# 193

This number is a prime.

The smallest Francesca-Carlotta prime, i.e., if a Fibonacci-like sequence
is formed with the first term equal to the number of digits in *n* and the second
term equal to the sum of the decimal digits in *n*, then *n* itself occurs as a term in the
sequence after the first two terms. [Russo]

193 * 10^{70} + 1 has only 2 prime factors. [Brown]

The only odd prime *p* known for which 2 is not a primitive
root of 4p^2 + 1.

The smallest prime whose reversal is a Smith number. [Loungrides]

The square of 193 (37249) concatenated with its reverse (which is a prime) results in a palindrome that is the product of 2 palindromes, one non-prime (1001) and one prime (3721273). [Trotter]

The longest decisive game of chess (as of 1980) was played between Stepak and Masian in Israel, and lasted a whopping 193 moves! [Patterson]

The smallest prime whose fifth power contains all digits from 1 to 9 (zeroless pandigital). [Gupta]

193/71 is the closest ratio of two primes less than 2000 to the number *e*.

193 can be formed from the sum of products of the first three twin primes pairs: 3*5 + 5*7 + 11*13 = 193 is prime. [Post]

193 can be written as the difference between the product and the sum of the first four primes. [Poo Sung]

The unique nontrivial Magic Hexagon is one with 19 cells and order (or side) 3. Note that 19 and 3 are two primes that concatenate to form 193. [Beedassy]

"There are 193 species of monkeys and apes, 192 of them are covered with hair." Desmond Morris, British zoologist and ethologist

A woman in Texas was convicted of murder in March 2004 for stabbing her husband 193 times.

The smallest prime which is one more than the product of three distinct composite numbers. [Porter]

The largest prime that is the sum of the reversals of two double-digit primes (i.e., 59 and 89). [Loungrides]

193 = 2*3*5*7 - (2+3+5+7), i.e., the product of the first four primes minus the sum of the first four primes. [Alves]

The only non-titanic prime of form 97^n-96^n, where n is an integer. [Loungrides]

The sum of all composite numbers in the twenties. [Homewood]

Starting with 2 at the top, there should be a palindromic prime pyramid of step size three of height around 193 (ending with a titanic prime), but to find the tallest such pyramid by exhaustive search would require checking about 10^30 different possibilities!

Australian professional tennis player Nick Kyrgios is officially 193 centimeters tall. (Prime Kyrgios?)

p_{44}# has average digit exactly 4 and is the
largest primorial with such a whole number average. [Merickel]

If A=1, B=2, … Z=26, then the expression "Sum of digits of this number is a prime" is true: SOD(19211315060409070920191506200809191421130205180919011618091305=193). [Sariyar]

If A=1, B=2, C=3, ..., Z=26, then 'PILLAI PRIME NUMBER' is a Pillai prime number. [Homewood]

The Knights Templar existed for 193 years. [Homewood]

There are 193 prime days in prime months added to the number of composite days in composite months in a leap year. [Homewood]

193 is the smallest prime number that appears in the square of its prime index (44^2 = 1936). The next such prime is 3112771 for which 224346^2 = 50331127716. [Gaydos]

If A = 1, B = 2, C = 3, ..., Z = 26, then 'PIERPONT PRIMES' is a Pierpont prime. [Homewood]

193 is the smallest prime p where p^(digit-sum of p) terminates in the digits of p and the last digit of p is the digit-length of p. [Worrom]