21.3 F ̈urstenberg’s topological proof made easy 609
Project: Tuncatable primes
Consider the prime number 73939133. The numbers obtained by trun-
cations from the right are all primes:
73939133 , 7393913 , 739391 , 73939 , 7393 , 739 , 73 , 7.More generally, we call a numberNa right-truncatable prime if every
number obtained from truncatingNfrom the right is a prime or 1.
A complete list of right-truncatable primes can be found in [Waltrom
and Berg].
Write a computer program to find all right-truncatable primes.
Similarly, define left-truncatable primes, and bi-truncatable primes as
those which are both left- and right-truncatable primes.
53 3797 73331 7393931
7331 373393 7393933
317 23333 593993 23399339
599 23339 719333 29399999
797 31193 739397 37337999
2393 31379 739399 59393339
3793 37397 2399333 73939133
Here are all the bi-truncatable primes:12357
11 13 17 23 31
37 53 71 73 113
131 137 173 311 313
317 373 1373 3137