# 19

This number is a prime.

Intercalation in the Chinese Calendar is after the eighth
month every 19 years and is called *ren ba yue*
(Double August). According to tradition, tragedy will
follow when the month is added at that time. [Gevisier]

Egyptian biochemist Rashad Khalifa (1935-1990) claimed that he discovered an intricate numerical pattern in the text of the *Qur'an* involving the number 19. Sura 74:30 reads: "Over it are nineteen."

In his August 1941 Afterward to Thomas Wolfe's book *The Hills Beyond*, NY, Wolfe's editor, Edward C. Aswell, remarks that Thomas Wolfe's second book, never published, was to have been titled K19. When Wolfe died, Aswell watched the train carrying his coffin go by. Train K19! [Haga]

The smallest prime that is equal to the product of its digits plus the sum of its digits: 19 = (1 * 9) + (1 + 9). [Losnak]

The Bahá'í calendar, established in the middle of the 19th century, is based on cycles of 19 years. Years are composed of 19 months of 19 days each. [Dybwad]

(19 - 1) divides (19^{19} - 1) a prime number of times. [Wagstaff]

19 is the smallest prime p such that 10*p {+ 1, 3, 7, and 9} are all primes. [Das]

19 is the smallest prime *p* such that *p* and *p*^{2} have the same sum of digits.

The recurring decimal cycles for 1/19 to (19 - 1)/19 form a true magic square.

Blaise Pascal deduced 19 theorems related to his famous triangle.

1111 * 111^{11} + 111111111 + 1 (19 ones) is prime. [Fougeron]

A street in Rome named St. John's Lane is only 19 inches wide.

The first prime repfigit number. A repfigit (*rep*etitive *fi*bonacci-like di*git*) 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. For example, if the digits of 19 start a Fibonacci-like sequence, then 19 appears as a term: 1, 9, 10, 19. These are also known as Keith numbers. [Beedassy]

The number of trailing 0's in 80!.

Amendment 19 to the United States Constitution gave women the right to vote. [Filler]

19 European nations endorsed the first international ban on human cloning.

2^{1} + 3^{2} + 5^{3} + 7^{4} + 11^{5} + 13^{6} + 17^{7} + 19^{8} is prime.

*Product 19* is a multi-vitamin and mineral cereal of toasted corn, oats, wheat, and rice.

The Rhind papyrus contained a problem to find *x* so that *x* plus one seventh of *x* will equal 19.

An *idiot* is someone with an intelligence quotient (IQ) less than or equal to 19. [Brenner]

19 = 8 + 2 + 8 + 1, and its reversal equals the square root of 8281.

Pont du Gard aqueduct in southern France was built in 19 B.C. [Feather]

In golf, the clubhouse bar is referred to as the 19th Hole.

19^{5} + 19^{2} + 19^{1} + 19^{3} +
19^{5} + 19^{6} + 19^{4} + 19^{0} =
52135640. [De Geest]

A gene on Chromosome 19 has been linked to Alzheimer's disease.

In the game of Go, two players alternate in placing black and white stones on a large (19-by-19 line) ruled board, with the aim of surrounding territory.

Consider a chess endgame where a King plus Opposite-Colored Bishops (i.e., two Bishops each residing on opposite-colored squares) versus a King. The checkmate requires, at most, 19 moves (if the side with the bishops move first).

For *k* = 1, 2, 3, ... 19 at least one of the integers of the
form 6*k* + 1 or 6*k* - 1 is prime. [Crespi de Valldaura]

The smallest number of neutrons for which there is no stable isotope. [Hartley]

19 divides its following consecutive concatenated composite numbers (202122). [De Geest]

The largest prime on the Ishango bone. This tool (made from the fibula of a baboon) was found on the shore of Africa's Lake Edward and is believed to be at least 20000 years old. The numbers on one of its columns form a prime quadruple. It is now located on the 19th floor of the Royal Belgium Institute of Natural Sciences in Brussels.

For decades, mathematicians the world over would open their doors to find the homeless Paul Erdős (1913-1996) announcing, "My brain is open!" It is rumored that for 19 hours a day, seven days a week, stimulated by coffee, and later by amphetamines, he worked on mathematics. One of his greatest achievements was the discovery of an elementary proof for the prime number theorem.

If we pretend π = 60/19, then a radius of 57 gives a circumference of exactly 360. [Moody]

"The Sun" is numbered with 19 in Tarot cards.

The Metonic cycle, which involves the phase cycle of the Moon, is a period of about 19 Julian years. [Gevisier]

19 is the largest prime that can be expressed pandigitally in some base *b* > 1 (19 = 201 in base 3). [Keith]

(19^{19} - 2^{19})/(19 - 2) is prime. [Luhn]

Waring conjectured in 1770 that every positive integer can be expressed as a sum of at most 19 biquadrates (fourth powers). This was later proven by Balasubramanian, Deshouillers, and Dress.

Scores of people once died from the Anthrax bacterium following an accident at "Compound 19," a Soviet military facility in the city of Sverdlovsk (now called Yekaterinburg).

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). [Mander]

The smallest prime that yields another if its sum of digits is sandwiched between its digits. [Silva]

Flight 19 disappeared in the Bermuda Triangle. [Leonard]

The Statue of Liberty's torch shines through leaded glass, illuminated by 19 lamps. [Pitkin]

Osama bin Laden has 19 brothers. [NBC News]

In ancient Sweden the dates of the full moon were computed by runic calendar sticks (runstavar) with the full moon marked only at 19 fixed dates within each month. [Haga]

The composer Béla Bartók finished his Opus 19 in 1919, when he was 38 (twice 19) years old; the title in his native Hungarian (*A csodálatos mandarin*) has 19 letters. [Ace]

Steely Dan had a hit song called "Hey Nineteen."

A hoax chess machine nicknamed "the Turk" once sent Napoleon Bonaparte into a fury by beating him in 19 moves. [Hsu]

Inserting seventeen zeros between the two digits of 19 makes another prime of exactly 19 digits. Note that seventeen and 19 are twin primes. [De Geest]

The main building of the North Dakota State Capitol is a 19-story Art Deco skyscraper. It is the tallest building in North Dakota in terms of stories. [Bergane]

Hangeul (the Korean alphabet) has 19 consonants. [Poo Sung]

19 is the smallest prime whose reversal is composite. [Gupta]

The smallest prime using/ending with a composite digit. [Murthy]

The smallest number (coincidentally prime) with an additive persistence of 2. [Gupta]

The only prime that is equal to the difference of two prime cubes. [Gupta]

The decimal expansion of 19^{19} begins with the digits 19. This is not true for *p ^{p}*, where

*p*is any other prime less than 19,000,000,019. [Caldwell]

"19" is the term used to describe a worthless hand in the game of cribbage. [Cary]

The smallest invertible prime.

The Vice-President of the United States rates a 19-gun salute. [Dobb]

Sigmund Freud was 19 years older than Carl Jung.

(2^19-1)/(2-1) and (2^19+1)/(2+1) are both primes. [Dobb]

Earth's mass (5.9736 * 10^{24}) and volume (1.083*10^{12}) are both multiples of 19. Earth's volume is in fact a multiple of 19^{2}.

The first prime number presenting and 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 9. [ThaCoDa]

The speed limit (in miles per hour) on the private roads of the Cambourne development near Cambridge, England. [Croll]

The 19th Fibonacci number is the smallest F(P) which is composite where P is itself prime. [Rupinski]

The only number or prime for which there is no palindrome with a digit sum n and beginning with n. [Murthy]

If p, q, r, s are consecutive prime numbers such that p > q > r > s > 19, then floor((p * q)/(r * s)) = 1. [Capelle]

19 is the |1 - 9|th prime number. [Caldwell]

19 people had been hanged by the time the Salem witch hysteria died down in 1692. [La Haye]

19 is the smallest two-digit number such that 19^19+19-1 is prime. [Opao]

The sum of 19 consecutive Fibonacci numbers starting from the 19th Fibonacci number is prime. [Opao]

There are exactly 19 primes beginning with the digit 2 among primes smaller than one thousand. [Capelle]

The smallest prime formed from distinct non-prime digits. [Silva]

19^19 - 2 is prime. Note that it starts with the digits 19. [Patterson]

19^{2} = 361 and 3*6+1 = 19. [Madras]

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. [Litman]

The smallest two-digit prime with a prime ASCII code: 3139 (in base 16) = 12601. [Necula]

19 divides the concatenation of the integers from 19 down to 1. [De Geest]

Professor Barabási and his team have found that the World Wide Web on average has 19 clicks of separation between webpages. [McAlee]

Article 19 of the Universal Declaration of Human Rights: "Everyone has the right to the freedom of opinion and expression; this right includes freedom to hold opinions without interference and to seek, receive and impart information and ideas through any media and regardless of frontiers." [McAlee]

2^19 - 19 is prime. [Schlesinger]

The smallest prime p such that p^p is pandigital. [Patterson]

K-19 (nicknamed "Hiroshima") was a Soviet submarine equipped with nuclear ballistic missiles.

19 is the smallest super-2 number, i.e., an integer n such that 2n^2 contains 2 consecutive 2s in its decimal representation. [De Geest]

The largest value of n less than a thousand, such that 2^{n}+3^{n}+5^{n}+7^{n} is prime. [Opao]

19 is the smallest prime equal to the product of twin primes plus their arithmetic mean (3*5 + 4 = 19). [Teofilatto]

Paul Hardcastle had a hit song called "19." [Wolfe]

The second (and last) trip of the USS *Absaroka* across the Atlantic to European waters ended in New York in February 1919. On December 24, 1941, the Japanese submarine I-19 fired two torpedoes at that same ship, which was carrying a cargo of lumber, two miles off Pt. Fermin (San Pedro, California). The ship didn't sink but one sailor was killed by falling lumber. [Haga]

19 is the smallest prime of the form 3p + 2q, where p and q are twin primes. [Teofilatto]

19 is the smallest prime with a digital root of 1. [McAlee]

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). [Beedle]

19 is the only prime p less than 30 that does not divide 30, where p + 30 is composite. [Axoy]

19 is the only known number for which both (10^n-1)/9 and (10^n+1)/11 are primes.

19 + 18 + ... + 1 + 0 = 190. [Brand]

phi(19) - π(19) = 1 + 9. 19 is the only prime with this property. [Firoozbakht]

The sum of the first powers of 9 and 10 and the difference between the second powers of 9 and 10. [Gardner]

Football legend Johnny Unitas wore jersey number 19. [Hutchins]

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 (also prime). [McCranie]

Here is the mathematical code to determine if a number is divisible by 19. Multiply everything in front of the last digit by nine 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. [Young]

19 is the smallest prime mentioned a prime number of times in the KJV Bible. [Opao]

The smallest multidigit number (coincidentally prime) that does not form a palindrome when added to its reversal. [Capelle]

The only two-digit prime n such that n!/reversal(n)+1 and n!/reversal(n)-1 are both prime. [Patterson]

The prime rate published in The Wall Street Journal was 19.00 on October 5, 1981. This remains the highest prime-numbered prime rate since that time. [Goelz]

Not counting Panno's resignation (1. c4 resigns), Bobby Fischer won 19 consecutive games at the World Championship Interzonal tournament and Candidates matches in 1970-71. [McCranie]

The Fractran algorithm (John Horton 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, 2.

D. H. Lehmer's electromechanical number sieve used 19 bicycle chains. [Bell]

The first verse of the *Qur'an* (known as "Basmalah") consists of 19 Arabic letters. [Yuksel]

The following are primes: 19, 109, 1009, 10009. No other digit can replace the 9 and yield four primes. [This is the first entry listed as a "Prime Curio" in the book *NUMBERS: Fun & Facts* by J. Newton Friend; Charles Scribner's Sons, New York (1954); Library of Congress Catalog No. 54-8690, p. 45.]

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. [Capelle]

An unistable polyhedron is stable on only one face. The simplest such polyhedron known requires 19 faces. Whether unistability is possible with fewer faces is an unsolved problem. [McCranie]

The only prime of form p^3-q^3, where p, q are primes, i.e., 3^3-2^3. [Loungrides]

The first prime p such that p^2 is the reversal of a prime (163). [Silva]

19 terms are required in the Gregory-Leibniz series, i.e., 4(1 - 1/3 + 1/5 - 1/7 + 1/9 - ...), for the first appearance of "3.1" in the decimal expansion of π. [Honaker]

In chess positions with a king and pawn versus a king in which pawn promotion can be forced, at most 19 moves are required to promote the pawn (with best play by both sides). [McCranie]

The smallest prime which is the sum of two semiprimes in two different ways. [Post]

19^0 + 19^1 + ... + 19^18 (19 terms) is prime. [Caldwell]

The largest prime that is palindromic in Roman numerals alphabetically is XIX (19). [Beedassy]

The smallest titanic hexagonal-congruent prime has 19 ones on each of its six sides. Therefore each side of this hexagon is a repunit prime.

C19A became the largest iceberg in the world after the previous largest iceberg cracked into two different pieces. (It is the size of Brunei.) [Junie]

19 is the "age of
majority" adopted under federal jurisdiction in two US
states, *viz*., Nebraska, Alabama. [Beedassy]

"Let me tell you how it will be. There's one for you, 19 for me." Lyrics by George Harrison from the song "Taxman" by The Beatles. [Post]

The sum of all single-digit semiprimes. Insert two 0's between its digits and you will have the sum of the cubes of those semiprimes. [Silva]

The index *p* of the largest known Mersenne prime
*M*_{p} = 2^{p} - 1
having an associated perfect number
*M*_{p}*2^{p - 1} that
is short of a prime by 1. [Beedassy]

The only prime number p such that sod(p*reversal(p)) is p itself, where sod is sum of digits. [Kholdi]

19 = 1*5 + 3*3 + 5*1. [Poo Sung]

Charles Darwin produced 19 works: 15 books and 4 monographs. Ref: What Darwin Really Said, Benjamin Farrington, preface by Stephen Jay Gould, NY: Schocken, 1982, p.xvi. [Post]

19 is the smallest prime such that there exists a multiple having the same sum of digits as its digital root, e.g., 75 = 19 x 3; 7 + 5 = 12, 1 + 2 = 3, and 3 = 3. [Kholdi]

The largest natural number n for which the sum of digits is not smaller than n/2. [Capelle]

The number of topologically distinct planar configurations without discontinuities that are possible using six matches. [Beedassy]

Both numbers reversal(19! - 1) and reversal(19! + 1) are primes. 19 is the largest known prime with this property. [Firoozbakht]

The number of characters in *www.PrimeCurios.com* is prime. [Matheny]

19 is the only known prime of the form n^n - 8. The next prime in this form (if it exists) will have more than 34000 digits. [Firoozbakht]

The MathScience Innovation Center in Richmond, Virginia, is governed by a 19-member board consisting of a superintendent and school board member from each consortium division and several at-large members.

19 is the smallest prime which is the sum of three discrete composites (4 + 6 + 9). [Post]

Some positions (e.g., "superflip") on the original Rubik's Cube cannot be solved in 19 or less face turns.

Only known prime of the form p*prime(p)^p + 1, where p is prime. [Firoozbakht]

Each individual batch of Maker's Mark Whisky is less than 19 barrels. [Leonard]

The number of emirps that can be shown on a 12-hour digital clock. [Fellows]

There are 19 visible diamond patterns on the surface of a fully formed rhombic triacontahedron when structured using a series of phi-ratio pyramids. An example being Roger von Oech's Ball of Whacks. [Trace]

The last 19 digits of 17^18 is prime. [Gupta]

The number of letters in the anagrammatic title "A Superb Mosaic - Dare it !" that fittingly qualifies the "PRIME CURIOS DATABASE" with a poetic touch. [Beedassy]

Appears to be the largest of the set of primes that cannot be represented as the sum of four distinct primes {2,3,5,7,11,13,19}. [Post]

19 = sigma(1*9) + phi(1*9). It is the only known prime with this property. [Firoozbakht]

If the congruences proposed by Sierpinski are solved, a 19-digit number k is obtained as their smallest solution. [Slate]

The smallest prime that is the sum of first p-th primes. [Silva]

0nly the first 19 places of Mascheroni's calculation of Euler's constant were correct. [Post]

There are exactly 19 primes between 2^{5}-1 and 2^{7}-1. Is this the only example of *a prime number of primes* between two consecutive Mersenne primes?

The Longest Single Arch Steel Span Bridge in the Western Hemisphere is located northeast of Fayetteville, WV, on US Highway 19 across the New River Gorge.

(11, 13, 17, 19) is the first prime quadruple (p, q, r, s) such that s divides pqr+1. [Loungrides]

*NINETEEN: God's Signature in Nature and Scripture* by Edip Yuksel is described as a comprehensive demonstration of the prophetic miracle.

Pandigital palindromic primes start as 19-digit numbers. [Beedassy]

Thomas Jefferson argued that "Every constitution, then, and every law, naturally expires at the end of NINETEEN years. If it be enforced longer, it is an act of force, and not of right." Thomas Jefferson to James Madison, 1789. [Yuksel]

Gauss gave a sufficient condition for a regular n-gon to be constructible when he was only 19 years old. [Post]

There are 19 ways of expressing the smallest three-digit prime as the sum of three distinct two-digit primes. [Silva]

Take the nine pairs (a,b) with a+b=19; take the sum a*b+19 for all these nine pairs; ALL the sums are primes. 19 is the largest prime that will do this. [Bergot]

The only known prime p of form 4*q+7, where q and 4*p+7 are prime. [Loungrides]

The first prime of form (pqrs-1)/t where p, q, r, s, t are consecutive primes, case (2, 3, 5, 7, 11). Note that it is the only known prime of this form. [Loungrides]

10*n^2 + 19 produces 19 consecutive primes for n = 0 to 18. The digits of the 19th add up to 19. [Homewood]

There are 19 distinct-odd-digit emirp pairs. [Loungrides]

There are 19 ways to total 19 using 19 letters, e.g., ONE PLUS EIGHT PLUS TEN. [Homewood]

The only known prime p such that p raised to power p is a Cyclops number (19^19 = 1978419655660313589123979). [Pol]

"19th Nervous Breakdown" is a song written by Mick Jagger and Keith Richards . [Post]

The largest prime strobogrammatic palindromic number in its Roman numeral representation. [Post]

There are 19 Sophie Germain primes whose sums of reciprocals of digits equal one. The smallest is 86843 and the largest is 98689889. [Gaydos]

The are no twin primes between 19^2 and (19 + 1)^2. [Jung]

19 = 10011 in base two and 10011 is triangular in base ten.

The third term of the sequence where 2^2*3^3*...*a(n)^a(n) + 1 is prime, a(n) is prime, a(n)>a(n-1), and a(n) is minimal. [Honaker]

It is a 4-digit number: The tens are double the ones, the thousands are double the tens, and the sum of the digits is 19. What is the unknown number? [Booj]

5^19 is the smallest pandigital number of form p^q where p is a prime digit, i.e., 5^19=19073486328125. [Loungrides]

There are an estimated e*10^19 molecules in every cubic centimeter of of air. [Bannon]

19 authors going back to Nicodemus are reported to have made the claim that the perfect numbers had units digits that invariably alternated between 6 and 8, until Pierrot Cataldi exploded the number-theoretical myth. [Dickson]

sod(M15 exponent) = sod(M30 exponent) = sod(M31 exponent) = 19. [Harrison]

19 is the first invertible prime. [Pinto]

In the first million digits of π, the number 6859 occurs at position 910522 counting from the first digit after the decimal. If we sum the digits of the position number, i.e., 9+1+0+5+2+2, we get the prime number 19. If we take the cube root of 6859, we also get 19. [Mayers]

After the death of the Japanese emperor's century-year-old uncle there were 19 living members of the imperial family. [Merickel]

Consider a cake shaped as a circular disc. As many as 19 pieces of can result from 9 (or "one nine") slices. [Salinas-Calvo]

The binary representation of 10^19 contains 19 ones. [Gaydos]

There are 19 natural numbers less than one hundred that contain the digit 1. The same can be said for any digit (1 thru 9). [Green]

One tablespoon of ground cinnamon contains 19 calories. [Dr. Axe]

Mia Faith Honaker was born at exactly 8:19 p.m. (EST) in Bristol, Tennessee. The 8th prime number is 19.

Q: How many terms of the series 1 + 1/3 + 1/4 + ... + 1/11 + 1/13 + ... (which excludes all denominators containing 2) is required to produce a sum greater than 19? [Honaker]

19 is the two-digit solution (BE) to the alphametic (BE)^2 = MOB. [Madachy]

Sexual peak for *Homo sapiens
* is roughly at age 19.

Using the first three primes to get complex numbers 2+3*i and 3+5*i, multiply them to get the third number -9+19*i to be used as the three points (2,3), (3,5), and (-9,19) creating a triangle, which will have an area of 19, the same as the last y-value. [Bergot]

Consider i + j = 19 for 0 < i, j < 19 and i * j + 19 is prime for ALL cases: 1*18+19=37, 2*17+19=53, 3*16+19=67, 4*15+19=79, 5*14+19=89, 6*13+19=97, 7*12+19=103, 8*11+19=107, 9*10+19=109. This also works for 2 and 7. Can it work for a prime greater than 19? [Bergot]

There are 19 brilliant numbers with digits in strictly descending order. [Gaydos]

The smallest Lunar prime.

10/1 + 10/3 + 10/6 + ... + 10/171 + 10/190 = 19. Note that the denominators are the first 19 triangular numbers. [Petrov]

The first 19 superabundant and highly composite numbers are the same.

The smallest sum of three triangular integers equal to a prime: 19 = 3 + 6 + 10. [Rivera]

A "Black Moon" occurs once every 19 years. [Byrd]

19^19 begins with the digits 19. Can you find the next prime number like this? [Wallrodt]

The sum of the four 3-letter integers (one+two+six+ten). [Gaydos]

The only known prime formed from concatenation of first n Kaprekar numbers (case n=2). [Gupta]

The smallest prime whose reversal is not prime. [Silva]

19 squared can be written as the sum of three consecutive squared triangular numbers (6^2 + 10^2 + 15^2). [Bergot]

19 is the smallest prime with the property such that 19 divides reversal of 19-th prime. [Sariyar]

There are 19 national park service sites in Virginia. [Halstead]

The smallest Loeschian prime of form x^2+x*y+y^2, where x, y are successive primes, case (x=2, y=3), i.e., 2^2+2*3+3^2=19. [Loungrides]

The sequence of smallest odd prime numbers with exactly *n* circular loops begins 19, 83, 89, 809, 1889, 8089, ... . Circular loops occur in the digits 0, 6, 8, or 9 only. Note that the digit 8 contains two loops. [Mutter]

The official name for the disease initially dubbed the Wuhan coronavirus is Covid-19.

If you plot the seven points (2,3), (3,5), (5,7), (7,11), (11,13), (13,17), (17,19) and calculate the area within this irregular non-convex 7-gon, you will get exactly 19. [Rivera]

19 is the smallest prime containing a composite digit. [Silva]

John Paul Jones (sometimes referred to as the "Father of the American Navy") was found dead lying face-down on his bed in his third-floor Paris apartment, No. 19 Rue de Tournon. The cause of death was interstitial nephritis. [Sheridan]

The smallest prime number p whose fifth power is the sum of a positive square and cube: p^5 = x^2 + y^3, where x, y > 0. (Can you figure out the values for x and y?)

The "period 19 phenomena" ended up being a legitimate clue into the transposition scheme used in the Z340 cipher. Note that the first repeated symbol (a backwards "p") occurs at the 19th position.