from __future__ import division
from eulermath import primesieve
# Get all the diagonal values for a given (odd) side length
def getdiags(side):
offset = (side-2)**2 + (side-1)
diag = range(offset, side**2+1, side-1)
return diag
if __name__ == "__main__":
ntotalprime = 0 # Starting on side length 1 we have zero primes
ndiag = 1 # with only 1
pside = 26507
side = 3
fracprime = 1.00
# Only increment this if we have to
print "Pre-computing prime list, please hold on..."
primes = set(primesieve(pside**2+1))
while side < 50 or fracprime > 0.1:
diag = getdiags(side)
nprime = len(primes.intersection(diag))
ntotalprime += nprime
ndiag += 4
fracprime = ntotalprime/ndiag
print side, fracprime
side += 2
print ("Side length for which the ratio of primes is < 10% is: " +
repr(side-2))
break
return isperm
#for n in primes:
# pn = n-1
# Euler's totient can be approximated by
# phi(n) ~= n-1
# So n/phi(n) ~= n/(n-1) ~= 1 for large n
# We want this to be a minimum, so if phi(n) > n would be okay.
# But this doesn't happen. So the best we can get is; phi(n) = n
# Also note phi(p) = p-1 for prime values
# So we only have to test the primes to 10**7
# Unfortunately, none of the primes are permutations of each other...
# So start with large n...
maxn = 10**7
primes = primesieve(maxn + 1)
nprimes = len(primes)
#cratio = (10,1,1)
ratios = []
for n in primes:
pn = n - 1
if checkperm(n,pn):
print "permutation found %d %d" % (n,pn)
#if n/pn < cratio[0]:
# cratio = (n/pn,n,pn)
#print "New low value! (ratio,prime,phi(n)) = (%f,%d,%d)" % cratio
cratio = (n/pn,n,pn)
print "Appending: (ratio,prime,phi(n)) = (%f,%d,%d)" % cratio
ratios.append(cratio)
#print "%f%% complete" % (n/maxn*100)
#print "%f%% complete" % (n/nprimes*100)
newprime[ind] = cint
# Check that the length is the same
if len(newprime) == len(int2array(array2int(newprime))):
subgroup.append(array2int(newprime))
pgroup.append(subgroup)
return pgroup
if __name__ == "__main__":
fam_test_size = 6
# We have the solutions for a 6 and 7 family size,
# make sure we get these back
print "Printing primes, family size, and minimum prime in family"
print "Also printing full familly for check"
for ndig in range(2, 9):
# We want these two to be discrete
primes = list(primesieve(10**ndig))
primescheck = set(primesieve(10**ndig))
# print "Primes"
# print primescheck
for prime in primes:
testlists = replaceprime(prime)
# print "After replacement:"
# print testlists
for test in testlists:
primes_in_test = primescheck.intersection(test)
# print primes_in_test
famsize = len(primes_in_test)
# print "Prime and family size:"
if famsize >= fam_test_size:
fam_test_size += 1
print
