# 173

This number is a prime. 173 is a prime of the form F(i)2 + F(j)2, where F(n) are Fibonacci numbers. [Russo] There are 173 stars included in the list near the back of the Nautical Almanac, an annual publication of the U.S. Naval Observatory. 173 * 10173 + (10173 - 1) is prime. [Luhn] The second prime formed from the first n consecutive digits in the decimal expansion of the square root of 3 (n=3). [Haga] 2^2 + 13^2 = 173, which is prime. [La Haye] The leading 3 digits in the decimal expansion of sqrt(3) is prime. [Carmody] The destroyer escort USS Eldridge (DE-173) is made invisible and teleported from Philadelphia, Pennsylvania, to Norfolk, Virginia, in an alleged 1943 incident known as the Philadelphia Experiment. [Moore] 173 is a curious prime which occurs twice in the properties of the curious prime 30103, as found by Jud McCranie and G. L. Honaker, Jr., in July 1998. 30103 is the only known multidigit palindromic prime found by averaging the divisors of a composite number: 30103 = (1 + 5 + 173 + 865 + 29929 + 149645)/6 and 30103 = (1 + 2 + 3 + 6 + 173 + 346 + 519 + 1038 + 29929 + 59858 + 89787 + 179574)/12. 30103 = average of divisors of 149645 and 30103 = average of divisors of 179574. [Post] The smallest prime inconsummate number, i.e., no number is 173 times the sum of its digits. [Conway] The smallest odd prime p to yield a palindromic prime in the form p^2+(p+1). [Silva] 173 = 1 + 2^2 + 2^3 + 2^5 + 2^7. The exponents are consecutive primes. [Noe] The Beast is said to have eaten 173 guys in the movie The Sandlot. The "beast" (in this case) is a ferocious dog. Vampire Bill Compton of the True Blood mythology is 173-years-old and can live among humans thanks to the invention of synthetic blood. Largest known prime whose square (i.e., 29929) and cube (i.e., 5177717) consist of different digits. [Gupta] Smallest odd prime to be the number of n-crossing knots having symmetry group Z1, namely with 11 crossings, also an odd prime. [Post] Concatenation of the numbers 1 through 173, left to right, is prime in both bases 3 and 6. [Merickel] The only prime whose sum of cubed digits equals its reversal: 13 + 73 + 33 = 371. [Beedassy] 173 divides 179*181*191+1. Are there four larger consecutive primes p < q < r < s such that p|qrs + 1? [Loungrides] The first 3-digit prime that is the last prime in a set of five primes in arithmetic progression, i.e., 173, 131, 89, 47, 5. [Loungrides] The smallest prime that is the reverse of (a^b+c^d), where a, b, c, d are the prime digits, i.e., 173=R(2^7+3^5). [Loungrides] When the sun goes down on the moon, temperatures can dip to minus 173 degrees Celsius. [Wells] There are in all 173 distinct configurations on a Euclidean plane for the arrangement of 4 circles, not necessarily all identical, not allowing osculations nor three or more common intersection points. [Note configuration here means circle-drawable, not just topologically distinct] [Beedassy] 173 and 179 are the smallest pair of consecutive primes that have the same Collatz trajectory length (31). [Gaydos] There are 173 prime days in composite months added to the number of composite days in prime months in both leap years and non leap years. [Homewood]

(There are 4 curios for this number that have not yet been approved by an editor.)