42 (another Prime Pages' Curiosity)
 Curios: Curios Search:   Participate: The nth Prime Page will now find any of the first 2.623˙1015 primes or π(x) for x up to 1017. The sum of the least consecutive primes ending in "1" (42 = 11 + 31). [Rivera] 42^2 is the smallest perfect square that is the mean of cubed twin primes. Curiosly, the difference of the twin prime cubed and the mean of the cubed twin primes is again a prime: 42^2 = 11^3 + 433 = 13^3 - 433. [Vrba] The 13th case of a prime concatenation of the form n & n-th prime is with n = 42 and n-th prime = 181 (42181). Coincidentally 181 is congruent to 13 modulo 42. Note that 18142181 is also prime. Furthermore the operations 181 - 42 and 42 + 181 yield primes resp. 139 and 223 leading us to these prime combinations with 42 in the middle : 13942223 (A) and 22342139 (B). Finally (B)(A) = 2234213913942223 is prime as well. [De Geest] In the first book of his Hitchhiker "Trilogy" Douglas Adams writes, "42 is the answer to life, the universe, and everything." Note that 42 lies between a twin prime pair {41, 43}. [Little] 42 = ((4)*(2)) * (prime(4)*prime(2)). Note that 42 is the only number less than 20000000 with this property. [Firoozbakht] 42^42 + (42) is prime. It is interesting that all numbers less than 42 with this property are are all prime factors of 42. [Firoozbakht] All five numbers 1 + 42, 1 + 4242, 1 + 424242, 1 + 42424242 and 1 + 4242424242 are prime. [Firoozbakht] The smallest integer that forms a pair of twin primes by concatenation with the previous and the next number (4241, 4243). [Silva] (There are 4 curios for this number that have not yet been approved by an editor.)   To link to this page use /curios/page.php?number_id=416 Prime Curios! © 2000-2016 (all rights reserved)