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GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) All integers ever tested in the Collatz problem eventually ends in the sequence 421. Collatz Challenge: The starting number 6 generates a Collatz trajectory of (63105168421) and via concatenation (63105168421) we get a prime. Can you find the first 421 "Hailstone primes?" The sequence begins 421, 63105168421, 1263105168421, etc. [Honaker, 1999] Jeu du 421 (quatrecentvingtetun) 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 nontitanic 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] Kepler421b has the longest yearâ€”that is, it has the longest orbital period around its starâ€”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 1digit primes and the number of 2digit primes. [Gaydos]
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