How do you prove a prime is infinitely fragile?

Consecutive primes which are widely digitally delicate.
https://people.math.sc.edu/filaseta/ConsecutiveDigitallyDelicatePrimes2021.pdf

Data from the paper:
https://people.math.sc.edu/filaseta/ConsecutiveWDDPrimes.html

Here is the bonus footage. https://youtu.be/wtzgbJuHSfM

And yes, the theme song (along with the remix) is on Bandcamp as 'pay what you want'. So you can download for free, or pay something to help support the channel. https://standupmaths.bandcamp.com/track/digits-are-forever-inc-prime-remix

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CORRECTIONS
- At 00:33 there is a "33" which should be "53". Mistake first spotted by Andrew Foong but I'm going to claim it's some hidden message about the number 33.
- I say k is a "positive integer" a bunch when it should be "non-negative integer" to include zero. Like at 06:30, 08:48 and 14:35 (thanks Martijn Oostrom!). The formal statement on-screen at 17:15 is the official correct version showing that n is positive but k is non-negative.
- Robin Houston noticed that the on-screen text at 4:19 says Erdös instead of Erdős. Excuse me while I delete the whole channel.
- Let me know if you spot any more mistakes!

As always: thanks to Jane Street who support my channel. They're amazing.
https://www.janestreet.com/

Music by Howard Carter
Lyrics and vocals by Helen Arney
Animations by William Marler
Filming and editing by Matt Parker
Maths graphics by Sam Hartburn and Matt Parker
Colour grading by Alex Genn-Bash
Design by Simon Wright and Adam Robinson

MATT PARKER: Stand-up Mathematician
Website: http://standupmaths.com/
US book: https://www.penguinrandomhouse.com/books/610964/humble-pi-by-matt-parker/
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Видео How do you prove a prime is infinitely fragile? канала Stand-up Maths