# 29

This number is a prime.

The first time that a mean prime gap (average number of composites between successive primes) is a positive integer occurs at 29. [Honaker]

The last prime in the smallest set of five primes in arithmetic progression.

Floccinaucinihilipilification contains 29 letters and is the longest nontechnical word in the first edition of the Oxford English Dictionary. Note that the letter *e* does not occur.

If an odd perfect number exists, it must have at least 29 prime factors (not necessarily distinct).

29 is the smallest prime of the form 7*n* + 1.

The B-29 Superfortress was a long-range heavy bomber aircraft flown by the U.S. Military in World War II and the Korean War. [Haga]

29 = sqrt(6! + (6! + 6)/6). [Mensa]

The extra day in a leap year is February 29. [Barnhart]

The number of visible notches on the Lebombo bone. This mathematical object was found at Border Cave in the Lebombo mountains of South Africa and is believed to be at least 43000 years old. It resembles the calendar sticks still used today by the Bushmen of Namibia. [Joseph]

The Danish and Norwegian alphabet consists of 29 letters.

The smallest Gilda prime. Note that if a Fibonacci-like sequence is formed with the first term equal to the absolute value between the digits of 29 (i.e., 7) and the second term equal to the digit sum of 29 (i.e., 11) then 29 itself occurs as a term in the sequence: 7, 11, 18, 29. [Russo]

2*n*^{2} + 29 is prime for *n* = 0 to 28. [Legendre]

Bobby Fischer was 29 years old at the time of his 1972 World Chess Championship victory in Reykjavik, Iceland. Twenty-nine is the largest prime factor of 1972. Was this "Fischer's prime?" (Note that Bobby was born at Michael Reese Hospital, "twenty-nine twenty-nine" South Ellis Avenue in Chicago, Illinois.)

29 may be written in two ways as combinations of the first four primes and the three basic arithmetic operations: 29 = (2*7)+(3*5) = (5*7)-(2*3). [Rupinski]

The legendary Mississippi blues musician Robert Johnson (1911-1938) recorded only 29 songs. [McCranie]

Euclid's 29th Proposition (*Elements*, Book I) was the first one to use his parallel postulate. [McCranie]

Largest prime such that sum of its digits is greater than number of primes up to it. [Gupta]

The smallest multidigit prime whose product of digits of its cube is also a cube. [Russo]

2^{29} is the largest power of 2 whose digits are all distinct. [Wu]

29 is the second integer parameter n_{2} in Gilson's formula α(n_{1}, n_{2}) = n_{2}cos(π/n_{1})tan(π/(n_{1}n_{2}))/π for the value of the *fine structure constant* α = α(137, 29) = 0.0072973525318....

The great majority of the works by which the postimpressionist painter Vincent Van Gogh is remembered were produced in 29 months of frenzied activity and intermittent bouts with epileptoid seizures and profound despair that finally ended in suicide. [de la Faille]

The British warship HMS *Dreadnought* rammed and sank the German submarine *U-29*. [Haga]

For any 6469693230 consceutive integers, 36495360 will have 29 as a lowest prime factor. [Schuler]

The MiG-29 is a Russian fighter aircraft.

Twentynine Palms (or 29 Palms), California, is located approximately halfway between Los Angeles and Las Vegas and is considered by many to be a prime destination. [Jen]

The largest known prime p such that 5^{p} contains no pair of consecutive equal digits. [Russo]

The 29th Fibonacci number (514229) is a prime ending in 29. [Gupta]

The only non-titanic prime of form p^{p} + 2, where p is prime. [Wanless]

The highest possible score of a single hand in the card game cribbage is 29. [McGowan]

29 is the smallest overdue prime (p/log(p) - q/log(q) > 1, where q is the preceding prime). [Schimke]

The smallest multidigit prime which on adding its reverse gives a perfect square (i.e., 29 + 92 = 11^2). [Gupta]

The Oxyrhynchus papyrus containing a complete diagram (dated A.D. 75-125) from Euclid's *Elements* has a red 29 on it that was presumably written there by B. P. Grenfell or A. S. Hunt of Oxford University. The fragment is now in the storage vaults of the Penn Museum (University of Pennsylvania Museum of Archaeology and Anthropology).

7^{2} + 8^{2} + ... + 28^{2} + 29^{2} is a square. [Capelle]

3^{29} - 2^{29} is prime. [Capelle]

A prime is formed by using 29 twice in the *Firoozbakht function*, i.e., fi(29, 29).

The smallest prime equal to the sum of three consecutive squares: 2^{2} + 3^{2} + 4^{2}. [Schlesinger]

TWENTY NINE can be written out with exactly 29 toothpicks.

29 can be written as a sum of primes in exactly 3 * 29 ways. [Hartley]

29^23 + 19^17 + 13^11 + 7^5 + 3^2 is prime. [Patterson]

The middle chapter of the Old Testament is Job 29.

The smallest prime of the form 6n-1 = 7m+1. [Necula]

29 is only known number m such that both m!-R_{m} and m!+R_{m} are primes. I.e., 29! - 111...1 (29 ones) and 29! + 111...1 (29 ones) are both primes. [Firoozbakht]

29 is the maximum number of squares a chess bishop can visit if it is only allowed to visit each square once. (Here, "visit" means that squares passed over in a move are also visited.)

The largest natural number n for which the sum of digits is not smaller than n/3. [Capelle]

2^9 + 9^2 is prime. [Losnak]

29 = (2 * 9) + (2 + 9). [Teofilatto]

29 people were able to escape through "Tunnel 29."

Track 29 is the line on which the display locomotive "Chattanooga Choo Choo" now rests in Chattanooga, Tennessee. [McCranie]

29 = 2*5 + 3*3 + 5*2. [Poo Sung]

29 people lost their life when the SS *Edmund Fitzgerald* sank on Lake Superior (17 miles north-northwest of Whitefish Point, Michigan; November 10, 1975). [McCranie]

A proof of the infinitude of prime numbers is in
Book IX (Proposition 20) of Euclid's *Elements*. Note that IX +
20 = 29. [Joyce]

Bhargava and Hanke proved that if an integer valued
quadratic form (such as 3*x*^{2} + 2*xy*
+ 4*y*^{2}) can represent the numbers 29
numbers: 1, 2, 3, 5, 6, 7, 10, 13, 14, 15, 17, 19, 21, 22,
23, 26, 29, 30, 31, 34, 35, 37, 42, 58, 93, 110, 145, 203
and 290; then it can represent every positive integer. [Caldwell]

Mrs. Prime reads her recantation in Chapter 29 of the 19th century classic *Rachel Ray* by British novelist Anthony Trollope.

There are 29 suras of the *Qur'an* that are prefixed with certain letters of the Arabic alphabet (or Qur'anic Initials). [Yuksel]

Saturn requires over 29 years to orbit the Sun. [Papoiu]

The smallest prime formed by concatenation of a prime and a semiprime. [Silva]

The IBM 29 card punch was first sold in 1964. It continued to be sold for two full decades.

The only two-digit prime which is the sum of the digits of all previous two-digit primes. [Silva]

Gauss is reported to have said, "There have been only three epoch-making mathematicians: Archimedes, Newton, and Eisenstein." Why have so few heard of the latter? Perhaps because Ferdinand Gotthold Max Eisenstein died at the age of 29.

"KOI 29?" is the equivalent French acronym for "WU?" meaning "What's up ?" in chat language. [Beedassy]

The five-and-a-half century old nature-worshipping Indian Bishnoi (meaning "twenty-nine" in Indian language] sect is founded on 29 principles. [Beedassy]

The only two-digit prime whose square is the sum of the squares of two consecutive two-digit numbers: (20^2+21^2). [Silva]

The prime *p* for which the harmonic series of odd
primes (1/3 + 1/5 + 1/7 + 1/11 + ... + 1/*p*) first
exceeds unity. [Beedassy]

The maximal number of regions into which a circle can be divided by 7 lines. [Green]

A prime *p* is the length of the hypotenuse of a
Pythagorean triangle if (and only if) *p* =
4*n*+1. The first primes for which the area of these
right triangle are equal are 29 and 37. (The area is the
product of the first four primes.) [Caldwell]

The smallest prime whose sum of the digits and difference of the digits are primes. [Silva]

In the famous movie "Airport" (1970), a bomb-disabled airplane makes a dramatic landing in a snow storm on Runway 29. [Papoiu]

The next prime after 29 is the (2+9)th prime. [Silva]

The largest prime whose square (841) can be displayed on a 12-hour digital clock. [Fellows]

π(29) = phi(29) - 2*9. [Firoozbakht]

The number of times The Beatles pronounce "yeah" in their 1963 hit "She Loves You" (... yeah, yeah, yeah). [Papoiu]

The number of emirps that can be displayed on a 24-hour digital clock. [Fellows]

The membership of the Mathematical Association of America is divided into 29 regional sections. [Green]

29 is the smallest prime p such that sigma((p-1)/2)=sigma((p+1)/2). [Jevtic]

The smallest prime p such that when its digits are rendered in the base p, the result is prime. In this case 29 (base 29) = 67. [Green]

In the *ddmmyyyy* date format, there are 29 palindromic dates in 21st century, beginning: 10 February 2001 (10022001), 20 February 2002 (20022002), 1 February 2010 (01022010), 11 February 2011 (11022011), and 21 February 2012
(21022012). [Post]

There are 29 words in what Gauss wrote to Bessel on April 9, 1830: "we must in humility admit that if number is merely a product of our minds, space has a reality outside our minds whose laws we cannot a priori state." [Post]

Smallest prime number of different topologies (or quasi-orders or transitive digraphs) with n labeled elements (case n = 3). [Post]

All ZIP Codes in the state of South Carolina begin with the digits '29'. [Green]

The most meatballs eaten in one minute is 29 by Takeru Kobayashi (Japan) for Fuji TV in New York, USA, on March 8, 2010.

There were 29 boilers on the RMS *Titanic*. [Hill]

The smallest number whose digital root does not divide its sum of digits. [Beedassy]

The number of volumes in the eleventh edition of "The Encyclopaedia Britannica" (1910-1911). The phrase "prime curios" appears on page 182.

The only double-digit prime whose the reversal can be represented as the sum of the reversals of two consecutive primes, i.e., R(29)=R(61)+R(67). Note that three concatenations of the primes 29, 61, 67 are primes, i.e., 612967, 616729 and 676129. [Loungrides]

The smallest prime of form p*q+r*s where (p, q, r, s) is a set of four consecutive primes, i.e., (2*7+3*5). [Loungrides]

An estimated one in 29 Caucasian Americans have the Cystic fibrosis gene. [Tittle]

The number of letters in the full name of the mathematician
in whose honor was coined the hypothesis that still
underlies the current core problem in the theory of primes:
*Georg Friedrich Bernhard Riemann*. [Beedassy]

The number that came into that hostelry (Some nine and twenty in a company). From "The Canterbury Tales" by Geoffrey Chaucer. [Repasi]

29 is the 10th prime number and it is preceded by 10/2=5 composites. There is no other Nth prime number that is preceded by N/2 composites. [Redwasp]

The smallest prime that is the sum of the reversals of two double-digit primes, i.e, 31 + 61. [Loungrides]

Version 3 of the QR Code (Quick Response Code) uses a 29-by-29 array of black squares on a white background to encode messages. QR Codes are often scanned by smart phones for the purpose of linking to a website whose URL is encoded in the array of black and white squares. [Green]

29 is the only known prime of form n^n+2, where n is any integer greater than 1, (case n=3). [Loungrides]

If A = 1, B = 4, C = 1, ... , Z = 8, using the decimal digits of π, then 'LUNAR' is a lunar prime. [Homewood]

The Bishnois community follows 29 principles.

The largest prime in the first case of primes of form 6*n+5 where n is an integer, i.e., 5, 11, 17, 23, 29. Note also that 29 is the smallest prime p in the first case of primes such that 6*p+5 are also primes, i.e., for p: 29, 31, 37, 41, 43 we create the primes 179, 191, 227, 251, 263. We also notice that the reverse concatenation of these primes p, i.e., 4341373129 is also prime. [Loungrides]

There are 29 total syllables in the names of the twelve months of the year. [Gaydos]

2^9+29 is the largest prime p of form a^b+ab, where ab is a double-digit prime, (p=541). [Loungrides]

Smallest odd prime p such that (2^p+1)/3 is composite. [Luen]

The only known non-titanic prime of form p=2^x+5^x, where x is prime, (case x=2). [Loungrides]

The largest prime p such that the product of first p odd numbers plus 2 is a non-titanic prime, i.e., 1*3*5*7*...*55*57+2. [Loungrides]

In the dd-mm-yyyy format, there are 29 Palindrome Days in the current century. (The last is 29-02-2092, a leap day!) [Inan]

The number of different quartets of 9-digit bemirps. [Cami]

29 PRIME, Inc., specializes in increasing businesses' visibility on the Internet.

The overall permissible length of a tennis racket is 29 inches. [Gupta]

29 is one more than a perfect number and one less than a primorial and a prime at the same time. [Hollesen]

29 percent of smokers in England say they want to quit, according to Prime Theory.

29 is the sum of digits of all non-trivial primes prior to 29. [Silva]

29 = (2*7) + (3*5), i.e., the first n primes placed in product pairs whereas the first factors are increasing and the second factors are decreasing, then added together. Can you find the next prime with this property? [Bergot]

Kurt Gödel weighed only 29 kilograms when he died.

The reversal of 29 is divisible by the preceding prime (23). [Bergot]

The sum of the first 29 semiprimes is divisible by 29 (1247/29=43 which is also a prime). [Gaydos]

The number of different 9-digit bemirp quartets. [Cami]

29 (exactly half) of the first 58 powers of two are zeroless numbers. [Gaydos]

29 is the smallest prime p such that 2p+1 divides 2^p+1. [Tattersall]

Prime formed with the only 1 even prime digit and the only 1 odd composite digit. Curiously, the sum of it´s digits is 11. [Silva]

29 + 2*Hn (where Hn stands for the n-th centered hexagonal number) yields 30 primes for n = 0 to 29. Recall that 29 + 2*n^2 (i.e., twice the n-th square number) yields 29 primes for n = 0 to 28. [Petrov]

The smallest Democratic prime. [Hilliard]

The smallest prime which yields another when sandwiched between the sum of its digits: 1291. [Silva]

"Big A Mountain" ranks #29 in Virginia peaks with one thousand feet of prominence. [Peakbagger]

The street grid for most of Manhattan is rotated approximately 29° clockwise from true east-west. [Petzold]

The first prime *p* of a twin-prime pair (*p*,
*q*) such that exactly *p* prime digits are used
in writing out the first *q* primes. [Beedassy]

The first 29 prime numbers all have different Collatz trajectory lengths. [Gaydos]

29! is the smallest factorial with no unique digits. Each digit that it has appears at least twice. [Gaydos]

Two researchers at the Ohio Supercomputing Center solved every position of the Rubik's Cube™ in the quarter-turn metric. It required about 29 CPU-years of idle computer time.

The first 29 primes have single-digit gaps following them. Can you find the next longer run? [Honaker]

"To LONDON 29 Miles" is on the Little Market House in Wycombe. [Croll]

There are 29 named ancient Buddhas.

There are 29 distinct-odd digit primes each consisting of all the odd digits. These primes are: 13597, 13759, 15739, 15937, 15973, 17359, 17539, 19753, 39157, 51973, 53197, 53719, 53917, 57139, 57193, 71359, 71593, 73951, 75193, 75391, 75913, 75931, 79153, 79531, 91573, 91753, 95317, 95713, 95731. [Loungrides]

The smallest prime number not appearing in a minimal magic die puzzle solution. [Matney]

29 divides the concatenations of natural numbers up to 31. Is there a larger twin prime pair like {29, 31} with this property? [Sariyar]

29 is the smallest positive whole number that cannot be made from the positive integers {1, 2, 3, 4}, using each exactly once with only the operations of addition, subtraction, multiplication and division permitted. [Fuqua]

Meteor Crater (or Barringer Crater) is a meteorite impact crater about 29 kilometers west of Winslow in the desert of northern Arizona, United States. [Hooper]

There are 29 letters in this sentence. [Nie]

In the World of Harry Potter, there are 29 Knuts in a Sickle. [Homewood]

The website "PrimePages" was maintained by Chris Caldwell at the University of Tennessee-Martin for 29 years.