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Finding efficiently primes, whose begining numbers are also primes. See the thread http://www.daniweb.com/software-development/cpp/threads/425821/prime-number-c in C++ forum for discussion on topic.

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```
import pretty # http://www.daniweb.com/software-development/python/code/345935/printing-things-nicely-pretty-printer-revisited
from functools import update_wrapper
import time
def is_prime_(n):
if n in (2, 3):
return True
elif n < 2 or not n % 2 or not n % 3:
return False
if n < 9:
return True
r = int(n ** 0.5)
f = 5
while f <= r:
if not n % f or not n % (f + 2):
return False
f += 6
return True
def timestr(t):
return ( ("%i min %.3f s" % divmod(t, 60)) if t > 60
else (("%.3f s" % t) if t > 1
else ("%.3f ms" % (t * 1000)) if t > 0.001 else ("%i us" % (t*10**6))
)
)
def timing(func):
def wrapper(*arg, **kwargs):
t1 = time.clock()
res = func(*arg, **kwargs)
t2 = time.clock()
print('%s took %s' % (func.__name__, timestr(t2-t1)))
return res
return update_wrapper(wrapper, func)
@timing
def special_primes(length = 8):
primes = [n for n in range(1,10) if is_prime(n)]
all_fit = [primes[:]]
for n in range(length-1):
#print('%i: %2i solutions: %s\n' % (n+1, len(primes), primes))
newprimes = [p * 10 + a for p in primes for a in 1,3,7,9 if is_prime(p * 10 + a)]
if not newprimes:
#print n+2, 'and longer impossible'
break
all_fit.append(newprimes)
primes = newprimes
return all_fit
if __name__ == '__main__':
s = special_primes()
print('\nLengths and counts:')
pretty.printer(list((ind, len(v)) for ind, v in enumerate(s, 1)))
print('Total solutions count: %i' % sum(map(len, s)))
print('\nThe numbers by lengths:')
pretty.printer(s)
""" Output:
special_primes took 9.128 ms
Lengths and counts:
[
(1, 4),
(2, 9),
(3, 14),
(4, 16),
(5, 15),
(6, 12),
(7, 8),
(8, 5)]
Total solutions count: 83
The numbers by lengths:
[
[2, 3, 5, 7],
[23, 29, 31, 37, 53, 59, 71, 73, 79],
[233, 239, 293, 311, 313, 317, 373, 379, 593, 599, 719, 733, 739, 797],
[2333, 2339, 2393, 2399, 2939, 3119, 3137, 3733, 3739, 3793, 3797, 5939, 7193, 7331, 7333, 7393],
[23333, 23339, 23399, 23993, 29399, 31193, 31379, 37337, 37339, 37397, 59393, 59399, 71933, 73331, 73939],
[233993, 239933, 293999, 373379, 373393, 593933, 593993, 719333, 739391, 739393, 739397, 739399],
[2339933, 2399333, 2939999, 3733799, 5939333, 7393913, 7393931, 7393933],
[23399339, 29399999, 37337999, 59393339, 73939133]]
"""
```

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