41 (number)

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{{Cite web |title=Sloane's A007703 : Regular primes |url=https://oeis.org/A007703 |website=The On-Line Encyclopedia of Integer Sequences |publisher=OEIS Foundation}}
• a Ramanujan prime{{Cite web |title=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 |url=https://oeis.org/A104272 |website=The On-Line Encyclopedia of Integer Sequences |publisher=OEIS Foundation}}
• a harmonic prime{{Cite web |title=Sloane's A092101 : Harmonic primes |url=https://oeis.org/A092101 |website=The On-Line Encyclopedia of Integer Sequences |publisher=OEIS Foundation}}
• a good prime{{Cite web |title=Sloane's A028388 : prime(n) such that prime(n)^2 > prime(n-i)*prime(n+i) for all 1 <= i <= n-1 |url=https://oeis.org/A028388 |website=The On-Line Encyclopedia of Integer Sequences |publisher=OEIS Foundation}}
• the 12th supersingular prime{{Cite web|url=https://oeis.org/A002267|title=Sloane's A002267 : The 15 supersingular primes|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-30}}
• a Newman–Shanks–Williams prime.{{Cite web|url=https://oeis.org/A088165|title=Sloane's A088165 : NSW primes|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-30}}
• the smallest Sophie Germain prime to start a Cunningham chain of the first kind of three terms, {41, 83, 167}.
• an Eisenstein prime, with no imaginary part and real part of the form 3n − 1.
• a Proth prime as it is 5 × 2³ + 1.{{Cite web|url=https://oeis.org/A080076|title=Sloane's A080076 : Proth primes|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-30}}
• the largest lucky number of Euler: the polynomial {{nowrap|f(k) {{=}} k{{sup|2}} − k + 41}} yields primes for all the integers k with {{nowrap|1 ≤ k < 41}}.
• the sum of two squares (4² + 5²), which makes it a centered square number.{{Cite OEIS |A001844 |Centered square numbers: a(n) is 2*n*(n+1)+1. Sums of two consecutive squares. Also, consider all Pythagorean triples (X, Y, Z equal to Y+1) ordered by increasing Z; then sequence gives Z values. |access-date=2024-02-09 }}
• the sum of the first three Mersenne primes, 3, 7, 31.{{Cite OEIS |A000668 |Mersenne primes (primes of the form 2^n - 1). |access-date=2024-02-09 }}
• 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.{{Cite web|url=http://oeis.org/A013646|title=Sloane's A013646: Least m such that continued fraction for sqrt(m) has period n.|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2021-03-18}}
• a prime index prime, as 13 is prime.

• 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{{Cite web |url=http://www.chavodel8.com/mexicanismos/numero-41.php |title=Reference 1 |access-date=2008-06-13 |archive-url=https://web.archive.org/web/20080531085502/http://www.chavodel8.com/mexicanismos/numero-41.php |archive-date=2008-05-31 |url-status=dead }}{{Cite web |url=http://www.islaternura.com/APLAYA/HOMOenHISTORIA/HomoHistoria2005/Los%2041%20en%20mexico/En%20el%20centenario%20de%20los%2041%20Diciembre2005.htm |title=Reference 2 |access-date=2008-06-13 |archive-url=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 |archive-date=2007-11-30 |url-status=usurped }}

{{Integers|zero}}

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Category:Integers