Semiprime
Two primes, one handshake.
A product of exactly two prime factors (possibly equal), like 4 = 2×2, 15 = 3×5 or 999997 = 757×1321. Squares of primes count too.
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Semiprimes are one step removed from primes: the range holds 210,035 of them, about 21%, making this one of the most common math features. Their density decays like ln ln n / ln n — slower than primes, so they get relatively more common the further out you go.
Semiprimes underpin modern cryptography: RSA boils down to multiplying two huge primes (a split-second job) and daring attackers to factor the result (a few centuries' work). That asymmetry — easy to multiply, brutal to factor — is the semiprime's commercial value.
Trivia: the smallest run of three consecutive semiprimes is 33 = 3×11, 34 = 2×17, 35 = 5×7. And the largest semiprime in range is 999997 = 757×1321, a mere 3 short of a million.