def findPrimesWithRepeats_old(upper_bound):
ps = primes_pp.primeSeive(upper_bound)
prime_list = ps.getPrimeList()
for p in reversed(prime_list):
if not hasDuplicate(p):
prime_list.remove(p)
return prime_list
def findPrimesWithRepeats(upper_bound):
ps = primes_pp.primeSeive(upper_bound)
prime_list = [p for p in ps.getPrimeList() if hasDuplicate(p)]
# for p in reversed(prime_list):
# if not hasDuplicate(p):
# prime_list.remove(p)
return prime_list
def findTruncatablePrimes(upper_limit):
prime_seive = primes_pp.primeSeive(upper_limit)
truncatable_primes = []
for i in xrange(10, upper_limit):
# print 'i: %d' % i
if checkPrimesFromRight(i, prime_seive) and checkPrimesFromLeft(i, prime_seive):
truncatable_primes.append(i)
return truncatable_primes
def main():
prime_sieve = primes_pp.primeSeive(1000)
print '-------------------------------------'
print testWithinGroup(1, 0.02, prime_sieve)
print '-------------------------------------'
print testWithinGroup(2, 0.02, prime_sieve)
print '-------------------------------------'
print testWithinGroup(3, 0.02, prime_sieve)
print '-------------------------------------'
print testWithinGroup(4, 0.02, prime_sieve)
print '-------------------------------------'
print testWithinGroup(5, 0.02, prime_sieve)
print '-------------------------------------'
print testWithinGroup(25, 0.02, prime_sieve)
def findLargestPrime():
print 'getting prime seive'
prime_seive = primes_pp.primeSeive(1e7)
print 'prime seive constructed'
max_prime = 0
# definitely no 2,8, or 9 digit pandigital primes, so don't check
for i in xrange(int(1e7),2,-1):
# max_n_digit_prime = findLargestNDigitPrime(n_digit, prime_seive)
if prime_seive.isPrime(i):
if isPandigital(i):
max_prime = i
break
print 'the max n-digit prime is %d' % max_prime
return max_prime
def findConsecutiveIntegers(num_integers, num_primes, terminal = None):
# - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
# if terminal == None: terminal = int(1e7)
if terminal == None: terminal = int(10**(2+num_primes))
print 'Generating primes from 2-%d' % terminal
prime_seive = primes_pp.primeSeive(terminal)
consecutive_integers = []
print 'Primes successfully generated'
for cand in xrange(terminal):
prime_factors = set(primes_pp.getPrimeFactors(cand, prime_seive))
if len(prime_factors) == num_primes:
consecutive_integers.append(cand)
else:
del consecutive_integers[:]
if len(consecutive_integers) == num_integers:
break
return consecutive_integers
def findSpecialOdd(upper_limit = 1000):
# Generate prime sieve and list of values that are twice a square
prime_seive = primes_pp.primeSeive(int(2*upper_limit))
list_of_2_square = [2*x*x for x in xrange(int(math.sqrt(upper_limit)+1))]
# variables to keep track of whether we found the result
found_special_odd = False
special_odd = -1
# Loop over values 2-upper limit
for i in xrange(2, upper_limit):
# trial will be the odd number generated by taking i*2+1
trial = (2*i) + 1
# trial will be flagged as "normal" if it can be written as a prime +
# twice a square
is_normal = False
# Check list of 2*squares
for twice_square in list_of_2_square:
if twice_square > trial:
break
# if trial - twice_square = prime, we found our special odd!
if prime_seive.isPrime(trial - twice_square):
is_normal = True
# Stop looking if we found the result
if not is_normal:
found_special_odd = True
special_odd = trial
break
# Print result
if found_special_odd:
print "Found odd that cannot be written as the sum of prime and twice a square!"
print '\t%d' % special_odd
else:
print "Did not find odd that cannot be written as the sum of prime and twice a square!"
return special_odd
def findLongestSum(terminal = 100):
print 'Generating primes from 2-%d' % terminal
prime_seive = primes_pp.primeSeive(terminal)
print 'Primes successfully generated'
special_sequences = []
prime_list = prime_seive.getPrimeList()
longest_prime = 2
max_length = 0
print 'Looping over %d primes' % len(prime_list)
for i, p in enumerate(prime_list):
if i%1000 == 0: print 'i: %d -- p: %d' % (i,p)
this_length = getLongestSum(p, prime_list)
if this_length > max_length:
longest_prime = p
max_length = this_length
print ''
print 'prime below %d with longest sum: %d' % (terminal, longest_prime)
print 'sum length: %d' % max_length
def findSpecialSequences(lower_bound = 1000, upper_bound = 3339, delta = 3330):
max_prime = 10**(int(math.log10(upper_bound)+1))
print 'Generating primes from 2-%d' % max_prime
prime_seive = primes_pp.primeSeive(max_prime)
print 'Primes successfully generated'
special_sequences = []
for cand in xrange(lower_bound, upper_bound):
n1 = cand
n2 = cand + delta
n3 = cand + 2*delta
if not prime_seive.isPrime(n1): continue
if not prime_seive.isPrime(n2): continue
if not prime_seive.isPrime(n3): continue
if not isPermutation(n1, n2): continue
if not isPermutation(n1, n3): continue
special_sequences.append([n1, n2, n3])
print 'Found %d special sequences' % len(special_sequences)
for ss in special_sequences:
print '%s -- %d%d%d' % (ss, ss[0], ss[1], ss[2])
return special_sequences