# 347

This number is a prime.

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The only non-titanic-prime (emirp) of form 7^p+(p+1) for p a prime, (p=3). [Loungrides]

(347, 743) is the first pair of emirps (p, q) such that 5^p and 5^q are both "apocalyptic numbers", i.e., numbers that contain the beast number. [Loungrides]

2^2*3^3*7^7*347^347-1 is the largest non-titanic prime of form 2^2*3^3*7^7*347^347*...* a(n-1)^a(n-1)*a(n)^a(n)-1, where n, a(n) and 2^2*3^3*...*a(n)^a(n) – 1 are prime, a(n)>a(n-1), and a(n) is minimal. Note that the previous such primes are: a(1) = 2^2-1 = 3, a(2) = 2^2*3^3-1 = 107, a(3) = 2^2*3^3*7^7*-1 = 88942643. [Loungrides]

The only emirp that can be represented as the number of lines in a Rhapsody of Homer’s Odyssey, (i.e. Rhapsody VΙI). This line says: «πὰρ δὲ γυνὴ δέσποινα λέχος πόρσυνε καὶ εὐνήν». [Loungrides]