# 71 Jeffery Marshall © 2002 71^2 = 7! + 1!. [Patterson] 71 = (4! + 4.4)/.4 71 divides the sum of primes 2 + 3 + 5 + 7 + 11 + ... + 61 + 67 + 71. Today, oceans cover 71% of Earth's surface. [Brissenden] The Citizen Band (CB) Ten-Code 10-71 translates to 'Proceed with transmission in sequence.' [Foster] Conway's constant is an algebraic number of degree 71. Only 7-1 of the 71 repfigit numbers less than 10^19 are prime. Divide 71 by the thirtieth prime number and multiply by the third prime number and you get π to the first 7 - 1 decimal places. [Schuler] A 71-digit prime is formed by intertwining the even (from 2 to 40) and the odd (from 1 to 39) numbers (214365...374039). [De Geest] 71 - 1 = 1 * 2 * 5 * 7 and 71 + 1 = 3 * 4 * 6. Note the products of partitions of consecutive numbers. [Poo Sung] The repunit R71=(1071-1)/9 is a semiprime and therefore relatively hard to factor. Note that its smallest factor contains all of the digits, except 7 + 1. The smallest prime formed from the concatenation of happy numbers in reverse order. [Gupta] The largest known prime p such that 2^p doesn't contain the digit 9. [Russo] Isaac Newton's "Proposition 71" concerns the proof of his assumption that a homogeneous sphere gravitationally attracts a particle external to the sphere as if all its mass were concentrated at its center. 71 divides all values of Ackerman's function A(m,n) for sufficiently large m. This is the largest prime less than a million of which this is (known to be) true. (The only other is 13.) [Hartley] 71 cubed is a concatenation of the first five odd numbers. [Davis] The smallest prime p such that p4 = q3 + r2 is soluble in positive integers : 714 = 1363 + 47852. [Beedassy] Mustafa Kemal Atatürk (1881-1938), founder of the Turkish Republic, died from cirrhosis in Istanbul in the opulent Dolmabahïe Palace, built by one of the last sultans, along the European shores of the Bosphorus, in room number 71. Note that concatenations of 1881 with 71; and 1938 with 71 are both prime! [De Geest] The largest of the supersingular primes, i.e., the set of primes that divide the order of the Monster group (an algebraic construction with 2^46 * 3^20 * 5^9 * 7^6 * 11^2 * 13^3 * 17 * 19 * 23 * 29 *31 * 41 * 47 * 59 * 71 elements). The Great Sanhedrin was the supreme religious body in the Land of Israel during the rabbinic period. Tannaitic sources describe it as an assembly of 71 sages. In 1935, Erdős and Szekeres proved that 71 points (no three on a single line) are required to guarantee there are six that form a convex hexagon, although 17 points are thought to be sufficient. (In 1998, the upper bound was reduced to 37.) Clint Eastwood is Inspector 71 in the movie Dirty Harry ('71). Between July 1948 and August 1950, Warwickshire leg spinner Eric Hollies batted a record 71 innings without once reaching double figures. Unique two-digit prime p such that (p^p-p!)/p is prime. [Gallardo] I. M. Pei's 71-foot tall transparent pyramid in the Louvre is mentioned in Dan Brown's The Da Vinci Code (among other fascinating numbers throughout the text). [Haga] Hotel 71 is a modern urban boutique hotel in Chicago. The smallest prime that remains prime when inserting one, two, three, or four zeros between each digit. [Capelle] The smallest prime revrepfigit (reverse replicating fibonacci-like digit) number: 7, 1, 8, 9, 17. [Earls] The smallest emirp p such that prime(p) is a palindrome. [Post] The smallest prime expressible as the sum of successive composite numbers in exactly two ways: 71 = 22+24+25 = 35+36. [Seidov] Having varied widely over the decades and constantly being narrowed, the Hubble's constant H0 (a measure of the Universe's observed expansion rate) current best estimates revolve around 71 km/s/Mpc (kilometers per second for each megaparsec or about 3.3 million light years away from the Earth). [Beedassy] The lesser member of the smallest twimirp, i.e., a member of a twin (i.e., differs by 2) emirp pair. In this case, the associated emirps are 17 and 37. [Green] The smallest emirp whose binary reversal (11100012) corresponds to another emirp (113). [Beedassy] 71 squared can be expressed as the sum of prime powers of two prime numbers: 71^2 = 2^7 + 17^3. [Wagler] An Indra in the Hindu Pantheon lives for 71 eons. [Haga] The smallest emirp p which taken together with the pth prime is also an emirp (71353). [Beedassy] The first occurrence of three successive emirps in the sequence of primes: 71, 73, 79. [Beedassy] The smallest prime greater than three that is not a member of a sexy pair of primes. [Silva] The smallest emirp that forms a pair of twin primes with the next emirp. [Silva] The largest known natural number n such that 2n does not contain the prime digit 5. It is also the case for the prime digit 7. [Capelle] The largest known positive integer n for which the sum of all primes smaller or equal to n divides the sum of all nonprimes smaller or equal to n. It's also the largest known positive integer n for which this sum of primes divides n(n+1)/2. Moreover, it's the only known case where n divides all these numbers. [Capelle] "71 Days: The Media Assault on Obama" by Michael Jason Overstreet is written like a political private diary. Place the emirps in order of 71,73,79 to get 17+37+79 = 133 = 7*19 with sum of digits 7+1+9 = 17, which is the first number in 17+37+73. Add 71+73+79=223 with sum of digits 2+2+3=7, the first digit of all 71,73,79. [Bergot] If two distinct positive integers have smallest prime divisor p, and every integer between them has smallest prime divisor < p, then p ≥ 71. [Helenius] Enterovirus 71 is a common cause of hand, foot, and mouth disease. Largest known prime p such that p^2 is a sum of distinct factorials. If there is a larger one, p^2 must be greater than 48! (about 1.24139 * 10^61). [Post] Mexico's PRIme political institution, the Institutional Revolutionary Party (PRI) ruled for 71 years (1929-2000). [Post] The smallest prime that is a proper divisor of the sum of all previous primes. [Silva] A "History of Mathematics" by Florian Cajori (who died aged 71) was the first popular presentation of the history of mathematics in the United States. 71π is closer to a prime than any multiple of π below it. [Blevins] The least odd number which is neither of the form p*2^m + 1 nor of the form p*2^m - 1 with p prime. [Wesolowski] Cube of 71 is concatenation of all odd numbers from 3 to 11, i.e., 71^3 = 357911 [Gupta] The 71st Fibonacci number plus 71! is a prime number. [Gaydos] Selah is a word used 71 times in the Psalms. 71 is the smallest prime p where the pth digit of π after the decimal point is a zero. [Homewood] There are no nines in the first 71 multiples of 125. Is there any number that has more than 71 nineless first n multiples? [Gaydos] The first member of the smallest pair of twin emirps. [Silva] The sum of the first 71 brilliant numbers (35821) is a brilliant number. [Gaydos] The first 2-digit prime to occur in the decimal expansion of e.

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