### Chop off their heads and conquer the Pentagon (week 147)

Chop off their heads! Task 1 this week asks us to write a script to generate first 20 left-truncatable prime numbers in base 10. A left-truncatable prime (LTP) is a prime number which, in a given base, contains no 0, and if the leading left digit is successively removed, then all resulting numbers are primes. In principle this is easy enough: generate the primes using a sieve of our good friend Eratosthenes, discard any containing zeroes, and check the remainder for being left-truncatable. I chose to exclude single digit primes, ie 2, 3, 5, and 7 because I felt that they did not meet the criterion of 'all resulting numbers are primes', because there are no resulting numbers. The next 16 LTPs are only 2 digits - they range from 11 to 97, and 4 more - 113, 131, 137 and 167 complete the required 20. The computing time is negligible. However, had the task asked for the first 1000, or 10 000 LTPs it would be worth applying a little optimisation. For example, the last digit of an L