357686312646216567629137 is a prime number
Big deal you say? Strike the initial 3 off. The remaining number is also prime. Continue striking them off, one at a time. All the remaining numbers are also prime. The number above is the largest of the “left-truncatable primes”, of which there are precisely 4260. How do I know? I wrote a program to find them (took only about 10 minutes in Python) and you can verify them on this webpage. This sequence is also A024785 in the Online Encyclopedia of Integer Sequences. You can also generate the list of right-truncatable primes (where each prefix is prime). There are only 83 of those, with the largest number being 73939133.