Largest Right-Truncatable Primes allowing 1

Theorem

Let $1$ be temporarily considered to be a prime number.

Under that consideration, the largest right-truncatable prime numbers are:

$1 \, 979 \, 339 \, 333$

$1 \, 979 \, 339 \, 339$

Proof

We have that:

$\ds $

$\ds 1 \, 979 \, 339 \, 333$

is prime

$\ds $

$\ds 1 \, 979 \, 339 \, 339$

is prime

For both, the truncation process is the same:

$\ds $

$\ds 197 \, 933 \, 933$

is the $10 \, 970 \, 817$th prime

$\ds $

$\ds 19 \, 793 \, 393$

is the $1 \, 252 \, 285$th prime

$\ds $

$\ds 1 \, 979 \, 339$

is the $147 \, 488$th prime

$\ds $

$\ds 197 \, 933$

is the $17 \, 815$th prime

$\ds $

$\ds 19 \, 793$

is the $2240$th prime

$\ds $

$\ds 1979$

is the $299$th prime

$\ds $

$\ds 197$

is the $45$th prime

$\ds $

$\ds 19$

is the $8$th prime

$\ds $

$\ds 1$

has been defined temporarily to be prime

This needs considerable tedious hard slog to complete it.
In particular: It remains to be demonstrated that there are no such primes which are larger
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Sources

1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $1,979,339,339$
1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $1,979,339,339$