If we count 1 as a prime digit, you can start with 1, 2, 3, 5, or 7 and build Snowball Primes — prime numbers that remain prime each time you add another digit. Start with 3? Add a 1, still prime. Start with 7? Add a 3, still prime. 73, add a 1? 731 — STILL PRIME.
In just a few hours, you can build the entire roster of Snowball Primes up to 8 digits by hand. DO IT. Why not? This is recreational math. Your parents will be proud of you.
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