# 181

This number is a prime. 181 is the 9th palindromic prime number. Note that 9 divides 18 and 81, whose sum of digits are both 9. There are 181 digits in 111!. [De Geest] The 181st prime is congruent to 1 (mod 181). [Haga] The prime value of x in the equation x2 = 2(3 * 5) - 7. 181 * 10181 + (10181 - 1) is prime. [Luhn] The sum of the first 181 primes minus 181 is prime. [Gevisier] The sum of the digits of the first 23 primes (2, ..., 83). [Trotter] The 181-digit palindromic number made up of all 7's except for the center nut being 181 (7777...7718177...77777) is a palindromic prime with a palindromic prime decimal length. [Fougeron] The first occurrence of two consecutive primes which are both nontrivial (more than one digit) palindromes: 181, 191. [Murthy] The smallest palindromic prime that remains prime through four iterations of the function f(x) = 2x + 5. [Russo] The smaller of the first occurrence of two successive primes using no prime digits (181, 191). [Murthy] The surface area of a pair Boeing 757 wings in square meters. 181 pennies currently minted in the U.S. weigh within a penny of a pound. 181 is the smallest odd prime (and fifth in all) exponent of 2 dissecting the interval between successive primes, i.e., 2^181 ± 165 are both prime with no intervening primes. [King] 181 = 92 + 102, i.e., the sum of two consecutive squares. [Mizuki] No ship of the United States Navy has ever been named USS Haynes. A fictitious USS Haynes (DE-181) was the setting for the surface half of the movie The Enemy Below; her part was played by USS Whitehurst (DE-634). [Haga] The smaller prime in the first multidigit "Gridgeman pair." A Gridgeman pair is two palindromic primes, which differ only in that their middle digits are x and x + 1 respectively. These are named in honor of Norman T. Gridgeman (1912-1995) who conjectured that there are an infinite number of primes in this form. [King] The smallest palindromic prime number whose sum of digits is composite. Note that 181 is also the smallest such that at least one of the digits is composite. [Capelle] 181^2 = 105^3 - 104^3, i.e., a solution to the Diophantine equation z^2 = x^3 - y^3. [Mizuki] It is conjectured that there is always a prime between xa and yb for all integers x, y, a, b > 1, except for the following ten pairs: (23,32), (52,33), (25,62), (112,53), (37,133), (55,562), (1812,215), (433,2822), (463,3122), and (224342,555). [Redmond and Sun] The smallest palindromic prime resulting from the sum of three consecutive emirps (37, 71, 73). [Silva] The smallest prime which is a d-digit palindrome base 10 as well as a d-digit palindrome for some base b different from 10. [Post] Every natural number greater than 181 can be written as sum of cubes of the first two primes. [Capelle] 181 candidates were nominated for the Nobel Peace Prize the year Al Gore won it. [Francis] The smallest prime decimal Goedelization of a theorem from propositional calculus, symbolizing "A is logically equivalent to A." [Post] Only number n such that prime(n) = 6n + 1. [Firoozbakht] The sum of strobogrammatic numbers less than or equal to 181 equals 666. Can you find another strobogrammatic prime of the form (5n^2+5n+2)/2? [Honaker] "Cosmos: A Spacetime Odyssey" premiered in 181 countries. The smallest multidigit palindromic prime that is equal to the sum of the digits of 181^n for n = 16, 18, 19 and 20. [Gupta] There are at least 181 Las Bolas Grandes ('The Great Stone Balls' in Spanish) of Costa Rico that survive whole. [Lothrop] The complex vitamin B12 molecule contains a total of 181 atoms. [Newmark] List all the whole numbers less than 1000, that is 0 - 999. The number of whole numbers in the list containing the digit 0 is 181. [Green] 181 is a palindromic Pythagorean prime, equal to the sum of the squares of 10 and 9. [Green] Sri Lanka was ruled by 181 monarchs from the Anuradhapura to Kandy periods. 181 equals the sum of the squares of three consecutive composite digits: 6^2+8^2+9^2. [Silva] The number of days in a non-leap year from January 1 to June 30. [Gupta] The smallest prime that can be represented as sum of squares of successive composite numbers, in two ways, i.e., 6^2+8^2+9^2 and 9^2+10^2. [Loungrides] 1000 is the 181st positive integer that contains at least one pair of equal digits adjacent to each other. [Gaydos] The smallest palindromic prime expressed as 2n^2+2n+1. [Silva] Bobby Fischer was believed to have an I.Q. of 181. [Maven]

(There are 12 curios for this number that have not yet been approved by an editor.)