def lrTruncPrime( n ):
"""Is n both left-trunc and right trunc prime?
>>> from euler37 import lrTruncPrime
>>> lrTruncPrime(3797)
True
>>> lrTruncPrime(997)
False
"""
lt= all( isprime(t) for t in leftTrunc(n) )
rt= all( isprime(t) for t in rightTrunc(n) )
return lt and rt
def answer():
bList = [ b for b in range(2,1000) if isprime(b) ]
#print bList
maxPList= []
maxPArgs= None
for a in range(0,1000):
for b in bList:
for sa, sb in ( (a,b), (-a,b), (a,-b), (-a,-b) ):
pList= list(primeFunc(sa,sb))
if len(pList) > len(maxPList):
maxPList= pList
maxPArgs= (sa, sb)
return maxPArgs
def circularPrimes( limit ):
"""
>>> from euler35 import circularPrimes
>>> cp100= circularPrimes( 100 )
>>> len(cp100)
13
>>> sorted( set( cp100 ) )
[2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, 97]
"""
cp= set()
for n in range(2,limit):
if isprime(n) and n not in cp:
rs= [ number(r) for r in rotations( digits(n) ) ]
circular= all( map( isprime, rs ) )
if circular:
for r in rs:
cp.add(r)
return cp
def primeFunc( a, b ):
"""Generate primes using :math:`n^2 + an + b`
For all values of n between 0 and max(abs(a),abs(b)).
>>> from euler27 import primeFunc
>>> e1= list(primeFunc(1,41)) # n^2+n+41
>>> len(e1)
40
>>> e2= list(primeFunc(-79,1601)) # n^2-79n+1601
>>> len(e2)
80
"""
for n in range(max(abs(a),abs(b))):
x= n*n+a*n+b
if x > 0 and isprime(x):
yield x
else:
break
def pandigitalPrimes(size):
"""Generate all pan-digital primes of a given size.
>>> from euler41 import pandigitalPrimes
>>> pd4 = list( pandigitalPrimes(4) )
>>> 2143 in pd4
True
>>> pd4
[1423, 2143, 2341, 4231]
"""
permN= Permutation( range(1,size+1) )
for p in permN.nextPerm():
ld= p[-1]
if ld % 2 == 0: continue # skip even numbers
if ld == 5: continue # skip 5's, also
n= number( p )
if isprime(n):
yield n
def big_prime( stop=1000000 ):
"""Largest prime less than the given number or 1."""
while stop != 1 and not isprime(stop):
stop= stop-1
return stop
def is_prime( n ):
if n not in memoized:
memoized[n]= isprime( n )
return memoized[n]
