I almost overlooked this article because I got turned off by the opening description in base 10, as there is a lot of math trivia out there that is specific to base 10 which holds little general significance.
But a little further down, the article discusses how this was discovered originally in base 3, and I think it's much simpler to understand in that context, since all primes except 3 (aka 10 base 3) end in just either 1 or 2:
"Looking at prime numbers written in base 3 — in which roughly half the primes end in 1 and half end in 2 — he found that among primes smaller than 1,000, a prime ending in 1 is more than twice as likely to be followed by a prime ending in 2 than by another prime ending in 1."
But a little further down, the article discusses how this was discovered originally in base 3, and I think it's much simpler to understand in that context, since all primes except 3 (aka 10 base 3) end in just either 1 or 2:
"Looking at prime numbers written in base 3 — in which roughly half the primes end in 1 and half end in 2 — he found that among primes smaller than 1,000, a prime ending in 1 is more than twice as likely to be followed by a prime ending in 2 than by another prime ending in 1."