The number
357,686,312,646,216,567,629,137
is a prime number.
If you remove any number of digits from the left side, the resulting number is also prime.
Numbers like this are called left-truncatable primes (they must not contain any zeros). There are exactly 4259 others ( BTW, 4259 is a prime).
There are also exactly 82 right-truncatable primes; the largest is 73939133.
Then there are 15 primes that are both left- and right-truncatable. The largest is 739397.
(For more on truncatable primes click here.)