# 2111

This number is a prime. The square root of 4456321. (The reversal of 4456321 is 1112 squared.) The smallest "prime year" of the 22nd century. The next prime years are 2113, 2129, 2131, 2137, 2141, 2143, 2153, 2161, and 2179. 2111 in base b is prime for all values of b from 3 to 10, with the exception of b=6. [Necula] The first salmonella outbreak associated with peanut butter had product code 2111 on the lid. 2111 = 1 + 2^2 + 2^3 + 2^5 + 2^7 + 2^11. The exponents are consecutive primes. [Noe] The smallest prime that together with its "look-and-say" description from the left in the digit-frequency order (i.e., 2 once, 1 thrice) forms a twin prime pair (2111, 2113) [Beedassy] The smaller of only two primes less than a googol formed by concatenating in descending order the first n multidigit numbers ending with 1, (case n=2). The other is 41312111 for n=4. [Loungrides] 2111 is the smallest start of a run of five primes obtained by the following procedure: replace each digit of 2111 with the digit's square to obtain a new prime, and up to five primes doing this recursively, i.e., 2111, 4111, 16111, 136111 and 1936111. [Rivera] 2111 is the smallest four-digit prime which remains prime when 2 is added to any of its digits. [Petrov]

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