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COMMENT
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a(10) = 10^273 - 273^10 is too large to include.
a(16) = 1 because primes of the form (16^k - k^16) do not exist, since 16^k - k^16 = (4^k - k^4)(4^k + k^4).
The corresponding numbers k such that a(n) = (n^k - k^n) are listed in A128355(n) = {0,5,4,0,14,7,20,11,10,273,14,13,38,89,68,0,...}, where k = 0 corresponds for definite a(n) = 1. Currently a(n) is not known for n = {17,18,22,25,26,27,28,...}.
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EXAMPLE
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a(1) = 1 because (1^k - k^1) = (1 - k) < 0 for k > 1.
a(2) = 7 because 2^5 - 5^2 = 7 is prime, but (2^k - k^2) is not prime for 1 < k < 5, (2^2 - 2^2) = 0, (2^3 - 3^2) = -1, (2^4 - 4^2) = 0.
a(4) = 1 because prime of the form (4^k - k^4) does not exist, 4^k - k^4 = (2^k - k^2)(2^k + k^2).
a(12) = 83695120256591 = 12^13 - 13^12 = A024152[ A122003(2) ].
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