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.^[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, {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.^[7]
• 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 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 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.