# 41

This number is a prime.

Brittany Finch © 2004 |

*p*is a "lucky number of Euler" if the values of

*n*^2 +

*n*+

*p*are all prime for

*n*from 0 to

*p*-2. There are only six of these and the largest is 41. The others are 2, 3, 5, 11, and 17. [Le Lionnais]

The sum of digits and period length of the reciprocal of 41 are equal.

The number of whacks accused murderess Lizzie Borden allegedly gave her father on August 4, 1892, in Fall River, Massachusetts. She was acquitted of the murders of her father and stepmother, and the house where the murders occurred is now a bed and breakfast.

The smallest prime such that the sum of factorials of its distinct digits is a square number (4! + 1! = 5^{2}).

The smallest two-digit prime for which the smallest positive primitive root is not prime. [Russo]

There are exactly 41 odd terms in the Collatz (or 3x+1) trajectory for 41.

The 41st heptagonal number (r(5r-3)/2, for r=41) is the concatenation of 41 with itself. [Heleen]

A molecule of benzylpenicillin (commonly known as penicillin G) has 41 atoms. [Scott]

Robert Goddard successfully launched the world's first liquid-fueled rocket on March 16, 1926. It reached an altitude of 41 feet. [Collins]

A prime number of length 41 can be constructed by concatenating the exponents of the first consecutive Mersenne primes, separated by 0's. (Hint: the number of exponents used is the reversal of 41.) [Hartley]

41 is the largest known prime formed by the sum of the first Mersenne primes in logical order (3 + 7 + 31). [Luhn]

For every pair of positive numbers that sum to 41, the square of the first one plus the second one is prime. [Chubio]

*Sum 41* is a video-obsessed pop punk band from Canada.

The most frequent sum of digits (known) is 41. [Morse]

The Sun's wobble speed is about 41 feet per second. [Marcy]

The smallest prime whose cube can be written as sum of three cubes in two ways (41^{3} = 40^{3} + 17^{3} + 2^{3} = 33^{3} + 32^{3} + 6^{3}). [Wu]

41 is the smallest prime beginning with a composite digit. [Murthy]

41 is the largest prime factor of Carmichael number 41041. It is also the smallest prime factor of Carmichael number 410041. [Gupta]

The largest known example such that 41!+1 and 41#-1 are both primes. [Gupta]

The smallest half-quartan prime: p = (x^4 + y^4)/2.

Starting with 41, if you add 2, then 4, then 6, then 8, etc., you will have a string of 40 straight prime numbers. [Patel]

The Old Homestead Steakhouse in New York City claims their theory is simple: "Nothing but prime, dry aged and grilled to perfection." Their domestically-raised, hand massaged Kobe beef and world famous $41 hamburger are trademarked. [Nussbaum]

The smallest non-palindromic prime which on subtracting its reverse gives a perfect cube (i.e., 41 - 14 = 3^3). [Gupta]

41 is a sum of two consecutive squares: 4^{2} + 5^{2}. [Schlesinger]

Kent leg spin bowler Tich Freeman conceded 4879 runs in 1929 and 69577 runs in his full career. 41 is the largest prime factor of 4879 and the smallest of 69577.

There are 41(41-1) ways to write 41 as a sum of Fibonacci numbers. [Hartley]

Symphony number 41 (*Jupiter*) was the last symphony that Wolfgang Amadeus Mozart wrote. [Obeidin]

The smallest sexy prime quadruplet that is not part of a sexy prime quintuplet starts at 41. I.e, 41+6, 41+6+6 and 41+6+6+6 are also prime. [Opao]

There is a 41 Gun Royal Salute in London for a Royal Birthday, a Royal Birth, the State Opening of Parliament, and the arrival of a foreign Head of State or Commonwealth Prime Minister.

Captain Cook lost 41 of his crew to scurvy on his first voyage to the South Pacific in 1768.

The formula (41 + *x*)^{2} - *x*, for *x* = 2 to 40, yields 34 primes. Composites (five in all) occur only where *x* is a square. [Sutherland]

41 divides the concatenation of the integers 41 down to 1. [De Geest]

Prince Judah, the title character in the epic film *Ben-Hur*, is
reduced to oarsman number 41, a nameless slave on a Roman battleship.

41!/41# - 41 is prime. [Patterson]

If R(n) is the digits of n reversed, then R(41^R(41)) is prime. [Patterson]

The largest 2-digit prime which remains prime when 2 is added to any of its digits. I.e., 61 and 43 are primes. [Opao]

The smallest prime that is not the difference between powers of 2 and 3.

41 is the first prime element of the Goodstein sequence starting with four. [Hartley]

41 is the smallest prime number to have the same period (five) in both decimal and hexadecimal number systems.

The prime number 41 is the record number of matches played by a player in an English cricket season (Bobby Abel in 1902).

The only known prime number that is not the sum of two triangular numbers and a nonnegative cube. [Capelle]

prime(1)^π(1) + prime(2)^π(2) + ... + prime(41)^π(41) is an emirp and 41 is the only multidigit number with this property. [Firoozbakht]

The smallest prime formed from reverse concatenation of two consecutive squares. [Gupta]

41 is the 5th centered square number. Note that 4 + 1 = 5. [Post]

41 is the sum of the first three factorials plus the first three self-powers: 1!+2!+3! + 1^1+2^2+3^3 = 41. [Gallardo]

The 41st Mersenne to be found = 2^24036583-1.

The smallest prime of the smallest set of three consecutive multidigit primes, i.e., {41, 43, 47}, whose sum of digits (5, 7, 11) is another set of three distinct primes. [Gupta]

George W. Bush's nickname for his father, George H. W. Bush.

The number of votes required to sustain a filibuster in the United States Senate. [McCranie]

Super Bowl XLI was the first prime-numbered Super Bowl to have prime final scores by both teams: Indianapolis Colts 29, Chicago Bears 17. It started with Devin Hester (#23) becoming the first player in Super Bowl history to return the opening kickoff for a touchdown. [Post]

In the movie "North by Northwest," a crop-dusting airplane attempts to mow down Cary Grant at Prairie Corners on Highway 41.

The largest prime that is not the sum of 4 nonzero squares. [Post]

The Durga Yantra is a symbolic image used to represent the goddess Durga (the first female divinity according to Hindu scriptures). It is possible to place the numbers from 1 to 18 at the intersections of this image so that the sum along each line segment is 41. [Keith]

5-digit multiples of 41 remain multiples of 41 when their digits are permuted cyclically. [Mix]

41 is the 14th number which is not composite. [Hollesen]

The total number of primes in the 4th and 1st prime centuries is 41. [Punches]

There is an END-41 sign just south of the southern entrance to Yosemite National Park.

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

President Franklin D. Roosevelt made 41 trips to Warm Springs, Georgia. [McCranie]

The smallest prime with a prime subscript (P =
*p*_{Q}, and Q = 13) to have a digit sum (5)
that is also a prime with a prime (3) subscript. Note that
the latter is itself *the* smallest prime with a prime
subscript (p = *p*_{q}, and q = 2), p and q
being the difference of digits of P and Q respectively. [Beedassy]

The reversal of 41 is the number of non-composite integers up to 41. [Silva]

The smallest prime that is the sum of two or more consecutive primes __or__ composites in a prime number of different ways: 11 + 13 + 17 = 2 + 3 + 5 + 7 + 11 + 13 = 41 = 20 + 21 = 12 + 14 + 15. [Beedassy]

The largest known number n for which the decimal expansion
of 11^{n} does not contain any
zero. [Capelle]

Ali Baba shouted 'Open Sesame' and 41 horsemen rode through the opening. [Green]

41 is the largest admissible number of consecutive primes with gaps below 10. For example, gaps of 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6, 6, 6, 4, 6, 8, 4, 6, 2, 4, 8, 6, 4, 8, 4, 6, 2, 6, 6, 4, 2, 4, 6, 8, 6, 4, 2. If computers continue to improve at the current rate then it may take more than a century before an occurrence is found. [Andersen]

The largest prime p equal to the sum of primes smaller or equal to π(p). [Capelle]

2 + 3 + 5 + ... + 31 = 37 (mod 41). Note that 31, 37, and 41 are consecutive primes and 41 is the smallest nontrivial prime with this property (2 + 3 = 5 (mod 7)). [Firoozbakht]

The 2nd century sculpture (sphere) of the kneeling god Atlas depicts 41 of the classical Greek constellations described by Ptolemy.

Change every digit to either 1, 3, or 7, and the result remains prime. [Wesolowski]

Smallest prime partial sum of position of first letter of n (in English) in alphabet: 41 = 26 + 15, since "zero" begins with the twenty-sixth letter and "one" begins with the the fifteenth letter. [Post]

Ham the Astrochimp's backup, Minnie, was the only female chimp trained for the Mercury program. She died at age 41 on Pi Day, 1998. [Street]

New Yorker Nicholas White was trapped in an elevator for 41 hours.

Rome was not built in a day, but Brazil's new capital of Brasilia was built in 41 months, from 1956 to 21 April 1960, when it was officially inaugurated. [Post]

41^2 + (4^2 + 1^2) +/- 1 are both prime. [Homewood]

The Martian day is about 41 minutes longer than the day on Earth. [Neal]

The largest prime of form pq+rs, where p, q, r, s are consecutive primes. [Loungrides]

The largest of three consecutive primes (p, q, r), such that r|(pq+1), i.e., 41 divides (31*37+1). Note that the quotient is a perfect number. [Loungrides]

All of the current distinct U.S. Coins (i.e., quarter, dime, nickel, and penny) add up to 41 cents. [Meyers]

The sixth prime digit sum of the contiguously concatenated digits of the Copeland-Erdös Constant, (i.e. 0.2357111317192 ...) has SOD(235711131719) = 41, and is the smallest such sum to have an adjacent sum of digits similarly formed, i.e. SOD(2357111317192) = 43, which is only a single-digit longer. Note that {41,43} are twin primes. [Harrison]

The smallest prime age that automatically disqualifies a mathematician as a potential recipient of Fields medal award. [Beedassy]

41 + p# is prime for p = 2, 3, 5, 7, 11, 13, 17, or 19 (i.e., the first eight primes). [Petrov]

J. M. Bergot asks, "Is 41 the least prime allowing for the most consecutive primorials to be added to it which give primes in all cases?"

The reversal of 41 is 14; add p^p, where p is prime to get the original prime (i.e., 14 + 3^3 = 41). Is there a larger prime with this property? [Bergot]

The product of the digits of 41 is 4, and the sum is 5; hence 4*41+5=169=13^2 and 41 is the 13th prime. Further, 5*41+4=209 and reversing the digits gives 902, add to 209 to get 1111, which is four one's or 41. [Bergot]

41 is the sum of digits of 2^29. If you say the reversal of 41 (i.e. "one four"), you'll know what is missing in 2^29. [Honaker]

In an era before calculators, C. L. Dodgson (Lewis Carroll)
summarized his work on simplifying ordinary arithmetical
calculations in *Nature*, which included division by 41.

First member of a pair of twin primes whose sum of the digits yield another pair of twin primes. [Silva]

Q: Zack is 41, yet his twin brother is two years older. How could this be? A: If we use the alphabet code, i.e., A = 1, B = 2, C = 3, ... , Z = 26, then Z+A+C+K = 41 and M+A+R+K = 43. [Hollifield]

41 (exactly half) of the first 82 Fibonacci numbers are zeroless numbers. [Gaydos]

The smallest multidigit prime which is palindromic in base sum of its digits (41 = 131 in base 5). [Sariyar]

The first player in classic *Connect Four* can force a win on or before the move 41 by starting in the middle column.

Maryam Mirzakhani was the first Iranian student to win a gold medal at the World Mathematical Olympiad, scoring 41 out of 42.

Conjectured number of numbers which can be expressed as the sum of two distinct primes in exactly two ways.