71

This number is a prime.

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 room 71 of the opulent Dolmabahïe Palace in Istanbul. He was the first president of Turkey to die in office. [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]

+ Hôtel 71 is located at 71 Saint-Pierre Street in Québec (Québec), Canada.

+ 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.

+ The are 71 Robotics icons per pack. [Flaticon]

+ The sum of the digits of the first 71 semiprimes is 666. [Gaydos]

+ 71 divides the sum of digits of the first 71 prime numbers, i.e., 71 divides (2 + 3 + 5 + 7 + 1+1 + … + 3+4+9 + 3+5+3) or 710. The sequence of such primes begin as 71, 367, 373, 9119749, ... . See PC42. [Sariyar]

+ The southern star Canopus (designated α Carinae) has expanded to 71 times the Sun's radius.

(There are 13 curios for this number that have not yet been approved by an editor.)

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