fromcollectionsimportdequedefperms(p):result=[]d=deque(str(p))for_inrange(len(str(p))):d.rotate(1)result.append(int(''.join(d)))returnresultprev_primes=[]forposs_primeinrange(2,1001):forninprev_primes:ifposs_prime%n==0:breakelse:# no breakprev_primes.append(poss_prime)result=[pforpinprev_primesifall(qinprev_primesforqinperms(p))]print(result)

This solution has a bug but happens to produce the correct output. This doesn't test all permutations of digits. An n digit integer has n! permutations, but this only tests n of them. For example, 241 has six permutations (241, 214, 421, 412, 124, 142) but this only tests three (241 , 412, 124) of them.

It happens to work because all the three digit permutable prime happen to belong to a family that contain repeated digits, so you never get a false positive. It will fail for larger numbers, it will report 1193 as a permutable number, but it's not (1139 is not a prime number). It's a circular number, solved by Jonathan's Go code below.

Amazingly the next number in the permutable prime sequence after 991 is 1111111111111111111.

You can of course easily fix the bug with itertools.permutations). Just replace perms(p) with this:

Nice one!

This solution has a bug but happens to produce the correct output. This doesn't test all permutations of digits. An n digit integer has n! permutations, but this only tests n of them. For example, 241 has six permutations (241, 214, 421, 412, 124, 142) but this only tests three (241 , 412, 124) of them.

It happens to work because all the three digit permutable prime happen to belong to a family that contain repeated digits, so you never get a false positive. It will fail for larger numbers, it will report 1193 as a permutable number, but it's not (1139 is not a prime number). It's a circular number, solved by Jonathan's Go code below.

Amazingly the next number in the permutable prime sequence after 991 is 1111111111111111111.

You can of course easily fix the bug with itertools.permutations). Just replace perms(p) with this: