41 (number)
Natural number From Wikipedia, the free encyclopedia
41 (forty-one) is the natural number following 40 and preceding 42.
Look up forty-one in Wiktionary, the free dictionary.
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, {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 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]
References
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