left-truncatable prime

Left-truncatable primes (or just truncatable primes) are prime numbers (without the digit zero) that remain prime no matter how many of the leading digits are omitted. For example, 4632647 is left-truncatable because it and each of its truncations (632647, 32647, 2647, 647, 47, and 7) are primes. We omit the digit zero to avoid trivial examples such as the prime 10⁶⁰+7:

1000000000000000000000000000000000000000000000000000000000007.

Each of its truncations is the prime 7.

The three largest left-truncatable primes are:

 959 18918 99765 33196 93967,
 966 86312 64621 65676 29137, and
3576 86312 64621 65676 29137.

We leave it to the reader to find the largest such primes in other bases.

See Also: RightTruncatablePrime, PermutablePrime, DeletablePrime, MinimalPrime, Primeval

References:

AG1977

I. O. Angell and H. J. Godwin, "On truncatable primes," Math. Comp., 31 (1977) 265--267.  MR 55:248

Caldwell87

C. Caldwell, "Truncatable primes," J. Recreational Math., 19:1 (1987) 30--33. [A recreational note discussing left truncatable primes, right truncatable primes, and deletable primes.]

Clark1973

H. J. Clark, "Letter to the editor," Computer Weekly,:360 (27 September 1973) 26.