# 43

This number is a prime.  London was founded as the Roman town of Londinium in A.D. 43. The (4*3)th lucky number. [Post] 43 reversed (34) is a Fibonacci number. The first 43 digits of 43! form a prime number. A frown uses 43 muscles. :-( 43 women survived at the Battle of Dannoura, yet the entire Heike battle fleet was destroyed. This occurred at the Japanese Inland Sea in April of 1185. The British mathematician and logician Augustus De Morgan was always interested in odd numerical facts and once noted that he had the distinction of being x years old in the year x^2. He was 43 in 1849. [Poo Sung] There exist three different two-digit prime numbers such that the average of all three is 43 and the average of any two is also prime. [Sole and Marshall] Planck time (~ 10-43 seconds) is the smallest measurement of time within the framework of classical mechanics. The smallest possible magic sum if you number the pips (dots) on an ordinary six-sided die with distinct positive integers such that the numbers on each face add up to the same magic constant. Can you find different sets of numbers for this puzzle that add to 43? What is the minimum number of guests that must be invited to a party so that there are either five mutual acquaintances, or five that are mutual strangers? At least 43, but the exact number is not yet known. The solutions to this type of problem are known as Ramsey numbers, named for British mathematician Frank P. Ramsey (1903-1930). The binary digits extracted from the decimal expansion of π truncated to 43 places and converted to base ten gives the 13-digit prime 7568622343067. [De Geest] In the days before the proliferation of area codes in the 1990's, there were two adjacent area codes that were multiples of 43: Pennsylvania's 215 (5 * 43) and Maryland's 301 (7 * 43). [Litman] Licor 43, also known as "Cuarenta Y Tres" (meaning 43 in Spanish), is a liqueur that has been made in Spain for over 1800 years, dating back to the time of the Carthaginians. It is a bright yellow color and derives its name from the fact that it is supposedly a mixture of 43 different ingredients. The smallest nontrivial y for which the Pellian x2 - 1847*y2 = 1 is soluble. Note that 1847 is also prime. [Beedassy] 43 is the smallest prime that is not the sum of two palindromes. [Russo] George Parker Bidder (1806-1878), an English calculating prodigy, could instantly recite a 43-digit number after it had been read to him backwards.

```       43
4483
444883
44448883
4444488883
are 5 primes
``` According to Benford's Law, the odds that a random prime begins with a prime digit is more than 43% (the odds are about 43.82%). [Rupinski] The smallest non-palindromic prime which on subtracting its reverse gives a perfect square (i.e., 43 - 34 = 3^2). [Gupta] The Antikythera mechanism (described as the first known mechanical computer) was found in less than 43 meters of water. [Russell] 43 is the smallest prime whose index (14) is divisible by the sum of its digits (4+3). [Murthy] The world's oldest known captive goldfish, Tish, died peacefully at home in his tank at the age of at least 43 in 1999. [Patterson] NASCAR races begin with 43 cars and drivers. [Dobb] Leonard Owen Johnson Associates reported in 2001 that tobacco smoke contains at least 43 chemicals that are known carcinogens. Ostriches can sprint in short bursts up to 43 miles per hour. The number of Carmichael numbers of six or fewer digits. [Patterson] DSS-43 is a large steerable parabolic antenna in Tidbinbilla, Australia, which is a tidbit of trivia. [Patterson] 43 appears in the title of the historical British comedy show Hancock's Forty-Three Minutes. It is possible to form three sums of primes with the prime value of 43 using the ten first primes: 2+5+7+29 = 3+17+23 = 11+13+19 = 43. [Gallardo] Barbie and Ken, the most popular fashion dolls in the world, broke up after 43 years. This was probably due to Ken's reluctance to get married. [Cross] The first flight test of NASA's X-43A prototype was a failure. 43^43 + 4 is prime. 43 is the smallest (and perhaps only) prime p such that p^p + (largest digit of p) is also prime. [Earls] For any 13082761331670030 consecutive integers, exactly 44144787456000 have the number 43 for a lowest prime factor. [Schuler] It was 43 seconds after "Little Boy" was released from Enola Gay that the mechanisms aboard the first nuclear weapon gave the signal to detonate over Hiroshima on August 6, 1945. 437 = 271818611107 = (2 + 7 + 1 + 8 + 1 + 8 + 6 + 1 + 1 + 1 + 0 + 7)7. [Madachy] 43 = 4*prime(4) + 3*prime(3). Note that 43 is the earliest number with this property. There are only two such numbers and both are primes. [Firoozbakht] The smallest prime formed from reverse concatenation of two consecutive numbers. [Gupta] 43 never becomes a palindrome by the reverse-and-add process if converted to base two. 43 is the fourth Centered Heptagonal (7-gonal) Number. Note that 4 + 3 = 7. [Post] Technetium (atomic number 43) is a crystalline metallic element and the first to be produced artificially. The 14th prime number. Note that the previous prime (41) is the reversal of 14. 437/23 = 3.1415.... [Plouffe] 4^4 - 3^3 is a prime with length π(π(π(43))). Note there is only one prime (43) and one composite number with this property. [Firoozbakht] The 43-meter telescope at the National Radio Astronomy Observatory (NRAO) in Green Bank, West Virginia, contains the largest equatorial mount ever built to date. The first time a twin's age in days, weeks, months and years can all be twin primes is when they (and their sibling) are 43 years old. Then, when they are 15887 days old, they are also 2269 weeks, or 521 months old. Note that some unfortunate twins were born in January, February, September or November. For these twins, after 15887 days they are 522 months old. They must wait until after their 1021st birthday before their ages in years, months, weeks and days are all twin primes. [Hartley] Richard Petty's race car was always numbered 43. The German-born Jewish mathematician Emmy Noether (1882-1935) published 43 research papers. Albert Einstein eulogized her in a letter that appeared in the New York Times on May 5, 1935, where he is quoted as saying, "In the judgment of the most competent living mathematicians, Fräulein Noether was the most significant creative mathematical genius thus far produced since the higher education of women began." [Wheeler] The only known prime number which cannot be expressed as 2a^2 + 3b^2 + 5c^2. [Underwood] The smallest prime that is not a Chen prime. [Lopez] John F. Kennedy became the youngest man elected President of the United States at the age of 43. [Pritesh] The sum of digits of 43^(4+3) is 43. [Silva] The angle of elevation in the hit song "Mathmaticious" by Drew D'Amelia. In November 2007, Navy ended a 43-game losing streak to Notre Dame. This was the longest such streak in the history of College Football. [Cuenta] The blog "Interstate Forty-Three" is dedicated to the number 43. A leaf beetle (Donacia) can pull 43 times its own weight. Fields medalist Alexander Grothendieck (1928-2014) was highly regarded as one of the most influential mathematicians of modern times. The subject of many stories and rumors, he withdrew from mathematics just before turning 43 years of age and avoided virtually all human contact. The number 'forty-three' is the smallest prime not mentioned in the KJV Bible text. In addition to all primes less than 43, we have the following: 61, 67, 83, 127, 137, 139, 223, 601, 743, and 22273. Are there others? The number of distinct heptiamonds (i.e., triangular polyominoes with 7 cells), counted with reflections but not turning over. [Beedassy] 43 of the 3-digit numbers are either emirps or palindromic primes. [Hines] Although Barack H. Obama said in his Inauguration Address: "Forty-four Americans have now taken the presidential oath," the number is actually 43, as Stephen Grover Cleveland was both the twenty-second and twenty-fourth President of the United States. [Post] The number of bathrooms in Biltmore House. [Dowdy] The only prime of the form p^4 + q^3, where p and q are consecutive primes. [Silva] There are 43 verses in the Old English epic poem Beowulf. [Wagler] The smallest nonintegral term in Göbel's sequence is a(43). 43 = 4^2 + 3^3. [Meller] The smallest prime (emirp) with additional digit "a" in representation for decimal 10 in base 11 number system. E.g., prime(2 * 7) = 3 * 11 + 2 * 5 = (3a)11. Note the first six primes. [Herault] The largest natural number n such that the sum of the digits of n2 is not smaller than n/2. [Capelle] The Frobenius number of the set {6, 9, 20}. Chicken McNuggets were once only available in lots of 6, 9, and 20. Therefore, 43 was the largest number of McNuggets you couldn't buy at that time! The largest known natural number n for which the decimal expansion of 4n does not contain any zero. [Capelle] Quisp, a 1960's alien from the planet "Q," weighs in at 43 pounds. Can you see the three consecutive primes in 43=4*7+5*3? [Silva] The largest prime "p" root vector parameter of any of the 99 subgroups of E_8 found by Mathematica computation of M.K. Ahsan and T. Hubsch, namely the subgroup SO_14 X SU_2. [Post] Smallest multidigit prime p such that the pth prime is palindromic. [Gupta] Largest known prime partial sum of number of positive knots with n crossings: 0 + 0 + 1 + 0 + 1 + 0 + 1 + 1 + 1 + 3 + 2 + 7 + 9 + 17 = 43. [Post] The number of Fibonacci primes less than a million. [Green] The Fifteen Puzzle can be solved in 43 moves using "multi-tile metric." [Norskog] Smallest prime partial sum of tricapped prism numbers. [Post] The number of syllables in the official name of the capital of Thailand. [Merickel] The largest prime less than a thousand which remains prime when 4 is added to any of its digits, i.e., 47, 83. Note that the concatenation of these new primes, 47, 83, i.e., 4783 is also prime. Furthermore, the concatenation in order of the first prime, 43, and the new primes, 47, 83 is also prime, i.e., 434783. [Loungrides] Max Yasgur's dairy farm in Bethel, New York, is 43 miles southwest of Woodstock. The first chorus from the Wurzels hit record The Combine Harvester (Brand New Key) includes 'I got twenty acres and you got 43.' [Snooks] 43 pairs of nerves make up the peripheral nervous system. [Pearson] The first 43 digits after the decimal point in the square root of 43 form a prime number. [Gaydos] The only prime number mentioned by Figaro at the opening of Mozart's "The Marriage of Figaro" as he measures the bedroom for him and Suzanna. [Bodine] The first known use of the word "curio" was back in 43 squared. The area of an isosceles triangle that has a prime perimeter of 43 with sides 5-19-19 is very close to the next prime after 43. [Bergot] Historically, over 43% of PRIMES alumni go to MIT. Onychophora (commonly known as velvet worms) can have up to 43 pairs of legs. [Attenborough] There are 43 proven Wagstaff primes. [Homewood] The only double-digit prime p such that (p!/(R(p))-1 is prime, i.e., (43!/34!)-1 = 204636013545599. [Patterson and Loungrides] The Ka'bah Shrine in Mecca has a max height of 43 feet. The Saraswati Supercluster in the direction of the constellation Pisces consists of at least 43 galaxy clusters and is one of the largest structures found in the universe. [Hooper] 43 is the fourteenth prime number and its reversal is the fourteenth reversal prime. [Gaydos] The sum of the first 43 palindromic composite numbers is divisible by 43. [Gaydos] The New Yorker, A Wyndham Hotel is a 43-story Art Deco hotel located in the Hell's Kitchen neighborhood of Manhattan, New York City, United States. Nikola Tesla died there in '43. [Clisby] The first non-Solinas prime. [Mathar] The largest prime number of final points for any one team in NFL Super Bowl History occurred after the Seattle Seahawks won their first title with 43 points at Super Bowl XLVIII on February 2, 2014. [Harber and Robbins] Sheldon disappears to a room with a chalkboard that has the prime number 43 written on it in The Big Bang Theory episode "The 43 Peculiarity." [Golliher]

(There are 31 curios for this number that have not yet been approved by an editor.)