This number is a prime.
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In 1941, Molsen proved that for n equal to or greater than 199, the interval n < p less than or equal to (8/7)n always contains a prime of each of the forms 3x+1, 3x-1. [Post]
Largest known prime partial sum of Dedekind numbers. Equivalently partial sum of number of monotone Boolean functions of n variables, or partial sums of number of antichains of subsets of an n-set: 2 + 3 + 6 + 20 + 168 = 199 is prime. Curously, the first 5 such partial sums are prime (2, 5, 11, 31, 199), and then no more primes are known. [Post]