Excellent! Out of curiosity, I fed your number (I called it n) to Pari-GP to see if there were any other small d's for which n+d might be prime. I excluded multiples of 2, 3, and 5. Assuming my mindless script was writ right, the answer is no.
? forstep(d=-1680,1680,[2,4,2,4,6,2,6,4],if(ispseudoprime(n+d),print(d)))
0
2
6
8
12
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