1093

This number is a prime.

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1093 divides every number of the form 3^(n!)-1, for n>6. [Galliani]

The addition at the end to 1093 of its third digit (from left), nine, produces 10939, which is prime. The same thing happens with the greater of the Wieferich primes, 3511. In fact, the addition at the end of one, which is the third digit of 3511 from left, produces 35111, which is prime. [Galliani]