991

This number is a prime.

+ 991, 99991, and 9999991 are each prime. [Avrutin]

+ This number, as well as 331 and 661, are all prime. Note that the product of these three primes is a Carmichael Number. [Patterson]

+ The largest three-digit permutable prime.

+ Equal to 11+22+33+44+55+66+77+88+99+1+99+88+77+66+55+44+33+22+11. [Silva]

+ 991^2 = 982081 and 982 + 0 + 8 + 1 = 991. [Meller]

+ Florida angler Allen Ogle caught a 991-pound Hammerhead Shark on May 30, 1982.

+ Every number greater than 991 can be expressed as a sum of abundant numbers.

+ 991 is a prime p such that p^71 can be partitioned into parts whose sum is equal to p. Compare the digits of 991^71 with 5 + 2 + 6 + 2 + 9 + 5 + 2 + 7 + 1 + 9 + 1 + 03 + 5 + 9 + 3 + 09 + 6 + 5 + 3 + 4 + 6 + 3 + 4 + 02 + 7 + 1 + 5 + 1 + 2 + 3 + 4 + 9 + 3 + 08 + 1 + 3 + 3 + 4 + 3 + 3 + 3 + 6 + 9 + 8 + 8 + 9 + 3 + 5 + 6 + 8 + 1 + 7 + 9 + 9 + 8 + 8 + 8 + 1 + 2 + 8 + 6 + 5 + 3 + 9 + 8 + 7 + 8 + 2 + 2 + 8 + 3 + 5 + 07 + 3 + 8 + 4 + 4 + 2 + 2 + 1 + 7 + 2 + 3 + 4 + 1 + 4 + 3 + 2 + 03 + 5 + 6 + 8 + 9 + 5 + 2 + 6 + 7 + 3 + 8 + 4 + 2 + 9 + 8 + 7 + 6 + 8 + 2 + 4 + 5 + 4 + 8 + 5 + 8 + 04 + 8 +4 + 04 + 4 + 07 + 5 + 8 + 6 + 00 + 9 + 7 + 7 + 1 + 9 + 8 + 6 + 2 + 1 + 4 + 1 + 5 + 4 + 6 + 3 + 4 + 5 + 3 + 4 + 3 + 9 + 6 + 4 + 1 + 4 + 4 + 4 + 5 + 7 + 3 + 5 + 09 + 4 + 5 + 3 + 1 + 7 + 4 + 5 + 2 + 3 + 6 + 07 + 8 + 9 + 6 + 1 + 1 + 4 + 7 + 6 + 06 + 8 + 8 + 9 + 5 + 2 + 2 + 4 + 7 + 7 + 9 + 9 + 8 + 5 + 00 + 9 + 05 + 9 + 4 + 1 + 3 + 7 + 9 + 1. Found by Giovanni Resta and Hjakan Summakoglu. [Rivera]

+ The smallest emirp that is the sum of reversals of first 31 (also an emirp) numbers, i.e., 1+2+3+...+92+03+13 = 991. [Sariyar]

+ The largest 3-digit emirp p that does not produce a prime by adding a trailing digit to p. Note that uniquely 167=π(991) and its reversal (761) both have this property. [Worrom]

+ Proven to be the largest permutable prime that is not a repunit prime. [Perrenoud]

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