There are 83 Right-Truncatable Primes in Base 10

Theorem
In base 10, there are 83 right-truncatable primes: 2, 3, 5, 7, 23, 29, 31, 37, 53, 59, 71, 73, 79, 233, 239, 293, 311, 313, 317, 373, 379, 593, 599, 719, 733, 739, 797, 2333, 2339, 2393, 2399, 2939, 3119, 3137, 3733, 3739, 3793, 3797, 5939, 7193, 7331, 7333, 7393, 23333, 23339, 23399, 23993, 29399, 31193, 31379, 37337, 37339, 37397, 59393, 59399, 71933, 73331, 73939, 233993, 239933, 293999, 373379, 373393, 593933, 593993, 719333, 739391, 739393, 739397, 739399, 2339933, 2399333, 2939999, 3733799, 5939333, 7393913, 7393931, 7393933, 23399339, 29399999, 37337999, 59393339, 73939133

Proof
For the one-digit numbers, only 2, 3, 5, 7 are primes.

For the two-digit numbers starting with 2, only 23 and 29 are primes.

For the two-digit numbers starting with 3, only 31 and 37 are primes.

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For the eight-digit numbers starting with 7393913, only 73939133 is prime.

For the eight-digit numbers starting with 7393931, none of them is prime.

For the eight-digit numbers starting with 7393933, none of them is prime.

For the nine-digit numbers starting with 23399339, none of them is prime.

For the nine-digit numbers starting with 29399999, none of them is prime.

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