- The recurring decimal cycles for 1/19 to (19 - 1)/19 form a true magic square.
- The R-value of standard attic ceiling is 19.
- Blaise Pascal deduced 19 theorems related to his famous triangle.
- 1111 x 11111 + 111111111 + 1 (19 ones) is a prime.
- The first prime Keith number. A Keith number is an n-digit integer N with the following property: If a Fibonacci-like sequence (in which each term in the sequence is the sum of the n previous terms) is formed, with the first n terms being the decimal digits of the number N, then N itself occurs as a term in the sequence. E.g., if the digits of 19 start a Fibonacci-like sequence, then 19 appears as a term (1, 9, 10, 19). Originally called rep- digit (repetitive Fibonacci-like digit) numbers.
- 21 + 32 + 53 + 74 + 115 + 136 + 177 + 198 is a prime.
- The Rhind Papyrus contained a problem to find x so that x plus one seventh of it will equal the prime number 19.
- The smallest prime that is equal to the product of its digits plus the sum of its digits.
- 19 = 8 + 2 + 8 + 1, and its reversal equals the square root of 8281. - 19 = 4! - 3! + 2! - 1!.
19 – The Secret Code of God Page 109 - For k = 1, 2, 3…...19 at least one of the integers of the form 6k + 1 or 6k - 1 is prime.
- The half-life of oxygen-19 is only 19 seconds.
- 19 divide its following consecutive concatenated composite numbers (202122).
- 19 is the largest prime that can be expressed pan digitally in some base b > 1 (19 = 201 in base 3).
- (1919 - 219)/ (19 - 2) is prime.
- Warring conjectured in 1770 that every positive integer can be expressed as a sum of 19 biquadrates (fourth powers). This was later proven by Bal Subramanian, Deshouillers, and Dress. - 19 times its reversal is the famous Hardy-Ramanujan number.
- 19 is the smallest prime which is the sum of three discrete primes (3 + 5 + 11).
- 19 is the first prime resulting from the sum of cubes of distinct fractions using only primes, i.e., 19 = (5/2)3 + (3/2)3.
- Inserting seventeen zeros between the two digits of 19 makes another prime of exactly 19 digits. Note that seventeen and 19 are twin primes.
1000000000000000009………Prime Number with 17- Zero’s in between 1 and 9.
- String of the first ten odd integers, from 1 up to 19, is a prime (135791113151719).
- 19 is the smallest prime whose reversal is composite.
- The smallest prime using/ending in a composite digit.
- The smallest number, coincidentally prime with an additive persistence of 2.
- The only prime which is equal to the difference of two prime cubes.
- The decimal expansion of 1919 begins with the digits 19. This is not true for pp, where p is any
other prime less than 10000019.
- The smallest invertible prime.
- (2^19-1)/ (2-1) and (2^19+1)/(2+1) are both primes.
- The first prime number presenting & meaning the same value within the "Western" world and the "Arabic" is the number 19. All other recognizable prime numbers are with the combination of a 1 and a 9.
19 – The Secret Code of God Page 110 - The 19th Fibonacci number is the smallest F(P) which is composite where P is itself prime. - The only number or prime for which there is no palindrome with a digit sum n and beginning with n.
- 19 is the |1 - 9|th prime number.
- 19 is the smallest two-digit number such that 19^19+19-1 is prime.
- The sum of 19 consecutive Fibonacci numbers starting from the 19th Fibonacci number is a prime.
- There are exactly 19 primes beginning with the digit 2 among primes smaller than one thousand.
- 19^19 - 2 is prime. It starts with the digits 19.
- 192 = 361 and (3 x 6) +1 = 19.
- 19 is the largest prime factor of 1444 - the smallest perfect square to end in three 4's. Note that 4 is the only non-zero digit that can repeat at the end of a perfect square, and the most consecutive 4's that can appear in such a place is three.
- The smallest two-digit prime with a prime ASCII code: 3139 (in base 16) = 12601. - 19^19 + 19 - 1 is prime (with prime digital sum). It starts with the digits 19.
- 19 divide the concatenation of the integers from 19 down to 1.
- 2^19 - 19 is prime.
- The smallest prime p such that p^p is pan digital.
- 19 is the smallest super-2 number (curiously prime), i.e., an integer n such that 2n^2 contains 2 consecutive 2s in its decimal representation.
- The largest value of n less than a thousand, such that 2n+3n+5n+7n is prime.
- 19 is the smallest prime equal to the product of Twin primes plus their arithmetic mean (3 x 5 + 4 = 19).
- 19 is only number m such that length (m^prime(m)) = m + prime(m).
- 19 is the smallest prime of the form 3p + 2q, where p and q are Twin primes.
19 – The Secret Code of God Page 111 - Any number that is divisible by 19 will have this property: multiply the last digit by 2, then add that number to the remaining digits and the resulting number will be divisible by 19. E.g., 625632 is divisible by 19 because all of following results are divisible by 19:(62563 + 4 = 62567); (6256 + 14 = 6270); (627 + 0 = 627); (62 + 14 = 76); (7 + 12 = 19); (1 + 18 = 19). - 19 is the only prime p less than 30 that does not divide 30, where p + 30 is composite.
- 19^(9+1) - (9-1) is a prime with prime digits.
- 19 + 18 + ... + 1 + 0 = 190.
- phi(19) - (19) = 1 + 9. 19 is the only prime with this property.
- Consider a square made of four rigid rods, hinged at the ends. How many rods of the same type must be added to make the square rigid in the plane? The answer is 19, which makes a total of 23 rods which is also a prime.
- Here is the mathematical code to determine if a number is divisible by 19. Multiply everything in front of the last digit by Nine - 9 and subtract the last digit. If you get zero, nineteen, or a multiple of nineteen, the number will be divisible by 19. For example 57. Five times nine minus seven equals 38. Since 19 divides evenly into 38, it divides evenly into 57. Next example 114. Eleven times nine minus four equals 95. Since 19 divides evenly into 95, it divides evenly into 114.
- 19 is the smallest prime mentioned 6 times in the Bible (KJV). - A gene on Chromosome 19 has been linked to Alzheimer's disease.
- The smallest multi-digit number, coincidentally prime that does not form a palindrome when added to its reversal.
- The only two-digit prime n such that n!/reversal(n)+1 and n!/reversal(n)-1 are both prime. - Not counting Panno's resignation (1. c4 resigns), Bobby Fischer won 19 consecutive games at the World Championship Inter-zonal tournament and Candidates matches in 1970-71.
- The Fractran algorithm (Conway's prime-producing machine) is an interesting but terribly inefficient way to generate prime numbers. It requires 19 steps to compute the first prime. - D. H. Lehmer's electromechanical number sieve used 19 bicycle chains.
- The following are primes: 19, 109, 1009, 10009. No other digit can replace the 9 and yield four primes. [Source: NUMBERS: Fun & Facts by J. Newton Friend; Charles Scribner's Sons, New York (1954); Library of Congress Catalog No. 54-8690, p. 45]
19 – The Secret Code of God Page 112 - Farideh Firoozbakht improved the Papadimitriou's conjecture and proposed that every prime number p greater than or equal to 19 can be written as p = 2q + 3r, where q and r are odd primes. - An unstable polyhedron is stable on only one face. The simplest such polyhedron known requires 19 faces and was discovered by Richard Guy. None with fewer faces have been found. - Number – 67 is the 19th Prime number.
- The first prime p such that p^2 is the reversal of a prime (163).
- 19 is the only known number for which both (10^n-1)/9 and (10^n+1)/11 are primes.
- Professor Barabasi and his team have found that the World Wide Web on average has 19 clicks of separation between web pages.
(Source:http://primes.utm.edu/curios/page.php/19.html)