991 (another Prime Pages' Curiosity)
 Curios: Curios Search:   Participate: GIMPS has discovered a new largest known prime number: 282589933-1 (24,862,048 digits) 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. 991^2 = 982081 and 982 + 0 + 8 + 1 = 991. [Meller] Florida angler Allen Ogle caught a 991-pound Hammerhead Shark on May 30, 1982. 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] (There are 4 curios for this number that have not yet been approved by an editor.) Prime Curios! © 2000-2019 (all rights reserved)  privacy statement