19.3.1 * Find all arithmetic sequences composed of prime numbers with a common difference of 10.

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Among the numbers $p, p+10, p+20$, there must be one number divisible by 3 (since $p+10 \equiv p+1$, $p+20 \equiv p+2(\bmod 3)$, and among the three consecutive integers $p, p+1, p+2$, one must be divisible by 3).

If $p, p+10, p+20$ are all prime numbers, then $p=3$, at which point $p+10=13, p+20=23$, so there exists only one arithmetic sequence of three primes with a common difference of 10, which is $3,13,23$.

Since $23+10=33$ is not a prime number, there is no arithmetic sequence of four primes (or more primes) with a common difference of 10.