Largest Right-Truncatable Primes allowing 1

From ProofWiki
Jump to navigation Jump to search

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
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 {{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.



Sources

Retrieved from "https://proofwiki.org/w/index.php?title=Largest_Right-Truncatable_Primes_allowing_1&oldid=618246"