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181 (another Prime Pages' Curiosity) |
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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 x 5) - 7. 181 x 10181 + (10181 - 1) is prime. [Luhn] The sum of the first 181 primes minus 181 is prime. [Gevisier] 181, a pal-prime, is the sum of the digits of the first 23 primes (2, ..., 83). [Trotter] The 181-digit palindromic number made up of all 7s except for the center nut being 181 (7777...7718177...77777) is a palindromic prime with a palindromic prime decimal length. [Fougeron] The first occurence 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 of 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 in a set of so-called "Gridgeman pairs." A Gridgeman pair is two palindromic primes, which differ only in that their central digits are x and x + 1 respectively. 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]
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