41 (number) explained

41 (forty-one) is the natural number following 40 and preceding 42.

In mathematics

41 is:

• the 13th smallest prime number. The next is 43, making both twin primes.
• the sum of the first six prime numbers (2 + 3 + 5 + 7 + 11 + 13).
• a regular prime.^[1]
• a Ramanujan prime.^[2]
• a harmonic prime.^[3]
• a good prime.^[4]
• the 12th supersingular prime.^[5]
• a Newman–Shanks–Williams prime.^[6]
• the smallest Sophie Germain prime to start a Cunningham chain of the first kind of three terms, .
• an Eisenstein prime, with no imaginary part and real part of the form 3n - 1.
• a Proth prime as it is 5 × 2³ + 1.^[7]
• the largest lucky number of Euler: the polynomial yields primes for all the integers k with .
• the sum of two consecutive squares (4² + 5²), which makes it a centered square number.^[8]
• the sum of the first three Mersenne primes, 3, 7, 31.^[9]
• the sum of the sum of the divisors of the first 7 positive integers.
• the smallest integer whose reciprocal has a 5-digit repetend. That is a consequence of the fact that 41 is a factor of 99999.
• the smallest integer whose square root has a simple continued fraction with period 3.^[10]
• a prime index prime, as 13 is prime.

In other fields

• In Mexico "cuarenta y uno" (41) is slang referring to a homosexual. This is due to the 1901 arrest of 41 homosexuals at a hotel in Mexico City during the government of Porfirio Díaz (1876–1911). See: Dance of the Forty-One.^{[11] [12]}
• An international calling code for Switzerland.

References

1. Web site: Sloane's A007703 : Regular primes . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
2. Web site: Sloane's A104272 : a(n) is the smallest number such that if x >= a(n), then pi(x) - pi(x/2) >= n, where pi(x) is the number of primes <= x . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
3. Web site: Sloane's A092101 : Harmonic primes . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
4. Web site: Sloane's A028388 : prime(n) such that prime(n)^2 > prime(n-i)*prime(n+i) for all 1 <= i <= n-1 . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
5. Web site: Sloane's A002267 : The 15 supersingular primes. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-05-30.
6. Web site: Sloane's A088165 : NSW primes. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-05-30.
7. Web site: Sloane's A080076 : Proth primes. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-05-30.
8. 2024-02-09 .
9. 2024-02-09 .
10. Web site: Sloane's A013646: Least m such that continued fraction for sqrt(m) has period n.. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2021-03-18.
11. Web site: Reference 1 . 2008-06-13 . https://web.archive.org/web/20080531085502/http://www.chavodel8.com/mexicanismos/numero-41.php . 2008-05-31 . dead .
12. Web site: Reference 2 . 2008-06-13 . https://web.archive.org/web/20071130032556/http://www.islaternura.com/APLAYA/HOMOenHISTORIA/HomoHistoria2005/Los%2041%20en%20mexico/En%20el%20centenario%20de%20los%2041%20Diciembre2005.htm . 2007-11-30 . usurped .