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, thus it is a prime index prime because 13 is prime. The next prime number is 43, making both twin primes. It is a regular prime,a Ramanujan prime, a harmonic prime, a good prime, a Newman–Shanks–Williams prime, and the 12th supersingular prime. It is the smallest Sophie Germain prime to start a Cunningham chain of the first kind of three terms, {41, 83, 167}. It is an Eisenstein prime, with no imaginary part and real part of the form 3n − 1. It is a Proth prime because 41 = 5 × 2³ + 1.

It is the largest lucky number of Euler: the polynomial f(k) = k² − k + 41 yields primes for all the integers k with 1 ≤ k < 41.

It is the sum of the first six prime numbers (2 + 3 + 5 + 7 + 11 + 13) and the sum of the first three Mersenne primes, 3, 7, 31.

It is the sum of the sum of the divisors of the first 7 positive integers.

It is the sum of two consecutive squares (4² + 5²), which makes it a centered square number.

It is the smallest integer whose reciprocal has a 5-digit repetend. That is a consequence of the fact that 41 is a factor of 99999.

It is the smallest integer whose square root has a simple continued fraction with period 3.

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.