def nP4Quad(a, b):
'''
Calculate number of primes for n**2 + an + b
Where a, b are integers and n starts from 0
'''
n = 0 # Num of primes
while True:
if not eulerlib.isprime(n**2 + (a * n) + b):
break
n += 1
return n
def spiral(n):
if n % 2 == 0: return None
if n not in lookup:
start = (n - 2)**2 + 1
corner = start + n - 2
C = [corner]
for i in range(3):
corner += n - 1
C.append(corner)
r1 = (sum([1 for c in C if isprime(c)]), len(C))
r2 = spiral(n - 2)
lookup[n] = (r1[0] + r2[0], r1[1] + r2[1])
return lookup[n]
def spiral(n): if n % 2 == 0: return None if n not in lookup: start = (n-2)**2 + 1 corner = start + n-2 C = [corner] for i in range(3): corner += n-1 C.append(corner) r1 = (sum( [1 for c in C if isprime(c)] ) , len(C)) r2 = spiral(n-2) lookup[n] = (r1[0] + r2[0], r1[1] + r2[1]) return lookup[n]
from itertools import permutations
from eulerlib import isprime
for n in reversed(xrange(1,10)):
D = [str(d) for d in reversed(xrange(1,n+1))]
found = False
for p in permutations(range(len(D))):
n = int(''.join([D[i] for i in p]))
if isprime(n):
print n
found = True
break
if found:
break
from itertools import permutations
from eulerlib import isprime
for n in reversed(xrange(1, 10)):
D = [str(d) for d in reversed(xrange(1, n + 1))]
found = False
for p in permutations(range(len(D))):
n = int(''.join([D[i] for i in p]))
if isprime(n):
print n
found = True
break
if found:
break
import eulerlib
primes = []
for p in eulerlib.PrimesPlus():
primes.append(p)
if p > 4000: # Only use first few primes
break
def check(n):
''' Check to see if a comp num satisfies CG's properties '''
for p in primes:
for i in range(1, int(n)):
if p + (2 * (i ** 2)) == n:
return (p, i)
return None
for i in range(9, 10**5 + 1, 2):
if not eulerlib.isprime(i) and check(i) == None:
print(i)
break
'''
n = 0 # Num of primes
while True:
if not eulerlib.isprime(n**2 + (a * n) + b):
break
n += 1
return n
ma, mb, mprimes = 0, 0, 0
factor = 100
# b must be prime becuase otherwise test fails when n == 0
brange = eulerlib.primes(1000)
nbrange = []
for prime in brange:
nbrange.append(prime * -1)
brange += nbrange # Add neg version of the primes
###
# Search the problem space...
for a in range(-9 * factor, 10 * factor):
for b in brange:
if eulerlib.isprime(a + b + 1): # Cull at n == 1 (probably not needed)
nprimes = nP4Quad(a, b)
if nprimes > mprimes:
ma, mb, mprimes = a, b, nprimes
print("Solution: a = %d, b = %d, nprimes = %d, a*b = %d" %
(ma, mb, mprimes, ma * mb))
# Solution to Project Euler #49
#
# by Justin Ethier
#
import eulerlib
import itertools
# Find all 4 digit primes
primes = []
for p in eulerlib.PrimesPlus():
if p > 10**3:
if eulerlib.isprime(p):
primes.append(p)
if p > 10**4:
break
# Collect primes that are permutations of same digits
seqs = {}
for p in primes:
bucket = list(str(p))
bucket.sort()
key = int("".join(bucket))
if key in seqs:
# Existing bucket, add p
seqs[key].append(p)
else:
# New bucket, add p
seqs[key] = [p]
# Find solutions - that is, sequences of primes that increase by 3330