# 149

This number is a prime. Elvis Presley had no less than 149 songs to appear on the Billboard Hot 100 popularity chart in the United States. [Blanchette] There are 149 ways to put 8 queens on a 7-by-7 chessboard so that each queen attacks exactly one other queen. [Gardner] The smallest emirp formed from the digits of three consecutive perfect squares. [Gupta] The smallest three-digit prime containing 4 perfect squares, i.e., 1, 4, 9, 49. [Capelle] 149 is the smallest prime which retains the end (unit) digit of its successor (139). E. g., the next such prime is 191 which comes after 181. [Murthy] The only known prime in the concatenate square sequence. There are no others within the first 14916 terms. Note that a prime in the concatenate cube sequence has yet to be found. 149 and 191 are both prime. So are both 149*2^191+1 and 191*2^149+1. [Hartley] The smallest 3-digit prime with distinct digits in each position such that inserting a zero between any two digits creates a new prime. [Patterson] 149 = 6^2 + 7^2 + 8^2. [Schlesinger] 149 is equal to the sum of two squares as well as is equal to the sum (in arithmetic progression) of three primes which are not sum of two squares: 23 + 43 + 83 = 149. [Teofilatto] The smallest emirp with no prime digits. [Beedassy] The smallest emirp that yields another when each digit d is repeated d times: 14444999999999. [Silva] The numbers π(149)*149! - prime(149) and π(149)*149! + prime(149) are primes with prime length. [Firoozbakht] 149 is prime, but 1149, 2149, ..., 9149 are all composite. This is the smallest excluding two trivial prime numbers 2 and 5. [Poo Sung] For \$149 dollars, Atlas Sports Genetics will test your child's DNA and send you a report listing the sports where your child is likely to succeed. [Robinette] The smallest prime partial sum of extravagant numbers, also called prodigal numbers, or wasteful numbers: 4 + 6 + 8 + 9 + 12 + 18 + 20 + 22 + 24 + 26 = 149. [Post] 149 in binary is 10010101. The zeros are in prime positions 2, 3, 5 and 7, when read left-to-right. These are the four single-digit prime numbers. [Homewood] The largest 3-digit prime with distinct digits that creates another distinct-digit prime, i.e., 164729, when each of its digits is replaced by its cube. [Loungrides] The smallest n (prime) such that the sum of the first n-1 digits of 1/n is beastly. [Sand] Between 1 and 9 there are 4 primes. [Harber] The smallest prime number for which the sum of the square roots of the cubes of its digits equals its product of digits. [Gaydos] The smallest case of the product of the nth prime number and the nth composite number being a beast number is 859 * 194 = 166646 (n=149). [Gaydos] The sum of the first 149 positive integers with digits in ascending order is 149^2. [Gaydos]

(There are 20 curios for this number that have not yet been approved by an editor.)