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The only prime with period length three: 1/37 = 0.027 027 027 .... A prime which has a period length that it shares with no other prime is called a unique prime. The Carthaginian general Hannibal began his long march across the Pyrenees with 37 war elephants. [Polybius] 2^{3} + 5^{7} + 11^{13} + 17^{19} + 23^{29} + 31^{37} is prime. The last odd Roman numeral alphabetically is XXXVII (37). [Brahinsky] 37 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 9 = 37. Note that 12345679 * 3 = 37037037. [AlHumaid] William Shakespeare is thought to have written 37 plays. The least number of 5th powers needed to represent every possible integer. [Lagrange] All threedigit repdigits are divisible by 37.37 * 03 = 111 * 06 = 222 * 09 = 333 * 12 = 444 * 15 = 555 * 18 = 666 * 21 = 777 * 24 = 888 * 27 = 999. Mitochondrial DNA commonly found in most animals contains 37 genes. [Magliery] The degree of the first polynomial discovered whose set of positive values is the set of primes as the variables range over the natural numbers. Matijasevic showed this was possible in 1971, and Jones, Sato, Wada, and Wiens provided an example of such a polynomial with 26 variables (and degree 25) in 1976. It can conveniently be written down using the 26 letters of the English alphabet. The sum of the first 37 primes is a Fibonacci number. The French version of solitaire uses a board with holes for 37 pegs. The planet Jupiter's escape velocity is ~ 37 miles per second. In 1989, the "Amdahl Six" team found a prime larger than Slowinski's previous record prime by just 37 digits. It was the only nonMersenne prime to be the largest known prime since 1952. The prime p = 37, and its reversal q = 73, are the only known emirp pair such that p! + 1 and q! + 1 are both primes. [Punches] The German physician, pioneer psychiatrist, and medical professor Carl Reinhold August Wunderlich (18151877) is bestknown for his observations and conclusion that the mean healthy human body temperature is 37 degrees Celsius. The sum of the first five consecutive composite numbers (37 is 4 + 6 + 8 + 9 + 10). [Natch] 37 can be represented as 100101 in binary notation. Note that the 0s are in prime positions and the 1s are in nonprime positions when read lefttoright. [Keith] 4^{n} + 37 yields primes for n = 1, 2, 3, 4, 5, 6, and 7. [Trotter] Pliny the Elder (A.D. 2379) wrote many historical and technical works, but only his 37volume Historia Naturalis (Natural History) has survived. [Hadas] 37 is the smallest left and righttruncatable prime, whose digits are all odd primes. [Luhn] Ramanujan had 37 papers published in peerreviewed mathematical journals. [Croll] 37 and the 37th Mersenne prime exponent are emirps. [Wu] Any multiple of 37 when split and each side cubed then added is a multiple of 37. E.g., 37 itself: 3^{3} + 7^{3} = 370. [Mallett] e^(*sqrt(37)) is 'almost' an integer. [Croll] If the whole integer series is broken down into primes or prime factors of composites and then alternately added and subtracted, the only congruence where the value of the +/ figure equals that number occurs at 37. [Mallett] The smallest irregular prime. [Russo] 10^(10^100)+37 is the smallest number greater than googolplex with no known factors (as of August 2002). [Rupinski] 37 is the smallest prime such that the ReversethenAdd process in base two does not lead to a palindrome. [Russo] Physicist and Nobel laureate Richard Feynman (19181988) wrote only 37 research papers in his career. The most well known multiple of 37 is the beast number (666). The first occurrence of 666 in appears on digits 2441, 2442 and 2443, when including the initial 3 before the decimal point, i.e. the whole series of 's digits. The sum of these is 7326 or 11 * 666. [Mallett] Landon Curt Noll once sent out a curious email message related to 37. The largest prime number found in Euler's list of 65 "numeri idonei" (37 of the 65 are squarefree). [Younce] The Green Monster of Fenway Park in Boston is exactly 37 prime foot, 2 prime inches tall. [Patterson] The greatest prime factor of any 6digit repdigit is 37. [La Haye] In the movie Office Space, the waiter is wearing 37 pieces of flair. [Patterson] 37 is the fifth good prime. [Patterson] If a multidigit number (4 or more digits)is taken in groups of three (from the least significant group) and these are summed (repeatedly, if necessary) to produce a threedigit number which is divisible by 37, then the original number is also divisible by 37. [Fellows] Blue Moons occur 37 times every century on average. [Cooley] In the book A Painted House by John Grisham, the character Luke observed that his grandfather always drove his truck at exactly 37 miles per hour. Did it run most efficiently at this speed? There are exactly 37 Sophie Germain Primes < 1000. [Rock] One packet of artificial sweetener (Equal, NutraSweet) contains 37 milligrams of aspartame. [Rutherford] In the movie The Mothman Prophecies, Connie Parker has a prophetic dream in which she hears whispered to her "wake up, number 37." [La Haye] The William Penn Statue, 37 feet tall, is the largest single piece of sculpture on any building in the world. The statue stands on City Hall in Philadelphia. [Dobb] In 1953, baseball great Ted Williams played in only 37 games and had 37 hits. [Rachlin] All positive integers can be written as the sum of not more than 37 fifth powers (Chen Jingrun, 1964). (37) = 12 and (73) = 21. [Pe] The 37th Mersenne prime exponent, 3021377, starts with 3 and ends with 7 and also contains 37. This is the only known Mersenne exponent with this property. [Laurv] European Roulette is played using a wheel containing 37 numbered slots (1 to 36, plus a 0). 37 is a factor of all 3digit baseten repdigits. On Nickelodeon TV, the cartoon character Sponge Bob remarked that he has tried for his boating license 37 times. He corrected this to 38 twice, but obviously he has soaked up 37 in his spongy head! [Haga] The late 1960's serial killer who referred to himself as "Zodiac" claimed to have taken 37 lives in the San Francisco Bay area. "37 Heaven" is an online collection of 37 factoids. 2^37 + 3^31 + 5^29 + 7^23 + 11^19 + 13^17 + 17^13 + 19^11 + 23^7 + 29^5 + 31^3 + 37^2 is prime. (Note the bases increase through the first dozen primes while the exponents decrease.) [Patterson] The smallest prime p of the form (R(p)+1)/2, for R(p) the reversal of p. [Silva] There are 37 combinations of digits that cannot form the last two digits of a perfect cube. The cricket has been called the "Poor Man's Thermometer." If you count the number of chirps in fifteen seconds, then add 37, the sum will be very close to the prevailing Fahrenheit temperature at the cricket's location. [Haga] 37*773*3 = (73)*(7+3). [Losnak] 37 is the number of centered hydrocarbons with ten atoms. [Post] "37signals" is a privately held web design and web application company based in Chicago, Illinois. The company is named for 37 radio telescope signals identified as potential messages from extraterrestrial intelligence. The following 37word quotation is ascribed to the great Swiss mathematician Leonhard Euler (17071783): "Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the human mind will never penetrate." All American Express Card numbers begin with 37. [Gronos] The 37th composite number that has a prime factor sum of 37 (6664) minus its mirror image is equal to 37 times the 37th composite number. [Mallett] The smallest isolated prime (i.e., not a member of a twin prime pair) of form 6n + 1. [Beedassy] The number of hydrocarbon structures that can be drawn (excluding stereoisomers) for 4 carbons. [Post] The smallest Riesel prime whose emirp is also a Riesel prime. [Loungrides] An Ariane 5 rocket exploded 37 seconds after liftoff in 1996 because of a software error that resulted from converting a 64bit floating point number to a 16bit integer. 3! * 7! minus 37 is a palindromic prime. [Silva] The only twosided emirp whose the reversal is also a twosided emirp. [Loungrides] In the James Coburn film, "In Like Flint," the number of operations performed on the Presidential lookalike. The German passenger airship Hindenburg burned for 37 seconds upon attempted docking at Lakehurst, New Jersey, in 1937. [Haga] If three digits in arithmetic sequence are reversed and the two numbers added the result is divisible by 37. [Fellows] 37 and its reversal are the only primes formed from a pair of cousin primes. [Silva] If a threedigit number is divisible by 37, then the number formed by moving the first digit to the last place or the last digit to the first place is also divisible by 37. [Fellows] The largest known prime number p such that the binomial coefficient C(2p, p) is not divisible by the square of an odd prime. [Capelle] The largest known prime number p such that the decimal expansion of 2^{p} does not contain a multidigit palindromic substring. [Capelle] 37^{1} + 37^{1} + 37^{1} = 111. [Poo Sung] The only idoneal prime (emirp) formed by concatenating n idoneal primes (n=2). [Loungrides] There are 37 nonominoes with holes. [Post] The smallest prime which is one more than the product of two distinct composite numbers. [Porter] The only known number n such that the reversal of n^prime(n) is prime. [Firoozbakht] The smallest emirp p such that reversal(p^2) is prime. [Firoozbakht] The lesser prime of the smallest emirp pair both of which are Pythagorean, i.e., expressible as the sum of two squares: 37 = 1^{2} + 6^{2} ; 73 = 3^{2} + 8^{2}. Note that the derived palindromic prime of the form "primemirp" is also Pythagorean: 373 = 7^{2} + 18^{2}. [Beedassy] The largest known prime number that can be written as the sum of two positive squares, but not as the sum of three positive squares. [Capelle] The sum of the prime divisors of the two next numbers. [Silva] The smallest emirp p such that reversal(p + reversal(p)) is prime. [Firoozbakht] "Balloon Boy" (Falcon Heene) weighed 37 pounds on the day he reportedly floated away in a homemade flying saucer near Denver, Colorado. [Hess] The largest prime number p for which the sum of digits is not smaller than p/4. [Capelle] The sum of the prime digits appearing in all previous primes. [Silva] 2! + 3! + 5! + ... + 29! = 31 (mod 37). It is the largest known prime with this property and there exists only one other such prime. [Firoozbakht] In the movie "Cool Hand Luke" Paul Newman's inmate number on his prison uniform is 37. [Mercedes] 37 = prime(prime(3)  prime(7)). It is the smallest prime with this property. [Firoozbakht] The smallest emirp p such that prime(p) is emirp. [Firoozbakht] Songwriter Stephen Foster died at age 37 with only 37 cents in his pocket. [Post] The maximal number of regions into which a circle can be divided by eight lines. [Green] The smallest unique emirp. [Loungrides] The reversal of 2^{37} is prime. [Wesolowski] Smallest prime sum of distinct primorials which is not a primorial prime (37 = 30 + 6 + 1). [Post] The smallest emirp separated from its adjacent primes on each side by a prime number of successive composites. [Beedassy] 37*73 divides 2^{37*731}1. [Williams] 37 is the initial prime which is not a factor of the order of the Monster Group having cardinality 808017424794512875886459904961710757005754368000000000=2^46*3^20*5^9*7^6*11^2*13^3*17*19*23*29*31*41*47*59*61. This finite sporadic simple group has generated much interest and constitutes a group of symmetries on 196883 dimensions. This group was discovered in 1982 by Robert Griess. [Schiffman] The largest prime uniform number that has been retired by the New York Yankees. 37 and the next prime are the only known pair of consecutive odd primes for which there are factorial primes. [Wesolowski] The only nontitanic prime p of form p=6^x+1 for x a prime and the only nontitanic emirp for x any number, (case x=2). [Loungrides] The word August uses 6 letters and has 31 days. Note that 31 + 6 = 37. August is the only month of a nonleap year to produce a prime number in this manner. [Gudipati] Tyheem Henry was sentenced to over 37 years in solitary confinement for writing Facebook posts from prison. The smallest positive integer that is never prime when followed by a string of ones, i.e., 371, 3711, 37111, 371111, ... are all composite numbers for any number of ones. [Gaydos] It is the only known prime p such that pth triangular number is a Kaprekar number. [Gupta] The average divisor up to 37 is an integer. The only known prime example. [Ratushnyak] The emirp 37 divides the arithmetic average of the first 37 emirps. [Silva] A simple magic square that consists of numbers all starting with the letter 'T'. The curious will notice that 37 is the largest prime utilized. Found by Alex de Wit: 12 38 13 27 31 20 37 02 24 03 30 33 23 29 10 28.
(There are 26 curios for this number that have not yet been approved by an editor.)
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