# 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 *x*^{2} = 2^{(3 * 5)} - 7.

181 * 10^{181} + (10^{181} - 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 = 9^{2} + 10^{2}, 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
*x ^{a}* and

*y*for all integers

^{b}*x*,

*y*,

*a*,

*b*> 1, except for the following ten pairs: (2

^{3},3

^{2}), (5

^{2},3

^{3}), (2

^{5},6

^{2}), (11

^{2},5

^{3}), (3

^{7},13

^{3}), (5

^{5},56

^{2}), (

**181**

^{2},2

^{15}), (43

^{3},282

^{2}), (46

^{3},312

^{2}), and (22434

^{2},55

^{5}). [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) = 6*n* + 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]

Martha Graham created 181 ballets. [Baumgardner]

The palindromic ZIP Code of Andover MA is 181 with a zero on each end. [Schvanger]

Is 181 the only prime palindromic prime that produces another when added to its sum of digits? [Gaydos]