# There are 4260 Left-Truncatable Primes in Base 10

## Theorem

In base $10$, there are $4260$ left-truncatable primes:

- $2$, $3$, $5$, $7$, $13$, $17$, $23$, $37$, $43$, $47$, $53$, $67$, $73$, $83$, $97$, $113$, $137$, $167$, $173$, $197$, $223$, $283$, $313$, $317$, $337$, $347$, $353$, $367$, $373$, $383$, $397$, $443$, $467$, $523$, $547$, $613$, $617$, $643$, $647$, $653$, $673$, $683$, $743$, $773$, $797$, $823$, $853$, $883$, $937$, $947$, $953$, $967$, $983$, $997$, $1223$, $\ldots$, $357 \, 686 \, 312 \, 646 \, 216 \, 567 \, 629 \, 137$

## Proof

This article needs to be tidied.In particular: Find a way of presenting this without it being incomprehensibly confusingPlease fix formatting and $\LaTeX$ errors and inconsistencies. It may also need to be brought up to our standard house style.To discuss this page in more detail, feel free to use the talk page.When this work has been completed, you may remove this instance of `{{Tidy}}` from the code. |

Of the $1$-digit numbers, only $2$, $3$, $5$, $7$ are primes.

Of the $2$-digit numbers ending with $2$, none are prime.

Of the $2$-digit numbers ending with $3$, $13$, $23$, $43$, $53$, $73$, and $83$ are primes.

Of the $2$-digit numbers ending with $5$, none are prime.

Of the $2$-digit numbers ending with $7$, $17$, $37$, $47$, $67$, and $97$ are primes.

Of the $3$-digit numbers ending with $13$, $113$, $313$, $613$ are primes.

...

Of the $24$-digit numbers ending with $57 \, 686 \, 312 \, 646 \, 216 \, 567 \, 629 \, 137$, only $357 \, 686 \, 312 \, 646 \, 216 \, 567 \, 629 \, 137$ is prime.

Of the $25$-digit numbers ending with $357 \, 686 \, 312 \, 646 \, 216 \, 567 \, 629 \, 137$, none are prime.

This needs considerable tedious hard slog to complete it.In particular: Okay, so finish it thenTo discuss this page in more detail, feel free to use the talk page.When this work has been completed, you may remove this instance of `{{Finish}}` from the code.If you would welcome a second opinion as to whether your work is correct, add a call to `{{Proofread}}` the page. |

$\blacksquare$