# 421

This number is a prime. All integers ever tested in the Collatz problem eventually ends in the sequence 4-2-1.

Puzzio: The starting number 6 generates a Collatz trajectory of (6-3-10-5-16-8-4-2-1) and via concatenation (63105168421) we get a prime. Can you find the smallest titanic "Hailstone prime?" The sequence begins 421, 63105168421, 1263105168421, etc. [Honaker, 1999] Jeu du 421 (quatre-cent-vingt-et-un) is a French dice game. The first prime formed by the powers of 2 in numerical order from right to left. [Luhn] The sum of the letters of "prime number" if we use the alphaprime code. [Zirkle] A vigesimal repunit: 400 + 20 + 1 = 20^2 + 20^1 + 20^0 = 111_20. [McCandless] The only non-titanic prime concatenated in reverse order from consecutive powers of 2. [Loungrides] The largest prime formed by concatenating all distinct divisors of a composite digit. [Loungrides] Kepler-421b has the longest year—that is, it has the longest orbital period around its star—for any exoplanet yet seen crossing in front of its star. [Plait] The product of first 421 positive even numbers minus 1 (i.e., 2^421*421!-1) is the smallest titanic prime of form 2^p*p!-1, where p is a prime. [Loungrides] If we set 421 to the lowest possible numeral system (base five) it remains prime in base ten. [Bsivko] The concatenation of the number of 1-digit primes and the number of 2-digit primes. [Gaydos]