def findlargestpandigital():
for n in range(9, 1, -1):
pan = makepandigital(n, True)
for p in pan:
pint = array2int(p)
# print "Testing: " + repr(pint)
if isprime(pint):
print "Found the largest pandigital prime: " + repr(pint)
return pint
def isPp2Sq(num):
i = 1
rval = 0
while 2*(i**2) < num:
res = num - 2*(i**2)
if isprime(res):
# We can do the decomposition
rval = 1
break
i += 1
return rval
def istruncprime(n):
istp = 0
if (n > 10 and isprime(n)):
istplr = 1
istprl = 1
# if we have two digits we can pop another off
nt = n
while nt > 10:
nt = truncateLR(nt)
# print "nt: " + repr(nt) + " prime: " + repr(isprime(nt))
if (isprime(nt) == 0):
istplr = 0
break
if (istplr == 1):
nt = n
while nt > 10:
nt = truncateRL(nt)
# print "nt: " + repr(nt) + " prime: " + repr(isprime(nt))
if (isprime(nt) == 0):
istprl = 0
break
if (istplr and istprl):
istp = 1
return istp
def primefactors(n):
pf = []
while not isprime(n):
founddiv = False
pi = 1
while not founddiv:
pn = nthprime(pi)
# This prime evenly divides, factor it out
if n % pn == 0:
n = n/pn
pf.append(pn)
founddiv = True
pi += 1
# Note: we have also reduced n down to a prime, include it as well
pf.append(n)
return pf
from eulermath import isprime
if __name__ == "__main__":
# Start looking for primes at 3 - skip all the
# evens because they are not prime
# test case, the 10th prime is 29
# findpri = 10
findpri = 10001
indpri = 2 # The number of the prime we are - last found was 2
cint = 3 # Current integer to test for prime-ness
while (indpri < findpri):
cint += 2
# print "testing", cint, isprime(cint)
if isprime(cint) == 1:
indpri += 1
print "The", indpri, "th prime is:", cint
from eulermath import isprime
from eulermath import intcpermute
# print intcpermute(123)
# print isprime(4)
if __name__ == "__main__":
# nmax = 100 # Test case, shoud give 13
nmax = 1000000
n = 2
ncpri = 0
prilist = []
while n < nmax:
if n % 100000 == 0:
print "+10%"
if isprime(n):
for x in intcpermute(n):
if isprime(x) != 1:
break
else:
ncpri += 1
prilist.append(n)
n += 1
print "There are:", ncpri, "circular primes below", nmax
# print prilist
# Find the one other sequence of 4-digit permuted increasing primes
# The first is; 1487, 4817, 8147 (difference is 3330)
from eulermath import (isprime, int2array, array2int,
find_primes_in_list, find_arithemetric_series)
from itertools import permutations, combinations
if __name__ == "__main__":
# Start by finding all 4-digit primes
print "Finding arithemetric series of primes between 1001 and 9999:"
exclude = []
for trial in xrange(1001, 9999, 2):
if trial not in exclude:
if isprime(trial):
# Find the permutations of this number
tp = permutations(int2array(trial))
# Get the unique values and sort them
tpl = list(set([array2int(x) for x in tp]))
tpp = find_primes_in_list(tpl)
tpn = []
for x in tpp:
if x > 1000:
tpn.append(x)
# Exclude the others
for p in tpn:
exclude.append(p)
# Find any arithemetric series of length 3 in the prime list
aseries = find_arithemetric_series(tpn, 3)
if len(aseries) > 0:
print aseries
for series in aseries:
print series
from eulermath import isprime
if __name__ == "__main__":
# Test case, should give 17
# nmax = 10
nmax = 2000000
total = 2
n = 3
while (n < nmax):
if (isprime(n) == 1):
total += n
n += 2
print "The sum of primes below", nmax, "is", total
if __name__ == "__main__":
maxp = 10**6
# Import a list of the primes < 1M
prime_sm = []
pfile = open("eplist.dat")
for line in pfile:
prime = int(line)
if prime >= maxp:
break
else:
prime_sm.append(prime)
maxsum = 2
maxlen = 1
maxseq = []
for jj in range(len(prime_sm)):
for ii in range(jj):
seq = prime_sm[ii:jj]
seqsum = sum(seq)
if (seqsum < maxp):
if (isprime(seqsum)) and (len(seq) > maxlen):
maxsum = seqsum
maxlen = len(seq)
maxseq = seq
else: # we have exceeded the 1M mark
break
print maxsum
print maxlen
print maxseq
import sys
from eulermath import isprime
if __name__ == "__main__":
# n = 10
# n = 13195 #should give 29
n = 600851475143
x = 2
while x < n / 2:
# for x in range(n-1,n/2,-1):
# print "is", x, "a factor?"
if n % x == 0:
# This is a factor check if it is prime
b = n / x
c = isprime(b)
print "testing number:", b, c
if c == 1:
# We are a prime number
# Since we are going from large numbers
# To small, this must be the largst prime
print "The largest prime factor of", n, "is", b
break
x += 1
