8191

This number is a prime.

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All Mersenne primes are of the from 2^k - 1, and k must be prime. For 8191, k=13. The case of k=11 (the prime preceding 13) gives the smallest composite Mersenne number, with one of it's factors being 89. If you remove every other digit, you get 89 as well. [Meiburg]

Suppose you listed all primes, with three digits or less, using the digits in this number (1,8, and 9), without limiting the number of times a number can use each digit (i.e., it may have two nines). If they are now listed from least to greatest with signs in the order "+, +, -,", beginning with 11+18+19-181+191+199-811... the sum is 1381, which is a prime as well. [Meiburg]