Definition:Left-Truncatable Prime

Definition

A left-truncatable prime is a prime number which remains prime when any number of digits are removed from the left hand end.

Zeroes are excluded, in order to eliminate, for example, prime numbers of the form $10^n + 3$ for arbitrarily large $n$.

Sequence

The sequence of left-truncatable primes begins:

$2, 3, 5, 7, 13, 17, 23, 37, 43, 47, 53, 67, 73, 83, 97, 113, 137, 167, 173, 197, \ldots$

Examples

$357 \, 686 \, 312 \, 646 \, 216 \, 567 \, 629 \, 137$ is a Left-Truncatable Prime

The largest left-truncatable prime is $357 \, 686 \, 312 \, 646 \, 216 \, 567 \, 629 \, 137$.

Also see

• Definition:Right-Truncatable Prime
• Definition:Two-Sided Prime

• Results about left-truncatable primes can be found here.

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $357,686,312,646,216,567,629,137$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $357,686,312,646,216,567,629,137$

• Weisstein, Eric W. "Truncatable Prime." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/TruncatablePrime.html