41 (number)

"XLI" redirects here. For a medical condition, see X-linked ichthyosis. For the ISO 639-3 code, see Liburnian language.

← 40 41 42 →
← 40 41 42 43 44 45 46 47 48 49 → List of numbers Integers ← 0 10 20 30 40 50 60 70 80 90 →
Cardinal	forty-one
Ordinal	41st (forty-first)
Factorization	prime
Prime	13th
Divisors	1, 41
Greek numeral	ΜΑ´
Roman numeral	XLI, xli
Binary	1010012
Ternary	11123
Senary	1056
Octal	518
Duodecimal	3512
Hexadecimal	2916

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).
• the 12th supersingular prime ^[1]
• a Newman–Shanks–Williams prime. ^[2]
• 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. ^[3]
• the largest lucky number of Euler: the polynomial f(k) = k² − k + 41 yields primes for all the integers k with 1 ≤ k < 41.
• the sum of two squares (4² + 5²), which makes it a centered square number. ^[4]
• the sum of the first three Mersenne primes, 3, 7, 31. ^[5]
• 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. ^[6]
• 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 ^{[7] [8]}

References

1. "Sloane's A002267 : The 15 supersingular primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
2. "Sloane's A088165 : NSW primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
3. "Sloane's A080076 : Proth primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
4. Sloane, N. J. A. (ed.). "SequenceA001844(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.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-02-09.
5. Sloane, N. J. A. (ed.). "SequenceA000668(Mersenne primes (primes of the form 2^n - 1).)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-02-09.
6. "Sloane's A013646: Least m such that continued fraction for sqrt(m) has period n". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2021-03-18.
7. "Reference 1". Archived from the original on 2008-05-31. Retrieved 2008-06-13.
8. "Reference 2". Archived from the original on 2007-11-30. Retrieved 2008-06-13.