes.isprime(location.label):
# move up to 6 spaces ahead
for i in range(1, 6):
if self.locations[marker.index + i].occupied:
marker.index += i - 1 # space before this occupied one
return
def get_num_div(cur_num):
num_div = 1
factors = []
for i in range(2, int(np.floor(np.sqrt(cur_num)))):
if primes.isprime(i):
factors.append(i)
powers = []
ind = 0
for i in factors:
j = cur_num
powers.append(0)
cur_power = 0
while j % i == 0:
j = j / i
cur_power += 1
powers[ind] = cur_power
ind += 1
for i in powers:
num_div *= (i + 1)
return num_div
from time import time
from primes import isprime
##def isprime(p):
## if not p%2:
## return False
## for n in range(3,int(p**.5),2):
## if not p%n:
## return False
## return True
t1 = time()
p = 0
diags = 1
for square in range(3, 99999, 2):
diags += 4
for corner in range(1, 4):
if isprime((square - 2)**2 + corner * (square - 1)):
p += 1
if p / diags <= .1:
print(square)
break
print(time() - t1)
import primes print(primes.isprime(18)) print(primes.all_primes(18)) print(primes.prime_factors(18))
contin=1
x=25
while contin:
prime=[int(i) for i in str(primes.prime(x))]
for i in range(len(prime)-2):
for j in range(i+2):
for jj in range(j+1):
# if jj==0:
# am=Amount+1
# else
list2=list(prime)
count=0
for k in range(10):
list2[i+2]=list2[j+1]=list2[jj]=k
if primes.isprime(listToNum(list2)) and list2[0]!=0:
count+=1
if count==Amount:
print listToNum(prime)
print i+2
print j+1
print jj
for k in range(10):
list2[i+2]=list2[j+1]=list2[jj]=k
if primes.isprime(listToNum(list2)) and list2[0]!=0:
print listToNum(list2)
contin=0
x+=1
import time
import primes
startTime=time.clock()
length =7
n=7654321
contin=1
while True:
if n%1000==0:print n
if n<10**5:length =6
if n<10**4:length =5
if n<10**3:length =4
contin=1
for i in range(1,length+1):
if str(n).count(str(i))!=1:
contin=0
break
if contin:
if primes.isprime(n):
print n
break
n-=1
endTime=time.clock()
print endTime-startTime
from primes import prime_list, isprime, prime_list2 from itertools import product primes = prime_list2(10000) composites = [i for i in xrange(3, 10000, 2) if not isprime(i)] square2 = [2 * i * i for i in xrange(1, 100)] sums = list(set(sum(c) for c in product(primes, square2) if sum(c) % 2)) sums.sort() print sums[:25] print[c for c in composites if not c in sums][:25] result = False
def isprime(n):
if n <= max(P):
return n in P
return primes.isprime(n)
def check_for_sequence(primelist, start):
if start + 6660 > 9999:
return False
if not start in primelist:
return False
if not start + 3330 in primelist:
return False
if not start + 6660 in primelist:
return False
return True
primelist = []
for i in xrange(1000, 10000):
if isprime(i):
primelist.append(i)
def get_starts(primelist):
results = []
for i in primelist:
if check_for_sequence(primelist, i):
results.append(i)
return results
def check_permutations(number):
'''
Specialized function to see if a number,
when increased by 3330 is a permutation of itself
def test_is_prime(self):
self.assertTrue(primes.isprime(11))
self.assertTrue(not primes.isprime(10))
from primes import isprime
def check_for_sequence(primelist, start):
if start + 6660 > 9999:
return False
if not start in primelist:
return False
if not start + 3330 in primelist:
return False
if not start + 6660 in primelist:
return False
return True
primelist = []
for i in xrange(1000, 10000):
if isprime(i):
primelist.append(i)
def get_starts(primelist):
results = []
for i in primelist:
if check_for_sequence(primelist, i):
results.append(i)
return results
def check_permutations(number):
'''
Specialized function to see if a number,
when increased by 3330 is a permutation of itself
'''
num2 = number + 3330
import primes, itertools
pcalc = 1000000
Pl = list(primes.sieve(pcalc))
P = set(Pl) # SERIOUS speedup
isprime = lambda x: ((primes.isprime(x)) if (x >= pcalc) else (x in P))
to_1000 = list(itertools.takewhile(lambda x: x < 1000, Pl))
longest = 0
l_a = 0
l_b = 0
lim = 1000
for a in range(-lim + 1, lim):
for b in to_1000:
if not isprime(longest * longest + a * longest + b): continue
for i in itertools.count(1):
if not isprime(i * i + a * i + b):
if i + 1 > longest:
longest = i + 1
l_a = a
l_b = b
break
if a % 100 == 0:
print("a = {:>5}, longest so far: ({:>5}, {:>5}) -> {:>5}".format(a, l_a, l_b, longest))
print(l_a * l_b)
def nth(seq, n, default = None):
import itertools
return next(itertools.islice(seq, n - 1, None), default)
import itertools
import primes
print(nth((x for x in itertools.count(1) if primes.isprime(x)), 10001))
# project euler 58 from primes import isprime diagnumber = 1 diagprimes = 0 diagtotal = 1 # includes center sidelength = 1 # each level += 2 while True: sidelength += 2 for i in range(4): diagnumber += sidelength - 1 if isprime(diagnumber): diagprimes += 1 diagtotal += 4 if diagprimes / float(diagtotal) < 0.1: print sidelength break
def check_prime(list): #ensure all the members of a list are prime if all(isprime(int(number)) for number in list): return True return False
for i in range(len(mylist)):
sum+= mylist[-1-i]*10**i
return sum
##for 2 digits
contin=1
x=10
while contin:
prime=[int(i) for i in str(primes.prime(x))]
for i in range(len(prime)-1):
for j in range(i+1):
list2=list(prime)
count=0
for k in range(10):
list2[i+1]=list2[j]=k
if primes.isprime(listToNum(list2)) and listToNum(list2)>999:
count+=1
if count==Amount:
print listToNum(prime)
contin=0
x+=1
##for 3 digits
contin=1
x=25
while contin:
prime=[int(i) for i in str(primes.prime(x))]
for i in range(len(prime)-2):
for j in range(i+2):
for jj in range(j+1):
list2=list(prime)
import primes
import itertools
import sys
Pl = primes.precomp(1000000)
i = 0
for p in Pl:
i = i + 1
if p == 121313:
print(p)
s = str(p)
for a in '012':
nn = 10
fam = []
for b in '0123456789':
rr = s.replace(a, b)
if rr[0] == '0': break
if rr == s and a != b: break
if not primes.isprime(int(rr)):
nn -= 1
if nn < 8:
break
else:
fam.append(int(rr))
else:
print(p)
print(fam)
sys.exit(0)
def check_prime(list):
#ensure all the members of a list are prime
if all(isprime(int(number)) for number in list):
return True
return False
from primes import isprime from eulertools import is_pandigital import time start = time.time() record = 0 for number in xrange(1, 7654322): if is_pandigital(number): if isprime(number): record = number print record, time.time() - start
# Finds the primitive roots between 10 and 50 for primes between 1000 and 9999
import primes
import sys
p = input('Input your prime number: ')
if (p < 1000 or p > 9999):
print 'Only finds primitive roots for primes on interval [1000,9999]'
sys.exit(0)
if (primes.isprime(p) == 0):
print '%i is NOT prime' % (p)
sys.exit(0)
primroots = []
ordp = range(1, p)
for a in range(10, 51):
orda = []
for i in range(1, p):
orda.append(pow(a, i, p))
orda.sort()
if orda == ordp:
primroots.append(a)
print 'The primitive roots of %i on the interval [10,50] are %s' % (p,
primroots)
count=0
sum =0
tprimes=[]
while count < 1000000000000000:
primeList=[int(x) for x in str(primes.prime(n))]
good=1
for x in range(1,len(primeList)):
primeL=0
primeR=0
for i in range(len(primeList)-x):
# print primeList
primeL+=(10**(len(primeList)-x-i-1))*primeList[x+i]
primeR+=(10**(len(primeList)-x-i-1))*primeList[i]
# print primeR
if not (primes.isprime(primeL) and primes.isprime(primeR)):
good=0
break
if good:
tprimes.append(primes.prime(n))
count +=1
sum += primes.prime(n)
print tprimes
print sum
n+=1
print tprimes
print sum
endTime=time.clock()
print endTime-startTime
import primes l_numprimes=[] for a in range(-1000,1000): print a for b in range(-1000,1000): n = 0 while(True): if(primes.isprime(n**2+a*n+b)): n+=1 else: l_numprimes.append((n,a,b)) break l_numprimes.sort(reverse=True) print l_numprimes[0] """ First time through, brute force approach. Go from -1000 to 1000 in a and b. Check n while it's prime. Spun for awhile, printing a each time. Oh - had an infinite while loop. Added a break to the else. Much faster :) Changed sort to reverse = True. Got 71 consecutive primes, which is less than the 80 consecutive primes from -79 and 1601. Let's try it, I guess. (oh 1601 > 1000). Correct!
from primes import prime_list, isprime, prime_list2 from itertools import product primes = prime_list2(10000) composites = [i for i in xrange(3, 10000, 2) if not isprime(i)] square2 = [2 * i * i for i in xrange(1, 100)] sums = list(set(sum(c) for c in product(primes, square2) if sum(c) % 2)) sums.sort() print sums[:25] print [c for c in composites if not c in sums][:25] result = False
def isPrimeJoin(x,y):
return (primes.isprime(x*10**(len(str(y)))+y) and primes.isprime(y*10**(len(str(x)))+x))
def test_is_five_prime(self):
"""Is five successfully determined to be prime?"""
self.assertTrue(isprime(5))
import time
import primes
startTime=time.clock()
n=0
MAX=10**6
noPrimes=0
x=0
while primes.prime(x)<MAX/2:
sum=primes.prime(x)
n=1
while sum<MAX:
sum+=primes.prime(x+n)
n+=1
if primes.isprime(sum):
if n>noPrimes:
noPrimes=n
print noPrimes
print sum
x+=1
endTime=time.clock()
print endTime-startTime
# project euler 41 from primes import isprime def ispandigital(n): return all([False for i in range(len(n)) if n.find(str(i+1)) == -1]) for i in range(7654321, 1234567 - 1, -2): if ispandigital(str(i)) and isprime(i): print i break
import primes
import numpy as np
range_a = range(-999,1000)
range_b = range(-1000,1001)
max_num_primes = 0
for a in range_a:
for b in range_b:
cur_max_num = 0
n = 0
while primes.isprime(n*n + a*n + b):
cur_max_num += 1
n += 1
if cur_max_num > max_num_primes:
max_num_primes = cur_max_num
max_prod = a*b
a_max = a
b_max = b
print(max_num_primes)
print(a_max,b_max)
print(a_max*b_max)
import primes
i = 3
sum = 2
while i < 2e6:
if (primes.isprime(i)):
sum += i
i += 2
print(sum)
import time
import permute
import primes
startTime=time.clock()
oneper=(9997-1000)/100
for i in range(1000,9997):
if i%oneper==0:print i/oneper
for j in range(1,(9999-i)/2+1):
if primes.isprime(i) and primes.isprime(i+j) and primes.isprime(i+2*j):
if permute.isPerm([int(ch) for ch in str(i)],[int(ch) for ch in str(i+j)]) and permute.isPerm([int(ch) for ch in str(i)],[int(ch) for ch in str(i+2*j)]):
print i
print i+j
print i+2*j
endTime=time.clock()
print endTime-startTime
from itertools import count
from primes import isprime
n = 1
c = 0
for i in count(1, 2):
n += i
# skip bottom right (not actually diagonal)
n += i
c += isprime(n)
i += 1
n += i
c += isprime(n)
n += i
c += isprime(n)
# side length is i + 1
# number of numbers is i * 2 + 1
# c / (i * 2 - 1) < .1
# so 10c < i * 2 - 1
if 10 * c < i * 2 + 1:
print(i + 1)
break
import primes
import itertools
import sys
for i in reversed(range(1, 10)):
for perm in itertools.permutations(reversed('123456789'[:i])):
perm = ''.join(perm)
if primes.isprime(int(perm)):
print(perm)
sys.exit(0)
